Mathematical / Computational / Theoretical physics Books

Book SynopsisBased on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.Trade ReviewFrom the reviews:“This book introduces General Relativity at students level, especially intended for final year mathematics students. Different from other books with the same title, it really goes into the geometric details and tries to explain the given formulae … . The appendices present exercises and hints to their solutions.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)"I have the opportunity to comment on General Relativity … . I am happy to recommend … for an advanced undergraduate course on relativity or for self-study. … marvelous faithfulness to historical developments … characterizes the entire treatment. … In fact, the whole book is distinguished by this high quality of exposition. … It’s a fine book, beautifully written and clear, and I highly recommend it." (Michael Berg, MathDL, January, 2007)MAA Reviews:In December, 2003 I had the pleasure of reviewing the admirable book Special Relativity, by N.M.J. Woodhouse, and now I have the opportunity to comment on General Relativity by the same author. I am happy to recommend not just this sequel, but the indicated pair, for an advanced undergraduate course on relativity or for self-study.One particularly noteworthy feature of General Relativity is that woodhouse seeks to present the subject neither as a branch of differential geometry nor as the kind of physics mathematicians like me find unapproachable (and I'm afraid this doesn't particularly narrow the field). When just a rookie I dabbled in relativity largely from popularizations and biographical writings, and when I tried to learn some real general relativity in graduate school - for cultural reasons, I guess - it simply didn't take. But my interest in the subject, both specially and generally, has never flagged and Woodhouse’s books are tailor-made for even my lingering ambitions. In other words, for any slacker who feels he should have learned this beautiful material in his mathematical youth, but didn’t, and is now secretly (or not so secretly) desirous of doing it right, this is the book, or, more correctly, these are the books to read. Furthermore, as I already hinted, as far as teaching courses on these important subjects is concerned, obviously these books fit that bill very well too, given Woodhouse’s specific pedagogical intent.When it comes to the specific style and presentation of general relativity chosen by Woodhouse, marvellous faithfulness to historical developments, in particular Einstein’s own writings, characterizes the entire treatment. On p.7, already, the weak and strong equivalence principles are presented and analysed in a succinct and historically rooted fashion. The former, going back to Galileo’s pendulums (Woodhouse correctly says "pendula," of course) and famously connected with Eötvös’ experiment, entails that inertial mass and gravitational mass are the same; and the latter says that there are no obvservable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these observable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these incomparable axioms underlying Einstein’s revolution is a gem of exposition, covering the historical sweep of the attendant experiments (he even mentions a planned space experiment, "STEP," which will test the latter principle to within one part in 1018) and conveying what is to come as a result of these stipulations. Finally, I want to draw special attention to pp.23-27, where Woodhouse does a phenomenally good job of explicating the subject of tensors in Minkowski space, a subject which has always been a bit unsettling to me who was raised to visit tensor products in their homological algebraic home and I cannot resist mentioning Problem 1.5 on p.13, dealing with "Einstein’s birthday present."It’s a fine book, beautifully written and clear, and I highly recommend it. [Reviewed by Michael Berg, 20.1.2007]"Woodhouse … lets the physical intuition behind relativity inform every step of its logical development, making his treatment as digestible as any in print. He does introduce ab ovo what differential geometry he needs, and he takes the whole theory far enough to develop general relativity’s most exciting predictions, black holes and gravity waves, all in less than half the number of pages one might expect. Summing Up: Highly recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 44 (11), July, 2007)"The book is an outgrowth of a lecture course given over many years by the author and his colleagues to final-year applied mathematicians at the Mathematical Institute in Oxford, UK. The book is well-written and easy to follow because the author constructs the necessary apparatus layer-by-layer, from the bottom up, carefully motivating and justifying every new concept. Exercises are given at the end of every chapter … and numerous examples appear throughout the text. … its expository style is very appealing." (David A. Burton, General Relativity and Gravitation, Vol. 39, 2007)Table of ContentsNewtonian Gravity.- Inertial Coordinates and Tensors.- Energy-Momentum Tensors.- Curved Space—Time.- Tensor Calculus.- Einstein’s Equation.- Spherical Symmetry.- Orbits in the Schwarzschild Space—Time.- Black Holes.- Rotating Bodies.- Gravitational Waves.- Redshift and Horizons.

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Book SynopsisFirst published in 1987, this text offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding. Trade ReviewFrom the reviews of the second edition:“It is designed to teach analytical mechanics to second and third year undergraduates in the UK, and probably to third or fourth year undergraduates in the US. … This book offers a very attractive traditional introduction to the subject. … the author is well tuned to the difficulties even strong students encounter. … discusses the relevance of classical mechanics in modern physics, especially to relativity and quantum mechanics. This is a fine textbook. It would be a pleasure to teach or to learn from it.” (William J. Satzer, The Mathematical Association of America, March, 2010)Table of ContentsFrames of Reference.- One Degree of Freedom.- Lagrangian Mechanics.- Noether#x2019;s Theorem.- Rigid Bodies.- Oscillations.- Hamiltonian Mechanics.- Geometry of Classical Mechanics.- Epilogue: Relativity and Quantum Theory.

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Book SynopsisThis book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.Trade ReviewFrom the reviews: N.M.J. Woodhouse's comparatively short Special Relativity is a pleasure to read and therefore qualifies right off as a good source to use for learning about special relativity on your own. A lot of very nice material is touched on in its pages, presented in natural sequence consonant with history, and is not improperly belabored. It's also rather informal in style. One gets the sense of breezing along pretty fast while, in actuality, a lot of material is being dealt with... the selection of topics in the book is very nice indeed , and is historically sound and will therefore reward the reader with an element of culture to boot: he'll learn some history of modern physics... I wish this book had been around when I was a student. MAA Online ...an exciting and challenging book with which to introduce a modern mathematics student in a single course to the great ideas of Maxwell's theory and special relativity. The Australian Mathematical Society Gazette "There are many books on special relativity for undergraduates, and this one is notable in that it is specifically addressed to mathematicians. … this book will be found illuminating by students of mathematics … ." (Dr. P. E. Hodgson, Contemporary Physics, Vol. 45 (5), 2004) "This book is … aimed squarely at the undergraduate mathematician ... . The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. … There are lots of examples and nicely graded exercises throughout the text, and each chapter ends with a usefully annotated bibliography. The author’s friendly style, and the fact the material has been developed from taught courses make the book ideal for self-study … ." (Peter Macgregor, The Mathematical Gazette, Vol. 88 (512), 2004) "Meant as a resource for advanced undergraduate students, this book approaches special relativity theory from a mathematical perspective … . It is best used for mathematics majors … . the text is clear, well written, and has an adequate bibliography. Summing Up: Recommended. Upper-division undergraduates." (A. Spero, CHOICE, December, 2003) "This presentation is very elegant … . The book contains a large number of examples. Each chapter is followed by exercises, ranging from the rather simple to the more involved. This book is certainly a good introduction to special relativity, understandable for second-year students. But it is also interesting for readers searching for a concise and precise presentation of special relativity within the tensor formalism." (Claude Semay, Physcalia, Vol. 25 (4), 2003)Table of Contents1. Relativity in Classical Mechanics.- 1.1 Frames of Reference.- 1.2 Relativity.- 1.3 Frames of Reference.- 1.4 Newton’s Laws.- 1.5 Galilean Transformations.- 1.6 Mass, Energy, and Momentum.- 1.7 Space-time.- 1.8 *Galilean Symmetries.- 1.9 Historical Note.- 2. Maxwell’s Theory.- 2.1 Introduction.- 2.2 The Unification of Electricity and Magnetism.- 2.3 Charges, Fields, and the Lorentz Force Law.- 2.4 Stationary Distributions of Charge.- 2.5 The Divergence of the Magnetic Field.- 2.6 Inconsistency with Galilean Relativity.- 2.7 The Limits of Galilean Invariance.- 2.8 Faraday’s Law of Induction.- 2.9 The Field of Charges in Uniform Motion.- 2.10 Maxwell’s Equations.- 2.11 The Continuity Equation.- 2.12 Conservation of Charge.- 2.13 Historical Note.- 3. The Propagation of Light.- 3.1 The Displacement Current.- 3.2 The Source-free Equations.- 3.3 The Wave Equation.- 3.4 Monochromatic Plane Waves.- 3.5 Polarization.- 3.6 Potentials.- 3.7 Gauge Transformations.- 3.8 Photons.- 3.9 Relativity and the Propagation of Light.- 3.10 The Michelson-Morley Experiment.- 4. Einstein’s Special Theory of Relativity.- 4.1 Lorentz’s Contraction.- 4.2 Operational Definitions of Distance and Time.- 4.3 The Relativity of Simultaneity.- 4.4 Bondi’s fc-Factor.- 4.5 Time Dilation.- 4.6 The Two-dimensional Lorentz Transformation.- 4.7 Transformation of Velocity.- 4.8 The Lorentz Contraction.- 4.9 Composition of Lorentz Transformations.- 4.10 Rapidity.- 4.11 *The Lorentz and Poincaré Groups.- 5. Lorentz Transformations in Four Dimensions.- 5.1 Coordinates in Four Dimensions.- 5.2 Four-dimensional Coordinate Transformations.- 5.3 The Lorentz Transformation in Four Dimensions.- 5.4 The Standard Lorentz Transformation.- 5.5 The General Lorentz Transformation.- 5.6 Euclidean Space and Minkowski Space.- 5.7 Four-vectors.- 5.8 Temporal and Spatial Parts.- 5.9 The Inner Product.- 5.10 Classification of Four-vectors.- 5.11 Causal Structure of Minkowski Space.- 5.12 Invariant Operators.- 5.13 The Frequency Four-vector.- 5.14 * Affine Spaces and Covectors.- 6. Relative Motion.- 6.1 Transformations Between Frames.- 6.2 Proper Time.- 6.3 Four-velocity.- 6.4 Four-acceleration.- 6.5 Constant Acceleration.- 6.6 Continuous Distributions.- 6.7 *Rigid Body Motion.- 6.8 Visual Observation.- 7. Relativistic Collisions.- 7.1 The Operational Definition of Mass.- 7.2 Conservation of Four-momentum.- 7.3 Equivalence of Mass and Energy.- 8. Relativistic Electrodynamics.- 8.1 Lorentz Transformations of E and B.- 8.2 The Four-Current and the Four-potential.- 8.3 Transformations of E and B.- 8.4 Linearly Polarized Plane Waves.- 8.5 Electromagnetic Energy.- 8.6 The Four-momentum of a Photon.- 8.7 *Advanced and Retarded Solutions.- 9. *Tensors and Isomet ries.- 9.1 Affine Space.- 9.2 The Lorentz Group.- 9.3 Tensors.- 9.4 The Tensor Product.- 9.5 Tensors in Minkowski Space.- 9.6 Tensor Components.- 9.7 Examples of Tensors.- 9.8 One-parameter Subgroups.- 9.9 Isometries.- 9.10 The Riemann Sphere and Spinors.- Notes on Exercises.- Vector Calculus.

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Book SynopsisA new direction of research has recently emerged at the boundary between elementary particle physics and atomic spectroscopy: the investigation of weak interactions by optical methods. These studies have led to the discovery of parity nonconservation in atomic transitions, which has served as one of the first decisive confirmations of the unified model of electroweak interactions. In this integrated picture of the subject the author considers the effects of space-inversion and time-reversal violation in atoms, molecules and condensed matter. The book is intended for physicists, and for theoretical and experimental physicists specializing in atomic, nuclear and elementary particle physics.Table of ContentsPreface, List of Symbols, 1 The general structure of weak electron-nucleon interactions, 2 Qualitative consideration of parity nonconservation effects in atoms, 3 The hydrogen atom, 4 Calculation of the mixing of opposite-parity levels in heavy atoms, 5 Optical highly forbidden M l transitions in heavy atoms, 6 Optical activity of heavy-metal vapours. General considerations and calculations, 7 Observation of optical activity of heavy-metal vapours, 8 P-odd nuclear forces — another source of parity violation in atoms, 9 What else can be discovered about weak interactions from experiments with heavy atoms?, 10 Weak interactions and optical isomers, 11 Parity nonconservation in crystals,12 Weak interactions and low temperatures, 13 Searching for T-invariance violation in atoms and molecules, References, Addenda, Index

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Book SynopsisThis primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.Trade Review“Nuclear Lattice Effective Field Theory … is a great practical advantage to the reader. … Lähde and Meißner’s helpful primer has the potential to stimulate increased efforts by serving newcomers as an essential guide to the field.” (Ruprecht Machleidt, Physics Today, Vol. 72 (10), October, 2019)Table of ContentsIntroduction to Effective Field Theory.- Nuclear Forces in Chiral EFT.- Lattice Formulations.- Lattice Chiral Effective Field Theory.- Two and Three Nucleons on the Lattice.- Lattice Monte Carlo.- LIght and Medium-Mass Nuclei on the Lattice.- Further Developments.- Notations and Conventions.- Basics of the Nucleon-Nucleon Interaction.- Study of Rotational Symmetry Breaking Effects in an A Cluster Model.- Monte Carlo Sampling.- Hybrid Monte Carlo Action and Force.- Monte Carlo Calculation of Observables.-

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Book SynopsisThis book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.Trade Review“Ultimately, this short monograph will be of interest as a quick guide to researchers who need a notation reference, well organized overview of the literature, or an introduction to the subject, looking for connection with their own field; also for graduate students who are looking for a bird's eye view or need help with determining the learning path. It must be added that students especially will appreciate that the authors provide solutions to the exercises.” (Tomasz Artur Stachowiak, Mathematical Reviews, December, 2019)“The book represents a very useful tool for graduate students and beginning researchers in a large area of the theory and applications of the Dirac equation. It can be useful for all the stages of learning: from the initial acknowledgement to deep investigations. … The book will be very useful to everybody desiring to make an economy with special articles from various journals.” (Alex B. Gaina, zbMath 1416.81003, 2019)Table of ContentsIntroduction.- The Dirac equation in special relativity.- The spinorial covariant derivative.- Examples in (3+1) GR.- The Dirac equation in (1+1) GR.- The Dirac equation in (2+1) GR.- Scalar product.- Appendices.

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Book SynopsisClose Encounters of Art and Physics is a voyage in time through the abstract ideas harboured in the minds of humans, starting from the graffiti art of cave dwellers and extending to the street art of contemporary men and women. In seeking parallels with science, the author looks far back to the first geometric ideas of our ancestors as well as ahead to the contemporary science of present-day physicists. The parallelism and analogies between these two fields bear witness to a real entanglement in the human brain. The second part of the book contains about 25 colour images showing the author's stunning glass artwork representing ideas such as dark matter, quantum entanglement, cellular automata and many others that are almost impossible to capture in words. Furthermore, many of the physicists who have themselves made major contributions in these fields provide their comments and analysis of the works. The book provides entertaining and informative reading, not only for practicing artists and physicists, but also anyone curious about art and physics.Table of ContentsPart I Parallels Between Art and Physics.- Rock Paintings: Primordial Graffiti.- A Sense of the Beauty of Forms.- Were the Dark Ages Really Dark?.- Rebirth!.- The Age of Reason: The Enlightenment.- Impressive Impressions.- What You See Is Not What You Get.- Is Reality Really Real?.- Abstraction: Pure Thought.- Timeless Time.- Does it Belong to the Elite?.- Part II Collaborations.- What Time Is It?.- A Longer History of Time.- Just Call Me Jim.- Quintessence: The Spirit of the World.- Resolving the Unresolved.- The Brain Is an Orchestra.- Let’s Play Chess.- Are There Real Crystals in the Universe?.- Brain and Mind.- In Memory of Tom Kibble.- Conclusion.- Bibliography

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Book SynopsisTensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics. Trade Review“This book is particularly suitable for students and researchers who are new in this field. It is a timely book that provides a concise introduction of the important topics in this brand-new field with promising prospects. Furthermore, the book provides an up-to-date brief review, which is well suited as a reference for experience researchers.” (Hong-Hao Tu, zbMATH 1442.81003, 2020)Table of ContentsIntroduction.- Tensor Network: Basic Definitions and Properties.- Two-Dimensional Tensor Networks and Contraction Algorithms.- Tensor Network Approaches for Higher-Dimensional Quantum Lattice Models.- Tensor Network Contraction and Multi-Linear Algebra.- Quantum Entanglement Simulation Inspired by Tensor Network.- Summary.

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Book SynopsisThis primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author’s research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.Table of ContentsA Strings-less introduction to AdS-CFT.- A Practical Understanding of the Dictionary.- The first big success: η/s and Hydrodynamics.- Holographic Transport via analytic and numerical techniques.

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Book SynopsisThis book provides a complete and accurate atomic level statistical mechanical explanation of entropy and the second law of thermodynamics. It assumes only a basic knowledge of mechanics and requires no knowledge of calculus. The treatment uses primarily geometric arguments and college level algebra. Quantitative examples are given at each stage to buttress physical understanding. This text is of benefit to undergraduate and graduate students, as well as educators and researchers in the physical sciences (whether or not they have taken a thermodynamics course) who want to understand or teach the atomic/molecular origins of entropy and the second law. It is particularly aimed at those who, due to insufficient mathematical background or because of their area of study, are not going to take a traditional statistical mechanics course.Table of Contents

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Book SynopsisThis book provides a vivid account of the early history of molecular simulation, a new frontier for our understanding of matter that was opened when the demands of theoretical physicists were met by the availability of the modern computers. Since their inception, electronic computers have enormously increased their performance, thus making possible the unprecedented technological revolution that characterizes our present times. This obvious technological advancement has brought with it a silent scientific revolution in the practice of theoretical physics. In particular, in the physics of matter it has opened up a direct route from the microscopic physical laws to observable phenomena. One can now study the time evolution of systems composed of millions of molecules, and simulate the behaviour of macroscopic materials and actually predict their properties. Molecular simulation has provided a new theoretical and conceptual tool that physicists could only dream of when the foundations of statistical mechanics were laid. Molecular simulation has undergone impressive development, both in the size of the scientific community involved and in the range and scope of its applications. It has become the ubiquitous workhorse for investigating the nature of complex condensed matter systems in physics, chemistry, materials and the life sciences. Yet these developments remain largely unknown outside the inner circles of practitioners, and they have so far never been described for a wider public. The main objective of this book is therefore to offer a reasonably comprehensive reconstruction of the early history of molecular simulation addressed to an audience of both scientists and interested non-scientists, describing the scientific and personal trajectories of the main protagonists and discussing the deep conceptual innovations that their work produced.Trade Review“The authors focus mainly on the development of molecular dynamics, in which the motions of many atoms are simultaneously advanced and tracked in small time steps. They explain the scientific evolution of the field; provide biographies— and numerous photographs— of leading characters … . Computer Meets Theoretical Physics should be on the bookshelf of anyone interested in the history of science.” (Christoph Dellago, Physics Today, October, 2021)Table of ContentsA new science.- The origins of simulation.- The growth of molecular dynamics.- Molecular simulation lands in Europe.- CECAM and the development of molecular simulation.- Simulation comes of age.- Quantum systems and critical phenomena.- A first finishing line and some provisional conclusions.

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Book SynopsisSince the 17th century, physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non-intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics, computer science, engineering and chemistry among other disciplines, provided they have the math background even though lacking preparation in physics. In fact, no previous formal study of physics is assumed.Trade Review“The target audience is ‘advanced undergraduate mathematics students who had no or only very little prior knowledge of physics’. It would indeed be a rare variety of mathematics advanced undergraduates who would fit this bill. … an interesting supplement for students with a mathematical bent.” (Amitava Raychaudhuri, zbMATH 1458.81002, 2021)Table of ContentsIntroduction to this Path.- Viewpoint.- Neither Particle nor Wave.- Schrödinger's Equation.- Operators and Canonical Quantization.- The Harmonic Oscillator.- Interpreting: Mathematics.- Interpreting: Physics.- The Language of Hilbert Space.- Interpreting: Measurement.- The Hydrogen Atom.- Angular Momentum.- The Rotation Group SO(3).- Spin and SU(2).- Bosons and Fermions.- Classical and Quantum Probability.- The Heisenberg Picture.- Uncertainty (Optional).- Speaking of Quantum Theory (Optional).- Complementarity (Optional).- Axioms (Optional).- And Gravity?.- Measure Theory: A Crash Course.

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Book SynopsisThe revised and updated 2nd edition of this established textbook provides a self-contained introduction to the general theory of relativity, describing not only the physical principles and applications of the theory, but also the mathematics needed, in particular the calculus of differential forms.Updated throughout, the book contains more detailed explanations and extended discussions of several conceptual points, and strengthened mathematical deductions where required. It includes examples of work conducted in the ten years since the first edition of the book was published, for example the pedagogically helpful concept of a "river of space" and a more detailed discussion of how far the principle of relativity is contained in the general theory of relativity. Also presented is a discussion of the concept of the 'gravitational field' in Einstein's theory, and some new material concerning the 'twin paradox' in the theory of relativity. Finally, the book contains a new section about gravitational waves, exploring the dramatic progress in this field following the LIGO observations. Based on a long-established masters course, the book serves advanced undergraduate and graduate level students, and also provides a useful reference for researchers.Table of ContentsNewton’s law of universal gravitation.- The force law of gravitation.- Newton’s law of gravitation in local form.- Tidal forces.- The principle of equivalence.- The general principle of relativity.- The covariance principle.- Mach’s principle.- The special theory of relativity.- Coordinate systems and Minkowski diagrams.- Synchronization of clocks.- The Doppler effect.- Relativistic time-dilation.- The relativity of simultaneity.- The Lorentz contraction.- The Lorentz transformation.- The Lorentz invariant interval.- The twin paradox.- Hyperbolic motion.- Energy and mass.- Relativistic increase of mass.- Tachyons.- Magnetism as a relativistic second order effect.- Vectors, tensors and forms.- Vectors.- Four-vectors.- Tangent vector fields and coordinate vectors.- Coordinate transformations.- Structure coefficients.- Tensors.- Transformation of tensor components.- Transformation of basis 1-forms.- The metric tensor.- Forms.- Rotating and accelerated reference frames.- Rotating reference frames.- The spatial metric tensor.- Angular acceleration of the rotating frame.- Gravitational time dilation.- Path of photons emitted from the axis in a rotating frame.- The Sagnac effect.- Uniformly accelerated reference frames.- Covariant differentiation.- Differentiation of forms.- Exterior differentiation.- Covariant derivative.- The Christoffel symbols.- Geodetic curves.- The covariant Euler-Lagrange equations.- Application of the Lagrange formalism to free particles.- Equation of motion from Lagrange’s equations.- Geodesic worldliness in spacetime.- Gravitational Doppler effect.- The Koszul connection.- Connection coefficients and structure coefficients in a Riemannian (torsion free) space.- Covariant differentiation of vectors, forms and tensors.- Covariant differentiation of a vector field in an arbitrary basis.- Covariant differentiation of forms.- Generalization for tensors of higher rank.- The Cartan connection.- Curvature.- The Riemann curvature tensor.- Differential geometry of surfaces.- Surface curvature using the Cartan formalism.- The Ricci identity.- Bianchi’s 1st identity.- Bianchi’s 2nd identity.- Einstein’s field equations.- Energy-momentum conservation.- Newtonian fluid.- Perfect fluids.- Einstein’s curvature tensor.- Einstein’s field equations.- The 'geodesic postulate' as a consequence of the field equations.- The Schwarschild spacetime.- Schwarzschild’s exterior solution.- Radial free fall in Schwarzschild spacetime.- Light cones in Schwarzschild spacetime.- Analytical extension of the Schwarzschild coordinates.- Embedding of the Schwarzschild metric.- Deceleration of light.- Particle trajectories in Schwarzschild 3-space.- Motion in the equatorial plane.- Classical tests of Einstein’s general theory of relativity.- The Hafele-Keating experiment.- Mercury’s perihelion precession.- Deflection of light.- Black holes.- 'Surface gravity': gravitational acceleration on the horizon of a black hole.- Hawking radiation: radiation from a black hole.- Rotating black holes: The Kerr metric.- Zero-angular-momentum-observers.- Does the Kerr space have a horizon?.- Schwarzschild’s interior solution.- Newtonian incompressible star.- The pressure contribution to the gravitational mass of a static, spherically symmetric system.- The Tolman-Oppenheimer-Volkov equation.- An exact solution for incompressible stars – Schwarzschild’s interior solution.- Cosmology.- Comoving coordinate system.- Curvature isotropy – the Robertson-Walker metric.- Cosmic dynamics.- Hubble’s law.- Cosmological redshift of light.- Cosmic fluids.- Isotropic and homogeneous universe models.- Some cosmological models.- Radiation dominated model.- Dust dominated model.- Transition from radiation to matter dominated universe.- Friegmann-Lemaître model.- Inflationary cosmology.- Problems with the Big Bang models.- Cosmic inflation.

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Book SynopsisThis book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to pressing open problems in theoretical neuroscience and also machine learning. They enable a systematic and quantitative understanding of the dynamics in recurrent and stochastic neuronal networks. This book is intended for physicists, mathematicians, and computer scientists and it is designed for self-study by researchers who want to enter the field or as the main text for a one semester course at advanced undergraduate or graduate level. The theoretical concepts presented in this book are systematically developed from the very beginning, which only requires basic knowledge of analysis and linear algebra.Table of ContentsI. IntroductionII. Probabilities, moments, cumulantsA. Probabilities, observables, and momentsB. Transformation of random variablesC. CumulantsD. Connection between moments and cumulantsIII. Gaussian distribution and Wick’s theoremA. Gaussian distributionB. Moment and cumulant generating function of a GaussianC. Wick’s theoremD. Graphical representation: Feynman diagramsE. Appendix: Self-adjoint operatorsF. Appendix: Normalization of a GaussianIV. Perturbation expansionA. General caseB. Special case of a Gaussian solvable theoryC. Example: Example: “phi^3 + phi^4” theoryD. External sourcesE. Cancellation of vacuum diagramsF. Equivalence of graphical rules for n-point correlation and n-th momentG. Example: “phi^3 + phi^4” theoryV. Linked cluster theoremA. General proof of the linked cluster theoremB. Dependence on j - external sources - two complimentary viewsC. Example: Connected diagrams of the “phi^3 + phi^4” theoryVI. Functional preliminariesA. Functional derivative1. Product rule2. Chain rule3. Special case of the chain rule: Fourier transformB. Functional Taylor seriesVII. Functional formulation of stochastic differential equationsA. Onsager-Machlup path integral*B. Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) path integralC. Moment generating functionalD. Response function in the MSRDJ formalismVIII. Ornstein-Uhlenbeck process: The free Gaussian theoryA. DefinitionB. Propagators in time domainC. Propagators in Fourier domainIX. Perturbation theory for stochastic differential equationsA. Vanishing moments of response fieldsB. Vanishing response loopsC. Feynman rules for SDEs in time domain and frequency domainD. Diagrams with more than a single external legE. Appendix: Unitary Fourier transformX. Dynamic mean-field theory for random networksA. Definition of the model and generating functionalB. Property of self-averagingC. Average over the quenched disorderD. Stationary statistics: Self-consistent autocorrelation of as motion of a particle in a potentialE. Transition to chaosF. Assessing chaos by a pair of identical systemsG. Schrödinger equation for the maximum Lyapunov exponentH. Condition for transition to chaosXI. Vertex generating functionA. Motivating example for the expansion around a non-vanishing mean valueB. Legendre transform and definition of the vertex generating function GammaC. Perturbation expansion of GammaD. Generalized one-line irreducibilityE. ExampleF. Vertex functions in the Gaussian caseG. Example: Vertex functions of the “phi^3 + phi^4”-theoryH. Appendix: Explicit cancellation until second orderI. Appendix: Convexity of WJ. Appendix: Legendre transform of a GaussianXII. Application: TAP approximationInverse problemXIII. Expansion of cumulants into tree diagrams of vertex functionsA. Self-energy or mass operator SigmaXIV. Loopwise expansion of the effective action - Tree levelA. Counting the number of loopsB. Loopwise expansion of the effective action - Higher numbers of loopsC. Example: phi^3 + phi^4-theoryD. Appendix: Equivalence of loopwise expansion and infinite resummationE. Appendix: Interpretation of Gamma as effective actionF. Loopwise expansion of self-consistency equationXV. Loopwise expansion in the MSRDJ formalismA. Intuitive approachB. Loopwise corrections to the effective equation of motionC. Corrections to the self-energy and self-consistencyD. Self-energy correction to the full propagatorE. Self-consistent one-loopF. Appendix: Solution by Fokker-Planck equationXVI. NomenclatureAcknowledgmentsReferences

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Book SynopsisThis book, now in its third edition, offers a practical guide to the use of probability and statistics in experimental physics that is of value for both advanced undergraduates and graduate students. Focusing on applications and theorems and techniques actually used in experimental research, it includes worked problems with solutions, as well as homework exercises to aid understanding. Suitable for readers with no prior knowledge of statistical techniques, the book comprehensively discusses the topic and features a number of interesting and amusing applications that are often neglected. Providing an introduction to neural net techniques that encompasses deep learning, adversarial neural networks, and boosted decision trees, this new edition includes updated chapters with, for example, additions relating to generating and characteristic functions, Bayes’ theorem, the Feldman-Cousins method, Lagrange multipliers for constraints, estimation of likelihood ratios, and unfolding problems.Trade Review“The depth and the manner in which the material is treated will make it easy for the students to transition to more advanced topics such as deep learning, machine learning and artificial intelligence after perusing the book. … Roe’s book is a wonderful, forward looking introduction to probability and statistics and its applications. Hence, I have no hesitations whatsoever in recommending the book – both to the students and instructors.” (Mogadalai P Gururajan, Contemporary Physics, August 19, 2021)Table of Contents1. Front Matter Pages i-xi 2. Basic Probability Concepts 3. Some Initial Definitions 4. Some Results Independent of Specific Distributions 5. Discrete Distributions and Combinatorials 6. Specific Discrete Distributions 7. The Normal (or Gaussian) Distribution and Other Continuous Distributions 8. Generating Functions and Characteristic Functions 9. The Monte Carlo Method: Computer Simulation of Experiments 10. Queueing Theory and Other Probability Questions 11. Two-Dimensional and Multidimensional Distributions 12. The Central Limit Theorem 13. Inverse Probability; Confidence Limits 14. Methods for Estimating Parameters. Least Squares and Maximum Likelihood 15. Curve Fitting 16. Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment 17. Interpolating Functions and Unfolding Problems 18. Fitting Data with Correlations and Constraints 19. Beyond Maximum Likelihood and Least Squares; Robust Methods 20. Back Matter

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Book SynopsisThis state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.Table of ContentsIntroduction.- Number Systems.- Algebraic Equations.- Scalar Calculus.- Vector Calculus.

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Book SynopsisIs everything Information? This is a tantalizing question which emerges in modern physics, life sciences, astronomy and in today’s information and technology-driven society. In Powers of Two expert authors undertake a unique expedition - in words and images - throughout the world (and scales) of information. The story resembles, in a way, the classic Powers of Ten journeys through space: from us to the macro and the micro worlds . However, by following Powers of Two through the world of information, a completely different and timely paradigm unfolds. Every power of two, 1, 2, 4, 8…. tells us a different story: starting from the creation of the very first bit at the Big Bang and the evolution of life, through 50 years of computational science, and finally into deep space, describing the information in black holes and even in the entire universe and beyond…. All this to address one question: Is our universe made of information? In this book, we experience the Information Universe in nature and in our society and how information lies at the very foundation of our understanding of the Universe.From the Foreword by Robbert Dijkgraaf: This book is in many ways a vastly extended version of Shannon’s one-page blueprint. It carries us all the way to the total information content of the Universe. And it bears testimony of how widespread the use of data has become in all aspects of life. Information is the connective tissue of the modern sciences. […] Undoubtedly, future generations will look back at this time, so much enthralled by Big Data and quantum computers, as beholden to the information metaphor. But that is exactly the value of this book. With its crisp descriptions and evocative illustrations, it brings the reader into the here and now, at the very frontier of scientific research, including the excitement and promise of all the outstanding questions and future discoveries.Message for the e-reader of the book Powers of Two The book has been designed to be read in two-page spreads in full screen mode. For optimal reader experience in a downloaded .pdf file we strongly recommend you use the following settings in Adobe Acrobat Reader: - Taskbar: View > Page Display > two page view - Taskbar: View > Page Display > Show Cover Page in Two Page View - Taskbar: ^ Preferences > Full Screen > deselect " Fill screen with one page at a time" - Taskbar: View > Full screen mode or ctrl L (cmd L on a Mac) ***** Note: for reading the previews on Spinger link (and on-line reading in a browser), the full screen two-page view only works with these browsers: Firefox - Taskbar: on top of the text, at the uppermost right you will see then >> (which is a drop-down menu) >> even double pages - Fullscreen: F11 or Control+Cmd+F with Mac Edge - Taskbar middle: Two-page view and select show cover page separatelyTrade Review“The book … a very unusual collection of some facts about the relationship between the immaterial world represented by bits and the real physical world described by fundamental physical equations. This book continues the very categorical point of view of J. A. Wheeler … . The book presents short articles on various areas of modern science … in which it is shown that in these areas in some mysterious way there is a connection with the theory of information.” (Vladimir Dzhunushaliev, zbMATH 1479.83004, 2022)Table of ContentsForeword by Robbert DijkgraafChapter 0: IntroductionJoy-riding the Universe – by the authorWorking as an astronomer, data scientist and professor of astro-informatics for nearly fifty years, Edwin Valentijn has witnessed and first-hand engineered the dawn of the era of Big Data in science and society. Throughout his career, he became increasingly aware of the role of information in our world: in computers, in our society, and even in nature and in the Universe itself.The Information UniverseFollowing the increasing powers of two, the story paints a journey through the whole world of information, both in society and in nature. Each step opens a door into a new world: from the first bits with the Big Bang and the dawn of life, going through fifty years of human technology, all the way up to the information content of the whole Universe.What is Information? - Item pageThe basics of information are introduced.Chapter 1: The beginningSpace-time foam – Ti (0 bit: 20 =1)The very first power of two: 20, corresponds to the value one. This identifies the single, eternal, indistinguishable state: the primordial sea from which our Universe emerged – sometimes called the Space-time foam. I call this Ti, the reverse of It. This is one of the miraculous new notions in the story of the Powers of Two.Multiverse: Anthropic principle (Item page)From Ti, the primordial space-time foam, countless universes arise with widely different characteristics: the Multiverse. The Anthropic Principle is a philosophical consideration which states that we, people, will find ourselves in a universe that is suitable for intelligent life to emerge. Therefore, this Principle demonstrates that conditions in our Universe are not “fine-tuned” to the existence of human life and a “creator” doesn’t exist.Big bang (1 bit: 21 =2 states)At the Big Bang the first bit is created. From the indistinguishable unity of the primordial foam Ti, “the zeros were separated from the 1’s”: the first bit corresponds to two possible states. This bit is the first step on our journey to capture the ever-increasing complexity of our expanding Universe in terms of information, through the increasing powers of two.What is a bit? (Item page)The bit is at the core of the concept of information. A bit is any system that can have two states. Humans assign meanings to these states, which are illustrated with the concept of the traffic light: red or green, stop or go. The combination of multiple bits creates an exponentially increasing number of possible states, and hence meanings.Multicellular life (2 bit: 22 =4 states) / (4 bit: 24 =16 states)?Life started with exchanging information between cells. This is fundamental for the evolution of any kind of life. It took at least two billion years for uni-cellular to evolve into multi-cellular organisms around 600 million years ago, and to start the exchange of information between their different cells. By exchanging information, cells collaborate and act as a unified whole: life.The game of life (Item page)The characteristic features of life (or any complex system in the Universe) can be created from information. A simple computer game is all you need to demonstrate this concept. A famous example is Conway's Game of Life, which is full of visuals of living, growing, moving and dying objects. This game was already made on the computers of the early 70's with just a few lines of code.Chapter 2: People's Information UniverseASCII (7 bit: 27 =128 states)There is currently no physical theory how the digital world connects to the human consciousness. In the world of Information Technology (IT) all information exchange is based on agreements between people. For instance, ASCII, a simple list relating each letter of the alphabet to a 7-bit string, connects the digital world to the human consciousness. Machu Picchu (8 bit: 28 =256, 1 byte)The Intiwatana stone, a giant rock carved by the Inca's of ancient Machu Picchu in Peru, can be considered as a first 8-bit hard disk. Why so? As the sunrays lit the different surfaces of this huge rock throughout the year, it triggered the Inca's activities: sowing, harvesting, celebrating and praying.This ancient stone dissolves both the boundaries between heaven and earth, and those between the digital and natural Information Universe. In fact, the stone represents an ultimate picture of the cross-over between the in vivo and the in vitro Information Universe - a main theme of the book. In vitro being the man made technology to handle information and in vivo being the information built in nature, in this case the orbit and the light rays of the sun.First computers (16 bit: 216 =65.536, 2 byte)When computers emerged in the 1970's, astronomers first adopted them to steer their telescopes. Back then, a maximal effort to understand the mathematics of the problem was needed to squeeze the solution into the small computer memory. Nowadays, with large amounts of computing power and machine learning at their disposal, scientists and computer programmers often do the reverse.Star Peace vs. Star Wars (Item page)King Juan Carlos adored the harmony of galaxies as a source of inspiration for people on earth, in those days when Ronald Reagan was promoting his Star-wars programme. With this adoration in mind, in 1985, he gave an inspiring speech at the Royal inauguration of the international astronomical observatory on La Palma, Canary Islands. The inauguration was attended by, for those days, an unprecedented large crowd of European royals and government officials despite the great threat of terrorist attacks by the ETA. (the next and later spreads on facts vs fakes elucidate the relevance of this spread in the story line).Pre-internet Facts and Fakes (Item page)“Edwin Valentijn saved the life of the Dutch Queen Beatrix by catching her just before falling off a cliff at the inauguration on La Palma”, according to the headlines in Dutch newspapers. Fake news-stories are at all times alike and can only be dispelled by tracing links of information to their source, links or associations being a fundamental property of the Information Universe. Later, I discuss the less innocent case of overdrawing attention to terrorist attacks in the past decade.Hard disk (24 bit: 224 =1.6*107, 2 Mb)Only sixty years ago, a 5 MB hard disk weighed over five tons, and had to be loaded onto an aeroplane by using a truck. Now, we carry a thousand times more information in our trouser pocket. This demonstrates the amazing advance of information technology over the past decades. (Picture: first IBM hard disk loaded onto a plane).The telephone (Item page) As a precursor of the Internet, the telephone offered many of the same advantages and dangers, and was heavily discussed at its introduction. Whether telephone or the Internet, it all revolves around communication or copying of information. The telephone, as example of it, is one of the major discoveries of the 20th century. DNA (32 bit: 232 = 4*109, 500 Mb) – Guest author: Charley Lineweaver The information in the DNA creates life. All base pairs of the human DNA can be stored on a 500 Mb drive. How is this information communicated? How does a cell know it has to build part of a liver and not an eye, while they all have the same DNA? Apoptosis and the role of information exchange.Where does biological Information come from? (Item page) – Guest author: Charley Lineweaver Charley Lineweaver, expert on evolutionary biology, exoplanetology and astrobiology, will expand on the role of information in the evolution of life.Lifelines (Item page) – Guest author: Morris SwertzWhat is the role of nature versus that of nurture? A key question in modern health research. In Lifesciences, this question is addressed now using Big Data, like the astronomers who acquire huge data volumes to address the same question on the nature of galaxies. In Lifelines, a cohort of 165.000 people is studied over a period of 30 years using hospital data, blood samples and DNA scans.DVD (33 bit: 233 =9*109, 1 Gb)It’ s amazing how fast the digital image revolution went since 1989.30 years ago, Philips lab approached me since they had made a big discovery: it was possible to store many digital images on a CD. They were chasing me for digital images. While NASA had less than a thousand, I had 32.000 galaxy images obtained by scanning photographic plates from the European Southern Observatory – the first large digital image collection.Human Brain (36 bit: 236 =7*1010, 9 Gb) – Guest author: Katrin Amunts- JulichIn the large EU human brain project, the activities of the human brain are simulated in computers. This is a very difficult mission since the transistors in computers consume 100.000 billion times more energy than the synapsis of neurons. Our brains consist of 1011 neurons, corresponding to 9 Gb of data.Thinking of Karlheinz Meier, coordinator of the Human Brain Project in Heidelberg, Katrin Amunts will author two spreads on the role of information in the human brain.Neuromorphic computing – Guest author: Katrin AmuntsCurrently, it takes a hundred years of a supercomputer’s time to compete with the learning power of only a single day of the human brain. “Neuromorphic computing” researchers design electronic systems inspired by the human brain, in order to make computers many times faster and more energy efficient.CT scan (38 bit: 238 =3*1011, 34 Gb) – Guest author: Anders YnnermanNow it is possible to look inside animal and human bodies on touchscreens. Forensic investigations on, for instance, corpses of victims can be done with touch-screen tables. You can look inside, rotate, scroll and zoom animal and human bodies using tens of gigabytes of CT scan data. Prof. Anders Ynnerman explains how he does it.Terabytes (45 bit: 245 =4.4*1012, 1 Tb) - The largest (astronomical) datasetsDark energy and dark matter: two mysterious constituents of our Universe. How do astronomers get and handle the data from the VLT Survey Telescope on a high mountain top in Chile to shed lights on these ‘still too dark’ topics. This Telescope surveys the sky every hour at night generating Terabytes of astronomical data.Gravity as a lens (Item page) – Guest author: Margot BrouwerWhen light rays are bent by the gravity of a heavy object, this object acts as a lens. This effect can be used to map dark matter, which is invisible but constitutes 80% of the matter in our visible Universe. In 1915, Albert Einstein posed that gravity is equivalent to the curvature of the fabric of space and time itself, leading to the lensing effect.Weak gravitational lensing surveys – Guest author: Margot BrouwerTerabytes of astronomical data are reduced to a few numbers, describing how dark matter behaves and what is its true nature. https://www.youtube.com/watch?v=ZCyYGWqCmFw&t=23sEntering the Petabyte regime (53 bit: 253 =1*1015, 1 Pb)How do we technically acquire and deal with Petabytes of data?Dark Matter maps (Item page)A first dark matter map projected on the night sky. An ultimate encounter between the digital world of modern astronomical observations, and nature: the mysterious dark matter mapped on top of the everyday “night” stellar sky. A visualization that condenses Terabytes of astronomical data to a simple map.Metadata for Peta-data (62 bit: 262 =6*1017, 600 Pb)With pointers, one can connect everything in the Information Universe. Pointers are often inserted in Metadata (data about data) - an ultimate tool for dealing with Big Data. It is possible to create unique pointers to hundreds of Petabytes of data, using a string of less than 64 bits. This is what makes pointers so powerful and indispensable in current and future stages of the big data era; not only for astronomical research, but also for companies like Google, Amazon and Facebook.Downloading the Universe (Item page)The universe can be seen as a spreadsheet, certainly in the way we map it on our computers (in vitro), but also in nature (in vivo). Perceiving the Universe as a spreadsheet links bit to It.Meta data (Item page)A visualisation of the enormous complexity of data models which trace all pointers between data items. (picture: thrilling still from a full dome animation of a data model)Future (astronomical) datasets (item page)While current telescopes collect astronomical datasets of Terabytes, future telescopes such as the LSST and the Euclid satellite, instead, will collect Petabytes. These enormous amounts of data need a whole new approach to data management. For the Euclid satellite my “Universe as a spreadsheet” approach has been adopted.The Euclid satellite (Item page) – Guest author: Margot BrouwerEuclid is ESA’s new space mission to map the Dark Universe. At a distance of 1.5 million kilometres from Earth, this telescope will observe billions of galaxies. Its goal: to shed light on the nature of Dark Matter and Dark Energy, which make up 95% of our Universe. Dr. Margot Brouwer, Dutch scientific communication officer for Euclid, will explain more.The Information Universe (Item page)The resemblance of the overall structure of the real observed Universe (in vivo) with the simulated universe (in vitro), based on the concurrent cosmological model, gave a lot of credit to the latter. When we zoom out the Universe, we see billions of galaxies forming a web-like structure. Amazingly, astronomers can now compute and simulate these structures with very large supercomputers.The lost boy (Item page)Information is timeless, and knows no boundaries. It crosses over the in vivo and the in vitro Information Universe. This concept is well illustrated through daily life stories involving time. At the age of five, a boy loses sight of his older brother on a train in India, and eventually gets lost on the streets of Mumbai. Twenty years later, after being adopted by a family in Australia, he is able to find his natural mother (in vivo) through only searching on Google maps (in vitro).Qbits (50 qbit: 250 =1.1*1015 qbit, 1 Pbit) – Guest author: Lieven VandersypenUsing fundamental particles (quanta, such as electrons) to perform calculations and build computers, is one of the most exciting cross-overs between the in vivo and the in vitro Information Universe. Prof. Lieven Vandersypen, who leads a Quantum Computing group at TU Delft in the Netherlands, will explain how this technology will change the way we compute.Quantum entanglement (Item page) – Guest author: Lieven VandersypenThe states of two particles can be intimately linked (entangled), no matter how far they are separated. What Einstein famously dismissed as “spooky action at a distance”, can now be established on demand at TU Delft in the Netherlands. Prof. Vandersypen will explain how his research group, for the first time ever, both create and apply this entanglement in laboratory.Entanglement (item page) - EVThe Square Kilometre Array (64 bit: 264 =1.3*1018, 1 Eb) – Guest author: TBAThe Square Kilometre Telescope will collect data at the rate of the global internet traffic of 2013, in its endeavour to answer fundamental questions about the origin and evolution of the Universe, and its search for extra-terrestrial life.Cryptography (128 bit: 2128 =3.4*1038) – Guest author Tanja LangeEncrypted messages should not be decoded by adversaries, be they criminals or hostile countries. Cryptography enables secure communications and is one of the few applications which require 128-bit numbers. A guest author will explain more.Chapter 3: Deep spaceThe Desert (128-256 bit) Theoretical physics is not progressing much in the last decennia – some call it a crisis. Likely, an observational breakthrough is out of reach: the highest man-made information density on earth is produced by the high energy accelerators at CERN. But these accelerators have to be 1013 -1015 more powerful to reach the fundamental unit of information, which is probably at the same level of the Planck length. Unfortunately, there is no way to reach this unit of information with these instruments. This enormous gap in reaching all the domains in the Information Universe is illustrated in a figure and in a very sobering, but instructive table in the Appendix.Black holes (128-256 bit?) – Guest author: Manus VisserCan information disappear into a black hole? The Information paradox. Stephen Hawking wondered it and started a field in which space and time are described in terms of information. Dr. Manus Visser, expert on gravity and space-time, will explain more.Observing a Black Hole: Event Horizon Telescope – Guest author: Heino FalckeThe first image of a black hole. Prof. Heino Falcke, chair of the Event Horizon Telescope Science Council, will explain how information from a world-wide network of telescopes was combined using atomic clocks, to create the first ever image of a black hole. (Picture: first image of a black hole)Cogwheels: a deeper level – Guest author: Gerard 't HooftNobel laureate ‘t Hooft explains his views on cogwheels, carrying the fundamental information in the Universe.Gravitational waves – Guest author: Chris van den BroeckLinks: The Universe as a spreadsheetLinks, joins, references, URLs, blockchain, associations and even entanglement in physics are all different words for the same building block, forming the connections in the Information Universe.Cosmic Microwave Background – Guest author: Margot BrouwerParticles of light created in the hot and dense state of the Universe after the Big Bang are still flying through the Universe today. Together, these 1077 photons contain the largest amount of information known in the Universe. This information can still be accessed through telescopes, and brings us invaluable information about the dawn of our Universe.Emergent Gravity – Guest author: Erik VerlindeProf. Erik Verlinde, professor of theoretical physics at the University of Amsterdam, won the Spinoza prize for his new theory explaining gravity. In his theory, all matter, space and time consist of information and are all connected by entanglement. If this theory is correct, the information content of the entire Universe is 2399. This is the highest power described in this book, and actually, in physics.Chapter 4: It from BitOne big information processing machine – Guest author: Gerard 't Hooft (TBC)t Hooftt Hooft: : ““there is something happening at a different level of nature”there is something happening at a different level of nature”..On the origin of physical information. – Guest author: Stefano GottardiThe ear In the ear information is copied a dozen times!The eye – on the visual perception of data- climate change. Links to - facts and fakes- the system of ScienceThe System of ScienceHow does this system work? Discussing Hegel’s system of science, logic, technology, Nature, life, physics, consciousness.Artificial IntelligenceThe machine learning and the data-base oriented communities are still living on different planets. I discuss and revisit Tegmark’s recent book Life 3.0 by comparing 3 crosscuts through the Information Universe: i) the classical computer centric view ii) the data centric view iii) the artificial intelligence view.Information densityThe average information density of the universe can be compared to that of written text.Black Body radiation On the information aspects of the third big physical breakthrough of the 20th century (next to General relativity and quantum mechanics).EntropyDiscussing Shannon’s work and identifying that “Information only exists in relation to its environment”. Examples will be given.Cosmic information, cosmogenesis and dark energy by PadmanabhanCosmic information connects the cosmological constant to cosmogenesisIt from BitIs the Universe one big information processing machine?ConsciousnessVery little is known about the consciousness and I refrain from addressing the consciousness per se. A relevant list of about 5 facts we do know are listed. Any view on the relation between the consciousness and the Information Universe should at least deal with this list.Somnium – Musician Jacco Gardner performing at DOTLiveplanetarium at Eurosonic 2019 show case music festival- Inspired by Kepler’s Somnium – directed by EV The Information UniverseAn overview.Facts and fakesHow is all this related to the current facts and fakes issues on the Internet? How do you make sure that what you are reading is accurate and comes from a reliable source?The link between Open Science, FAIR and reliability of data.

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Book SynopsisIs everything Information? This is a tantalizing question which emerges in modern physics, life sciences, astronomy and in today’s information and technology-driven society. In Powers of Two expert authors undertake a unique expedition - in words and images - throughout the world (and scales) of information. The story resembles, in a way, the classic Powers of Ten journeys through space: from us to the macro and the micro worlds . However, by following Powers of Two through the world of information, a completely different and timely paradigm unfolds. Every power of two, 1, 2, 4, 8…. tells us a different story: starting from the creation of the very first bit at the Big Bang and the evolution of life, through 50 years of computational science, and finally into deep space, describing the information in black holes and even in the entire universe and beyond…. All this to address one question: Is our universe made of information? In this book, we experience the Information Universe in nature and in our society and how information lies at the very foundation of our understanding of the Universe.From the Foreword by Robbert Dijkgraaf: This book is in many ways a vastly extended version of Shannon’s one-page blueprint. It carries us all the way to the total information content of the Universe. And it bears testimony of how widespread the use of data has become in all aspects of life. Information is the connective tissue of the modern sciences. […] Undoubtedly, future generations will look back at this time, so much enthralled by Big Data and quantum computers, as beholden to the information metaphor. But that is exactly the value of this book. With its crisp descriptions and evocative illustrations, it brings the reader into the here and now, at the very frontier of scientific research, including the excitement and promise of all the outstanding questions and future discoveries.Message for the e-reader of the book Powers of Two The book has been designed to be read in two-page spreads in full screen mode. For optimal reader experience in a downloaded .pdf file we strongly recommend you use the following settings in Adobe Acrobat Reader: - Taskbar: View > Page Display > two page view - Taskbar: View > Page Display > Show Cover Page in Two Page View - Taskbar: ^ Preferences > Full Screen > deselect " Fill screen with one page at a time" - Taskbar: View > Full screen mode or ctrl L (cmd L on a Mac) ***** Note: for reading the previews on Spinger link (and on-line reading in a browser), the full screen two-page view only works with these browsers: Firefox - Taskbar: on top of the text, at the uppermost right you will see then >> (which is a drop-down menu) >> even double pages - Fullscreen: F11 or Control+Cmd+F with Mac Edge - Taskbar middle: Two-page view and select show cover page separatelyTrade Review“The book … a very unusual collection of some facts about the relationship between the immaterial world represented by bits and the real physical world described by fundamental physical equations. This book continues the very categorical point of view of J. A. Wheeler … . The book presents short articles on various areas of modern science … in which it is shown that in these areas in some mysterious way there is a connection with the theory of information.” (Vladimir Dzhunushaliev, zbMATH 1479.83004, 2022)Table of ContentsForeword by Robbert DijkgraafChapter 0: IntroductionJoy-riding the Universe – by the authorWorking as an astronomer, data scientist and professor of astro-informatics for nearly fifty years, Edwin Valentijn has witnessed and first-hand engineered the dawn of the era of Big Data in science and society. Throughout his career, he became increasingly aware of the role of information in our world: in computers, in our society, and even in nature and in the Universe itself.The Information UniverseFollowing the increasing powers of two, the story paints a journey through the whole world of information, both in society and in nature. Each step opens a door into a new world: from the first bits with the Big Bang and the dawn of life, going through fifty years of human technology, all the way up to the information content of the whole Universe.What is Information? - Item pageThe basics of information are introduced.Chapter 1: The beginningSpace-time foam – Ti (0 bit: 20 =1)The very first power of two: 20, corresponds to the value one. This identifies the single, eternal, indistinguishable state: the primordial sea from which our Universe emerged – sometimes called the Space-time foam. I call this Ti, the reverse of It. This is one of the miraculous new notions in the story of the Powers of Two.Multiverse: Anthropic principle (Item page)From Ti, the primordial space-time foam, countless universes arise with widely different characteristics: the Multiverse. The Anthropic Principle is a philosophical consideration which states that we, people, will find ourselves in a universe that is suitable for intelligent life to emerge. Therefore, this Principle demonstrates that conditions in our Universe are not “fine-tuned” to the existence of human life and a “creator” doesn’t exist.Big bang (1 bit: 21 =2 states)At the Big Bang the first bit is created. From the indistinguishable unity of the primordial foam Ti, “the zeros were separated from the 1’s”: the first bit corresponds to two possible states. This bit is the first step on our journey to capture the ever-increasing complexity of our expanding Universe in terms of information, through the increasing powers of two.What is a bit? (Item page)The bit is at the core of the concept of information. A bit is any system that can have two states. Humans assign meanings to these states, which are illustrated with the concept of the traffic light: red or green, stop or go. The combination of multiple bits creates an exponentially increasing number of possible states, and hence meanings.Multicellular life (2 bit: 22 =4 states) / (4 bit: 24 =16 states)?Life started with exchanging information between cells. This is fundamental for the evolution of any kind of life. It took at least two billion years for uni-cellular to evolve into multi-cellular organisms around 600 million years ago, and to start the exchange of information between their different cells. By exchanging information, cells collaborate and act as a unified whole: life.The game of life (Item page)The characteristic features of life (or any complex system in the Universe) can be created from information. A simple computer game is all you need to demonstrate this concept. A famous example is Conway's Game of Life, which is full of visuals of living, growing, moving and dying objects. This game was already made on the computers of the early 70's with just a few lines of code.Chapter 2: People's Information UniverseASCII (7 bit: 27 =128 states)There is currently no physical theory how the digital world connects to the human consciousness. In the world of Information Technology (IT) all information exchange is based on agreements between people. For instance, ASCII, a simple list relating each letter of the alphabet to a 7-bit string, connects the digital world to the human consciousness. Machu Picchu (8 bit: 28 =256, 1 byte)The Intiwatana stone, a giant rock carved by the Inca's of ancient Machu Picchu in Peru, can be considered as a first 8-bit hard disk. Why so? As the sunrays lit the different surfaces of this huge rock throughout the year, it triggered the Inca's activities: sowing, harvesting, celebrating and praying.This ancient stone dissolves both the boundaries between heaven and earth, and those between the digital and natural Information Universe. In fact, the stone represents an ultimate picture of the cross-over between the in vivo and the in vitro Information Universe - a main theme of the book. In vitro being the man made technology to handle information and in vivo being the information built in nature, in this case the orbit and the light rays of the sun.First computers (16 bit: 216 =65.536, 2 byte)When computers emerged in the 1970's, astronomers first adopted them to steer their telescopes. Back then, a maximal effort to understand the mathematics of the problem was needed to squeeze the solution into the small computer memory. Nowadays, with large amounts of computing power and machine learning at their disposal, scientists and computer programmers often do the reverse.Star Peace vs. Star Wars (Item page)King Juan Carlos adored the harmony of galaxies as a source of inspiration for people on earth, in those days when Ronald Reagan was promoting his Star-wars programme. With this adoration in mind, in 1985, he gave an inspiring speech at the Royal inauguration of the international astronomical observatory on La Palma, Canary Islands. The inauguration was attended by, for those days, an unprecedented large crowd of European royals and government officials despite the great threat of terrorist attacks by the ETA. (the next and later spreads on facts vs fakes elucidate the relevance of this spread in the story line).Pre-internet Facts and Fakes (Item page)“Edwin Valentijn saved the life of the Dutch Queen Beatrix by catching her just before falling off a cliff at the inauguration on La Palma”, according to the headlines in Dutch newspapers. Fake news-stories are at all times alike and can only be dispelled by tracing links of information to their source, links or associations being a fundamental property of the Information Universe. Later, I discuss the less innocent case of overdrawing attention to terrorist attacks in the past decade.Hard disk (24 bit: 224 =1.6*107, 2 Mb)Only sixty years ago, a 5 MB hard disk weighed over five tons, and had to be loaded onto an aeroplane by using a truck. Now, we carry a thousand times more information in our trouser pocket. This demonstrates the amazing advance of information technology over the past decades. (Picture: first IBM hard disk loaded onto a plane).The telephone (Item page) As a precursor of the Internet, the telephone offered many of the same advantages and dangers, and was heavily discussed at its introduction. Whether telephone or the Internet, it all revolves around communication or copying of information. The telephone, as example of it, is one of the major discoveries of the 20th century. DNA (32 bit: 232 = 4*109, 500 Mb) – Guest author: Charley Lineweaver The information in the DNA creates life. All base pairs of the human DNA can be stored on a 500 Mb drive. How is this information communicated? How does a cell know it has to build part of a liver and not an eye, while they all have the same DNA? Apoptosis and the role of information exchange.Where does biological Information come from? (Item page) – Guest author: Charley Lineweaver Charley Lineweaver, expert on evolutionary biology, exoplanetology and astrobiology, will expand on the role of information in the evolution of life.Lifelines (Item page) – Guest author: Morris SwertzWhat is the role of nature versus that of nurture? A key question in modern health research. In Lifesciences, this question is addressed now using Big Data, like the astronomers who acquire huge data volumes to address the same question on the nature of galaxies. In Lifelines, a cohort of 165.000 people is studied over a period of 30 years using hospital data, blood samples and DNA scans.DVD (33 bit: 233 =9*109, 1 Gb)It’ s amazing how fast the digital image revolution went since 1989.30 years ago, Philips lab approached me since they had made a big discovery: it was possible to store many digital images on a CD. They were chasing me for digital images. While NASA had less than a thousand, I had 32.000 galaxy images obtained by scanning photographic plates from the European Southern Observatory – the first large digital image collection.Human Brain (36 bit: 236 =7*1010, 9 Gb) – Guest author: Katrin Amunts- JulichIn the large EU human brain project, the activities of the human brain are simulated in computers. This is a very difficult mission since the transistors in computers consume 100.000 billion times more energy than the synapsis of neurons. Our brains consist of 1011 neurons, corresponding to 9 Gb of data.Thinking of Karlheinz Meier, coordinator of the Human Brain Project in Heidelberg, Katrin Amunts will author two spreads on the role of information in the human brain.Neuromorphic computing – Guest author: Katrin AmuntsCurrently, it takes a hundred years of a supercomputer’s time to compete with the learning power of only a single day of the human brain. “Neuromorphic computing” researchers design electronic systems inspired by the human brain, in order to make computers many times faster and more energy efficient.CT scan (38 bit: 238 =3*1011, 34 Gb) – Guest author: Anders YnnermanNow it is possible to look inside animal and human bodies on touchscreens. Forensic investigations on, for instance, corpses of victims can be done with touch-screen tables. You can look inside, rotate, scroll and zoom animal and human bodies using tens of gigabytes of CT scan data. Prof. Anders Ynnerman explains how he does it.Terabytes (45 bit: 245 =4.4*1012, 1 Tb) - The largest (astronomical) datasetsDark energy and dark matter: two mysterious constituents of our Universe. How do astronomers get and handle the data from the VLT Survey Telescope on a high mountain top in Chile to shed lights on these ‘still too dark’ topics. This Telescope surveys the sky every hour at night generating Terabytes of astronomical data.Gravity as a lens (Item page) – Guest author: Margot BrouwerWhen light rays are bent by the gravity of a heavy object, this object acts as a lens. This effect can be used to map dark matter, which is invisible but constitutes 80% of the matter in our visible Universe. In 1915, Albert Einstein posed that gravity is equivalent to the curvature of the fabric of space and time itself, leading to the lensing effect.Weak gravitational lensing surveys – Guest author: Margot BrouwerTerabytes of astronomical data are reduced to a few numbers, describing how dark matter behaves and what is its true nature. https://www.youtube.com/watch?v=ZCyYGWqCmFw&t=23sEntering the Petabyte regime (53 bit: 253 =1*1015, 1 Pb)How do we technically acquire and deal with Petabytes of data?Dark Matter maps (Item page)A first dark matter map projected on the night sky. An ultimate encounter between the digital world of modern astronomical observations, and nature: the mysterious dark matter mapped on top of the everyday “night” stellar sky. A visualization that condenses Terabytes of astronomical data to a simple map.Metadata for Peta-data (62 bit: 262 =6*1017, 600 Pb)With pointers, one can connect everything in the Information Universe. Pointers are often inserted in Metadata (data about data) - an ultimate tool for dealing with Big Data. It is possible to create unique pointers to hundreds of Petabytes of data, using a string of less than 64 bits. This is what makes pointers so powerful and indispensable in current and future stages of the big data era; not only for astronomical research, but also for companies like Google, Amazon and Facebook.Downloading the Universe (Item page)The universe can be seen as a spreadsheet, certainly in the way we map it on our computers (in vitro), but also in nature (in vivo). Perceiving the Universe as a spreadsheet links bit to It.Meta data (Item page)A visualisation of the enormous complexity of data models which trace all pointers between data items. (picture: thrilling still from a full dome animation of a data model)Future (astronomical) datasets (item page)While current telescopes collect astronomical datasets of Terabytes, future telescopes such as the LSST and the Euclid satellite, instead, will collect Petabytes. These enormous amounts of data need a whole new approach to data management. For the Euclid satellite my “Universe as a spreadsheet” approach has been adopted.The Euclid satellite (Item page) – Guest author: Margot BrouwerEuclid is ESA’s new space mission to map the Dark Universe. At a distance of 1.5 million kilometres from Earth, this telescope will observe billions of galaxies. Its goal: to shed light on the nature of Dark Matter and Dark Energy, which make up 95% of our Universe. Dr. Margot Brouwer, Dutch scientific communication officer for Euclid, will explain more.The Information Universe (Item page)The resemblance of the overall structure of the real observed Universe (in vivo) with the simulated universe (in vitro), based on the concurrent cosmological model, gave a lot of credit to the latter. When we zoom out the Universe, we see billions of galaxies forming a web-like structure. Amazingly, astronomers can now compute and simulate these structures with very large supercomputers.The lost boy (Item page)Information is timeless, and knows no boundaries. It crosses over the in vivo and the in vitro Information Universe. This concept is well illustrated through daily life stories involving time. At the age of five, a boy loses sight of his older brother on a train in India, and eventually gets lost on the streets of Mumbai. Twenty years later, after being adopted by a family in Australia, he is able to find his natural mother (in vivo) through only searching on Google maps (in vitro).Qbits (50 qbit: 250 =1.1*1015 qbit, 1 Pbit) – Guest author: Lieven VandersypenUsing fundamental particles (quanta, such as electrons) to perform calculations and build computers, is one of the most exciting cross-overs between the in vivo and the in vitro Information Universe. Prof. Lieven Vandersypen, who leads a Quantum Computing group at TU Delft in the Netherlands, will explain how this technology will change the way we compute.Quantum entanglement (Item page) – Guest author: Lieven VandersypenThe states of two particles can be intimately linked (entangled), no matter how far they are separated. What Einstein famously dismissed as “spooky action at a distance”, can now be established on demand at TU Delft in the Netherlands. Prof. Vandersypen will explain how his research group, for the first time ever, both create and apply this entanglement in laboratory.Entanglement (item page) - EVThe Square Kilometre Array (64 bit: 264 =1.3*1018, 1 Eb) – Guest author: TBAThe Square Kilometre Telescope will collect data at the rate of the global internet traffic of 2013, in its endeavour to answer fundamental questions about the origin and evolution of the Universe, and its search for extra-terrestrial life.Cryptography (128 bit: 2128 =3.4*1038) – Guest author Tanja LangeEncrypted messages should not be decoded by adversaries, be they criminals or hostile countries. Cryptography enables secure communications and is one of the few applications which require 128-bit numbers. A guest author will explain more.Chapter 3: Deep spaceThe Desert (128-256 bit) Theoretical physics is not progressing much in the last decennia – some call it a crisis. Likely, an observational breakthrough is out of reach: the highest man-made information density on earth is produced by the high energy accelerators at CERN. But these accelerators have to be 1013 -1015 more powerful to reach the fundamental unit of information, which is probably at the same level of the Planck length. Unfortunately, there is no way to reach this unit of information with these instruments. This enormous gap in reaching all the domains in the Information Universe is illustrated in a figure and in a very sobering, but instructive table in the Appendix.Black holes (128-256 bit?) – Guest author: Manus VisserCan information disappear into a black hole? The Information paradox. Stephen Hawking wondered it and started a field in which space and time are described in terms of information. Dr. Manus Visser, expert on gravity and space-time, will explain more.Observing a Black Hole: Event Horizon Telescope – Guest author: Heino FalckeThe first image of a black hole. Prof. Heino Falcke, chair of the Event Horizon Telescope Science Council, will explain how information from a world-wide network of telescopes was combined using atomic clocks, to create the first ever image of a black hole. (Picture: first image of a black hole)Cogwheels: a deeper level – Guest author: Gerard 't HooftNobel laureate ‘t Hooft explains his views on cogwheels, carrying the fundamental information in the Universe.Gravitational waves – Guest author: Chris van den BroeckLinks: The Universe as a spreadsheetLinks, joins, references, URLs, blockchain, associations and even entanglement in physics are all different words for the same building block, forming the connections in the Information Universe.Cosmic Microwave Background – Guest author: Margot BrouwerParticles of light created in the hot and dense state of the Universe after the Big Bang are still flying through the Universe today. Together, these 1077 photons contain the largest amount of information known in the Universe. This information can still be accessed through telescopes, and brings us invaluable information about the dawn of our Universe.Emergent Gravity – Guest author: Erik VerlindeProf. Erik Verlinde, professor of theoretical physics at the University of Amsterdam, won the Spinoza prize for his new theory explaining gravity. In his theory, all matter, space and time consist of information and are all connected by entanglement. If this theory is correct, the information content of the entire Universe is 2399. This is the highest power described in this book, and actually, in physics.Chapter 4: It from BitOne big information processing machine – Guest author: Gerard 't Hooft (TBC)t Hooftt Hooft: : ““there is something happening at a different level of nature”there is something happening at a different level of nature”..On the origin of physical information. – Guest author: Stefano GottardiThe ear In the ear information is copied a dozen times!The eye – on the visual perception of data- climate change. Links to - facts and fakes- the system of ScienceThe System of ScienceHow does this system work? Discussing Hegel’s system of science, logic, technology, Nature, life, physics, consciousness.Artificial IntelligenceThe machine learning and the data-base oriented communities are still living on different planets. I discuss and revisit Tegmark’s recent book Life 3.0 by comparing 3 crosscuts through the Information Universe: i) the classical computer centric view ii) the data centric view iii) the artificial intelligence view.Information densityThe average information density of the universe can be compared to that of written text.Black Body radiation On the information aspects of the third big physical breakthrough of the 20th century (next to General relativity and quantum mechanics).EntropyDiscussing Shannon’s work and identifying that “Information only exists in relation to its environment”. Examples will be given.Cosmic information, cosmogenesis and dark energy by PadmanabhanCosmic information connects the cosmological constant to cosmogenesisIt from BitIs the Universe one big information processing machine?ConsciousnessVery little is known about the consciousness and I refrain from addressing the consciousness per se. A relevant list of about 5 facts we do know are listed. Any view on the relation between the consciousness and the Information Universe should at least deal with this list.Somnium – Musician Jacco Gardner performing at DOTLiveplanetarium at Eurosonic 2019 show case music festival- Inspired by Kepler’s Somnium – directed by EV The Information UniverseAn overview.Facts and fakesHow is all this related to the current facts and fakes issues on the Internet? How do you make sure that what you are reading is accurate and comes from a reliable source?The link between Open Science, FAIR and reliability of data.

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Book SynopsisThe field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.Table of ContentsWeierstrass Elliptic Function.- Weierstrass Quasi-periodic Functions.- Real Solutions of Weierstrass Equation.- Applications in Classical Mechanics.- Applications in Quantum Mechanics.- Epilogue and Projects for the Advanced Reader.

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Book SynopsisThis book introduces physics students to concepts and methods of finance. Despite being perceived as quite distant from physics, finance shares a number of common methods and ideas, usually related to noise and uncertainties. Juxtaposing the key methods to applications in both physics and finance articulates both differences and common features, this gives students a deeper understanding of the underlying ideas. Moreover, they acquire a number of useful mathematical and computational tools, such as stochastic differential equations, path integrals, Monte-Carlo methods, and basic cryptology. Each chapter ends with a set of carefully designed exercises enabling readers to test their comprehension.Table of ContentsChapter 1 - Introduction Chapter 2 - Concepts of finance Chapter 3 - Portfolio theory and CAPM Chapter 4 - Stochastic processes Chapter 5 - Black-Scholes differential equation Chapter 6 - The Greeks and risk management Chapter 7 - Regression models and hypothesis testing Chapter 8 - Time series Chapter 9 - Bubbles, crashes, fat tails and Levy-stable distributions Chapter 10 - Quantum finance and path integrals Chapter 11 - Optimal control theory.

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Book SynopsisThis textbook provides an introduction to string field theory (SFT). String theory is usually formulated in the worldsheet formalism, which describes a single string (first-quantization). While this approach is intuitive and could be pushed far due to the exceptional properties of two-dimensional theories, it becomes cumbersome for some questions or even fails at a more fundamental level. These motivations have led to the development of SFT, a description of string theory using the field theory formalism (second-quantization). As a field theory, SFT provides a rigorous and constructive formulation of string theory. The main focus of the book is the construction of the closed bosonic SFT. The accent is put on providing the reader with the foundations, conceptual understanding and intuition of what SFT is. After reading this book, the reader is able to study the applications from the literature. The book is organized in two parts. The first part reviews the notions of the worldsheet theory that are necessary to build SFT (worldsheet path integral, CFT and BRST quantization). The second part starts by introducing general concepts of SFT from the BRST quantization. Then, it introduces off-shell string amplitudes before providing a Feynman diagrams interpretation from which the building blocks of SFT are extracted. After constructing the closed SFT, the author outlines the proofs of several important properties such as background independence, unitarity and crossing symmetry. Finally, the generalization to the superstring is also discussed.Trade Review“The book under review offers a comprehensive self-contained description of string field theory (SFT) and the tools necessary to build it. … For each chapter the author has collected the most relevant references. This, together with various examples, figures, remarks and, especially, a suitable amount of details, has produced a compulsively readable textbook quite useful for students and newcomers. … The last version of the draft of the book can be accessed on the author's professional web page.” (Farhang Loran, Mathematical Reviews, April, 2022)Table of ContentsIntroduction.- Worldsheet path integral: vacuum amplitudes.- Worldsheet path integral: scattering amplitudes.- Worldsheet path integral: complex coordinates.- Conformal field theory in D dimensions.- Conformal field theory on the plane.- CFT systems.- BRST quantization.- String field.- Free BRST string field theory.- Introduction to off-shell string theory.- Geometry of moduli spaces and Riemann surfaces.- Off-shell amplitudes.-Amplitude factorization and Feynman diagrams.- Closed string field theory.- Background independence.- Superstring.- Momentum-space SFT.

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Book Synopsis​This book covers applications of R to the general discipline of radiation dosimetry and to the specific areas of luminescence dosimetry, luminescence dating, and radiation protection dosimetry. It features more than 90 detailed worked examples of R code fully integrated into the text, with extensive annotations. The book shows how researchers can use available R packages to analyze their experimental data, and how to extract the various parameters describing mathematically the luminescence signals. In each chapter, the theory behind the subject is summarized, and references are given from the literature, so that researchers can look up the details of the theory and the relevant experiments. Several chapters are dedicated to Monte Carlo methods, which are used to simulate the luminescence processes during the irradiation, heating, and optical stimulation of solids, for a wide variety of materials. This book will be useful to those who use the tools of luminescence dosimetry, including physicists, geologists, archaeologists, and for all researchers who use radiation in their research.Table of Contents1. Introduction.- 2. Analysis and Modeling of TL Data.- 3. Analysis of Experimental OSL Data.- 4. Dose Response of Dosimetric Materials.- 5. Monte Carlo Simulations With Fixed Time Interval.- 6. Luminescence as a Stochastic Life-and-Death Process.- 7. Delocalized Transitions: The R Package RLumCarlo.- 8. Localized Transitions: The R Package RLumCarlo.- 9. Quantum Tunneling and Luminescence Models.- 10. Quantum Tunneling: The R Package RLumCarlo.- 11. Comprehensive Quartz Models Using Program KMS.- 12. Quartz Models Using the R-Package RLumModel.

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Book SynopsisThis book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell model to the domain of weakly-bound near-threshold states and resonances, offering a systematic tool to understand and categorize data on nuclear spectra, moments, collective excitations, particle and electromagnetic decays, clustering, elastic and inelastic scattering cross sections, and radiative capture cross sections of interest to astrophysics. The approach is of interest beyond nuclear physics and based on general properties of quasi-stationary solutions of the Schrödinger equation – so-called Gamow states. For the benefit of graduate students and newcomers to the field, the quantum-mechanical fundamentals are introduced in some detail. The text also provides a historical overview of how the field has evolved from the early days of the nuclear shell model to recent experimental developments, in both nuclear physics and related fields, supporting the unified description. The text contains many worked examples and several numerical codes are introduced to allow the reader to test different aspects of the continuum shell model discussed in the book.Table of ContentsIntroduction.- The Discrete Spectrum and the Continuum.- One- and Two-Particle Systems.- Shell Model in Berggren Basis.- No-Core Gamow Shell Model.- Unification of Nuclear Structure and Nuclear Reactions.- Collective Phenomena.- Conclusions and Open Problems.

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Book SynopsisThis book provides a solid foundation in the Python programming language, numerical methods, and data analysis, all embedded within the context of astronomy and astrophysics. It not only enables students to learn programming with the aid of examples from these fields but also provides ample motivation for engagement in independent research. The book opens by outlining the importance of computational methods and programming algorithms in contemporary astronomical and astrophysical research, showing why programming in Python is a good choice for beginners. The performance of basic calculations with Python is then explained with reference to, for example, Kepler’s laws of planetary motion and gravitational and tidal forces. Here, essential background knowledge is provided as necessary. Subsequent chapters are designed to teach the reader to define and use important functions in Python and to utilize numerical methods to solve differential equations and landmark dynamical problems in astrophysics. Finally, the analysis of astronomical data is discussed, with various hands-on examples as well as guidance on astronomical image analysis and applications of artificial neural networks.Table of ContentsChapter 1. Introduction.- Chapter 2. Getting Started with Python.- Chapter 3. Computing and Displaying Data.- Chapter 4. Functions and Numerical Methods.- Chapter 5. Solving Differential Equations.- Chapter 6. Astronomical Data Analysis.

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Book SynopsisFor a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​Table of ContentsIntroduction (Aguirre, Merali, Sloan).- Undecidability and Unpredictability: Not Limitations, but Triumphs of Science (Markus Müller).- Indeterminism and Undecidability (Klaas Landsman).- Unpredictability and Randomness (Rade Vuckovac).- Indeterminism, Causality and Information: Has Physics ever been Deterministic? (Flavio Del Santo).- Undecidability, Fractal Geometry and the Unity of Physics (Tim Palmer).- A Gödelian Hunch from Quantum Theory (Hippolyte Dourdent).- Epistemic Horizons: This Sentence is ..... (Jochen Szangolies).- Why is the Universe Comprehensible? (Ian Durham).- Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes (David Wolpert, David Kinney).- Computational Complexity as Anthropic Principle: A Fable (Rick Searle).- Appendix (Aguirre, Merali, Sloan).

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Book SynopsisFor a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.​Table of ContentsIntroduction (Aguirre, Merali, Sloan).- Undecidability and Unpredictability: Not Limitations, but Triumphs of Science (Markus Müller).- Indeterminism and Undecidability (Klaas Landsman).- Unpredictability and Randomness (Rade Vuckovac).- Indeterminism, Causality and Information: Has Physics ever been Deterministic? (Flavio Del Santo).- Undecidability, Fractal Geometry and the Unity of Physics (Tim Palmer).- A Gödelian Hunch from Quantum Theory (Hippolyte Dourdent).- Epistemic Horizons: This Sentence is ..... (Jochen Szangolies).- Why is the Universe Comprehensible? (Ian Durham).- Noisy Deductive Reasoning: How Humans Construct Math, and How Math Constructs Universes (David Wolpert, David Kinney).- Computational Complexity as Anthropic Principle: A Fable (Rick Searle).- Appendix (Aguirre, Merali, Sloan).

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Book SynopsisThis book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.Trade Review“Each topic is discussed in a brief chapter, at a technical level that could be followed by first-year students of physics and mathematics, but also by wider parts of the public. Each chapter contains a statement of the topic, a brief history, and describes a number of examples … . The book makes a pleasant reading, full of wit and of surprising turns. I think that it can be useful to the general reader … motivate students … .” (Luca Peliti, Journal of Statistical Physics, Vol. 185, 2021)Table of ContentsChapter 1 - Introduction.- Chapter 2 - Atoms, Irreversibility, Probability, Statistical Mechanics, Entropy.- Chapter 3 - Probability, Entropy, Chaos.- Chapter 4 - Chaos, Prediction.- Chapter 5 - Prediction, Turbulence, Models.- Chapter 6 - Models, Richardson.- Chapter 7 - Boltzmann, Statistical Mechanics, Brownian Motion.- Chapter 8 - Boltzmann, Atoms, Statistical Mechanics, Mesoscale Systems.- Chapter 9 - Prediction: Chaos, Poincaré, Richardson, Models, Big data.- Chapter 10 - Statistical Mechanics: Atoms, Boltzmann, Maxwell.

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Book SynopsisThis textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.Trade Review“This text approaches the reader with shocking breadth and niggardly depth. … Around each definition, there is short---and pleasant---narrative and then a number of examples are described. Chapters end with a list of straightforward exercises … . As a stand-alone mathematical dictionary, the text under review may serve a purpose … .” (Ryan Grady, MAA Reviews, January 30, 2022)Table of ContentsPreface and Acknowledgements.- Sets and Relations.- Mappings and Functions.- Rings and Fields.- Linear Vector Spaces.- Algebras.- Basic Topology and Topological Groups.- Topological Vector Spaces.- Measure, Integration and Hilbert Space.- Operators and Spectra.- Annotated Bibliography and a Guide to Further Reading.- Index.

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Book SynopsisThis book introduces the phenomenology of gravitational lensing in an accessible manner and provides a thorough discussion of the related astrophysical applications. It is intended for advanced undergraduates and graduate students who want to start working in this rapidly evolving field. This includes also senior researchers who are interested in ongoing or future surveys and missions such as DES, Euclid, WFIRST, LSST. The reader is guided through many fascinating topics related to gravitational lensing like the structure of our galaxy, the searching for exoplanets, the investigation of dark matter in galaxies and galaxy clusters, and several aspects of cosmology, including dark energy and the cosmic microwave background. The author, who has gained valuable experience as academic teacher, guides the readers towards the comprehension of the theory of gravitational lensing and related observational techniques by using simple codes written in python. This approach, beyond facilitating the understanding of gravitational lensing, is preparatory for learning the python programming language which is gaining large popularity both in academia and in the private sector.Table of ContentsPART I: Generalities1. Light deflection1.1. Deflection of a light corpuscle1.2. Deflection of light according to General Relativity1.3. Deflection by an ensable of point masses1.4. Deflection by an extended mass distribution1.5. Light propagation through an inhomogeneous universe1.6. Python examples2. The general lens2.1. Lens equation2.2. Lensing potential2.3. First order lens mapping2.4 Magnification2.5 Lensing to the second order2.6 Time delay surface2.7 Python examplesPART II: Applications of gravitational lensing1. Microlensing1.1 The point mass lens1.2 Standard microlensing light curve1.3 Microlensing parallax1.4 Optical depth and event rate1.5 Astrometric microlensing1.6 Multiple point lenses1.7 Planetary microlensing1.8 Python examples2. Strong lensing by galaxies and galaxy clusters2.1 Axially symmetric lenses2.2 Power-law lens2.3 Softened lenses2.4 Elliptical lenses2.5 Substructures2.6 External shear2.7 Parametric lens modeling2.8 Non-parametric lens modeling2.9 Searches for strong lenses2.10 Cosmic telescopes2.11 Strong lensing cosmography2.12 Time-delay cosmology2.13 Python examples3. Weak lensing by virialized structures3.1 Shear measurements3.2 Tangential and cross component of the shear3.3 Lens mass measurements3.4 Two-dimensional mass mapping3.5 Mass-sheet degeneracy3.6 Python examples4. Weak lensing by the large-scale-structure4.1 Effective convergence4.2 Limber’s equation4.3 Shear correlation functions4.4 Shear in apertures and aperture mass4.5 E- and B-modes4.6 Python examples5. Lensing of the Cosmic Microwave Background5.1 Lensing of the CMB temperature5.2 Gravitational lensing of the CMB polarization5.3 Recovery of the gravitational potential5.4 Python examples

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Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.

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Book SynopsisThis book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory, relativistic chaotic dynamics, data analysis, relativistic chaotic dynamics, solvability issues in integro-differential equations, and inverse problems for parabolic differential equations, synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems Table of Contents1. Preface by Dr. Dimitri Volchenkov2. Chapter 1 . J. A. Tenreiro Machado, Shannon Information Analysis of the Chromosome Code.3. Chapter 2. Dimitri Volchenkov, Veniamin Smirnov, An Unfair Coin of the Standard & Poor’s 5004. Chapter 3. Relativistic chaotic scattering by Juan D. Bernal, Jesus M. Seoane, Miguel A.F. Sanjuan5. Chapter 4. Artificial Intelligence for Studying Perception of Ambiguous Images and Decision-Marking Processes in the Human Brain by Alexander N. Pisarchik, Anastasija E. Runnova, Nikita S. Frolov, and Alexander E. Hramov6. Chapter 5. Fuhong Min, Chuang Li, Multistability Coexistence of Memristive Chaotic System, and the Application in Image Decryption7. Chapter 6: Veniamin Smirnov, Zhuanzhuan Ma, And Dimitri Volchenkov, Extreme Events and Emergency Scales 8. Chapter 7: M. Edelman, Evolution of Systems with Power-Law Memory: Do We Have to Die?9. Chapter 8: Dimitri Volchenkov, Probability Entanglement and Destructive Interference in Biased Coin Tossing10. Chapter 9: Messoud Efendiev, Vitali Vougalter, On the solvability of some systems of integro-differential equations with drift.11. Chapter 10: Vitali Vougalter, Vitaly Volpert, Solvability in The Sense of Sequences For Some Non Fredholm Operators With The Bi-Laplacian 12. Chapter 11: Vitali Vougalter, The Preservation of Nonnegativity of Solutions of A Parabolic System With The Bi-Laplacian

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Book SynopsisThis book introduces the traditional and novel techniques required to study the thermodynamic and transport properties of quark–gluon plasma. In particular, it reviews the construction of improved holographic models for QCD-like confining gauge theories and their applications in the physics of quark–gluon plasma. It also discusses the recent advances in the development of hydrodynamic techniques, especially those incorporating the effects of external magnetic fields on transport. The book is primarily intended for researchers and graduate students with a background in quantum field theory and particle physics but who may not be familiar with the theory of strong interactions and holographic and hydrodynamic techniques required to study said interactions.Table of ContentsIntroduction: AdS/CFT and heavy ion collisions.- Holographic QCD theories.- Improved holographic QCD - construction of the theory.- Thermodynamics and the confinement/deconfinement transition.- Flavor sector.- Hydrodynamics and transport coefficients.- Hard probes.- ihQCD at finite B.- Conclusion and a look ahead.

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Book SynopsisThis book is intended to serve as a basic introduction to scientific computing by treating problems from various areas of physics - mechanics, optics, acoustics, and statistical reasoning in the context of the evaluation of measurements. After working through these examples, students are able to independently work on physical problems that they encounter during their studies. For every exercise, the author introduces the physical problem together with a data structure that serves as an interface to programming in Excel and Python. When a solution is achieved in one application, it can easily be translated into the other one and presumably any other platform for scientific computing. This is possible because the basic techniques of vector and matrix calculation and array broadcasting are also achieved with spreadsheet techniques, and logical queries and for-loops operate on spreadsheets from simple Visual Basic macros. So, starting to learn scientific calculation with Excel, e.g., at High School, is a targeted road to scientific computing. The primary target groups of this book are students with a major or minor subject in physics, who have interest in computational techniques and at the same time want to deepen their knowledge of physics. Math, physics and computer science teachers and Teacher Education students will also find a companion in this book to help them integrate computer techniques into their lessons. Even professional physicists who want to venture into Scientific Computing may appreciate this book.Table of Contents

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Book SynopsisThe volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.Table of Contents- Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods. - Quantum Drift-Diffusion Equations for a Two-Dimensional Electron Gas with Spin-Orbit Interaction. - A Kinetic BGK Relaxation Model for a Reacting Mixture of Polyatomic Gases. - On Some Recent Progress in the Vlasov–Poisson–Boltzmann System with Diffuse Reflection Boundary. - The Vlasov Equation with Infinite Mass. - Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture: Extension to Non-spherical Dust Particles. - Body-Attitude Alignment: First Order Phase Transition, Link with Rodlike Polymers Through Quaternions, and Stability. - The Half-Space Problem for the Boltzmann Equation with Phase Transition at the Boundary. - Recent Developments on Quasineutral Limits for Vlasov-Type Equations. - A Note on Acoustic Limit for the Boltzmann Equation. - Thermal Boundaries in Kinetic and Hydrodynamic Limits. - Control of Collective Dynamics with Time-Varying Weights. - Kinetic Modelling of Autoimmune Diseases. - A Generalized Slip-Flow Theory for a Slightly Rarefied Gas Flow Induced by Discontinuous Wall Temperature. - A Revisit to the Cercignani–Lampis Model: Langevin Picture and Its Numerical Simulation. - On the Accuracy of Gyrokinetic Equations in Fusion Applications.

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Book SynopsisThis book is comprised of the latest research into CSS methods, uses, and results, as presented at the 2020 annual conference of the Computational Social Science Society of the Americas (CSSSA). Computational social science (CSS) is the science that investigates social and behavioral dynamics through social simulation, social network analysis, and social media analysis. The CSSSA is a professional society that aims to advance the field of computational social science in all areas, including basic and applied orientations, by holding conferences and workshops, promoting standards of scientific excellence in research and teaching, and publishing research findings and results. The above-mentioned conference was held virtually, October 8 – 11, 2020. What follows is a diverse representation of new results and approaches to using the tools of CSS and agent-based modeling (ABM) in exploring complex phenomena across many different domains. Readers will therefore not only have the results of these specific projects upon which to build, along with a wealth of case-study examples that can serve as meaningful exemplars for new research projects and activities, they will also gain a greater appreciation for the broad scope of CSS.Table of ContentsDale Brearcliffe and Andrew Crooks: Creating Intelligent Agents: Combining Agent-Based Modeling with Machine LearningClaudius Gros: Envy splits societies into a lower and a upper classMarie Alaghband and Ivan Garibay: Effects of Non-Cognitive Factors on Post-Secondary Persistence of Deaf Students: An Agent-Based Modeling ApproachAndrew Collins: Comparing Agent-Based Modeling to Cooperative Game Theory and Human BehaviorPeter Chew and Jonathan Chew: Analyzing transnational narratives in Twitter: an unsupervised approach using PARAFACSantiago Núñez-Corrales, Milton Friesen, Srikanth Mudigonda, Rajesh Venkatachalapathy and Jeffrey Graham: In-Silico models with greater fidelity to social processes: towards ABM platforms with realistic concurrencySaeed Langarudi, Carlos Silva and Sam Fernald: Dynamics of Information Perception in Management of CommonsH. Van Dyke Parunak: Psychology from StigmergyEce Mutlu, Ivan Garibay and Amirarsalan Rajabi: CD-SEIZ: Cognition-Driven SEIZ Compartmental Model for the Prediction of Information Cascades on TwitterJiin Jung, Aaron Bramson, William Crano, Scott Page and John Miller: Cultural Drift, Indirect Minority Influence, Network Structure and Their Impacts on Cultural Change and DiversityLeticia Izquiero, Gamaliel Palomo, Arnaud Grignard, Luis Alonso, Mario Siller and Kent Larson: An agent-based model to evaluate the perception of safety in informal settlementsWilliam Leibzon: Study of Altruism as a Behavioral Trait in Game Theory Network Dynamics with Prisoner Dilemma GamesMatthew Koehler, David Slater, Garry Jacyna and James Thompson: Analyzing the potential impact of nonpharmaceutical interventions on the spread of COVID-19 (COVID-19 work in progress)Shigeaki Ogibayashi: An Agent-Based Model of Infectious Diseases that Incorporates the Role of Immune Cells and AntibodiesNicholas Willems, Cale Reeves, Vivek Shastry and Varun Rai: Heterogeneity in populations and behaviors: An agent-based model of the social spread of COVID-19 Vivek Shastry, Cale Reeves, Nicholas Willems and Varun Rai: Work In Progress: COVID-19 Policy Evaluation (CoPE) Tool: An agent-based model for ex-ante evaluation of policy designs and behavioral responses to COVID-19Amirarsalan Rajabi, Alexander Mantzaris, Ece Mutlu and Ivan Garibay: Investigating dynamics of COVID-19 spread and containment with agent-based modelingYoungsun Hwang, Joseph Immormino and Glenn-Iain Steinback: Purchasing Power to the People: An Agent-Based Simulation of Pandemic Economic RecoveryJacob Kelter, Andreas Bugler and Uri Wilensky: Agent-based models of Quadratic VotingBrian Tivnan, Carl Burke, Matthew Koehler, Matthew Mcmahon And Jason Veneman: Towards a model of the national market system: fragmented and heterogenous venuesHanin Alhaddad, Nisha Baral and Ivan Garibay: Online Rejection Influence on Behavior Deviancy and Radicalization: An Agent-Based Model ApproachNarjes Sadeghiamirshahidi, Anuj Mittal and Caroline Krejci: An agent-based model of digitally-mediated farmer transportation collaborationGraham Sack: Geometries of Desire: Simulating Rene Girard’s Mimetic TheoryMehdi Moghadam Manesh, Saeed Langarudi and Birgit Kopainsky: Can Institutionalization Prevent the Depletion of Groundwater Resources?

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Book SynopsisThis book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications.The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.Table of ContentsAlbeverio, S., De Vecchi, F.C.: Some recent developments on Lie Symmetry analysis of stochastic differential equations.- Applebaum, D., Ming, L.: Markov processes with jumps on manifolds and Lie groups.- Cordoni, F., Di Persio, L.: Asymptotic expansion for a Black-Scholes model with small noise stochastic jump diffusion interest rate.- Cruzeiro, A.B., Zambrini, J.C.: Stochastic geodesics.- DeVecchi, F.C., Gubinelli, M.: A note on supersymmetry and stochastic differential equations.- Ebrahimi-Fard, K, Patras, F.: Quasi shuffle algebras in non-commutative stochastic calculus.- Elworthy, K.D.: Higher order derivatives of heat semigroups on spheres and Riemannian symmetric spaces.- Gehringer, J., Li, X.M.: Rough homogenisation with fractional dynamics.- Holm, D.D., Luesink, E.: Stochastic geometric mechanics with diffeomorphisms.- Izydorczyk, L., Oudjane, N., Russo, F.: McKean Feynman-Kac probabilistic representations of non linear partial differential equations.- Lescot, P., Valade, L.: Bernestein processes, isovectors and machanics.- Marinelli, C., Scarpa, L.: On the positivity of local mild solutions to stochastic evolution equations.- Privault, N.: Invariance of Poisson point processes by moment identities with statistical applications.

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Book SynopsisMany people, including physicists, are confused about what the Second Law of thermodynamics really means, about how it relates to the arrow of time, and about whether it can be derived from classical mechanics. They also wonder what entropy really is: Is it all about information? But, if so, then, what is its relation to fluxes of heat?One might ask similar questions about probabilities: Do they express subjective judgments by us, humans, or do they reflect facts about the world, i.e. frequencies. And what notion of probability is used in the natural sciences, in particular statistical mechanics?This book addresses all of these questions in the clear and pedagogical style for which the author is known. Although valuable as accompaniment to an undergraduate course on statistical mechanics or thermodynamics, it is not a standard course book. Instead it addresses both the essentials and the many subtle questions that are usually brushed under the carpet in such courses. As one of the most lucid accounts of the above questions, it provides enlightening reading for all those seeking answers, including students, lecturers, researchers and philosophers of science.Table of ContentsWhat We Need from Thermodynamics.- What Are Probabilities?.- Dynamical Systems.- Statistical Mechanics 1 : The Nature of Equilibrium.- Statistical Mechanics 2: Irreversibility.- Demystifying Entropy.- Comparison with Quantum Mechanics.

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Book SynopsisThis book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing.Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.Table of Contents1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities:Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . . . . . . . . . 704.4.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 704.4.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.5 Matrix Representation of Permutations of Three Objects 734.5 Pythagoras and Geometry . . . . . . . . . . . . . . . . . . . . 745 Special Relativity I: The Basics 775.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.1 Frames5.2.2 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . 785.2.3 Newtonian Relativity and Galilean Transformations . . 835.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 The Fundamental Postulate . . . . . . . . . . . . . . . 855.3.2 The problem with Galilean Relativity . . . . . . . . . . 855.3.3 Michelson-Morley Experiment . . . . . . . . . . . . . . 875.3.4 Maxwell's Equations . . . . . . . . . . . . . . . . . . . 905.4 Summary of Consequences . . . . . . . . . . . . . . . . . . . . 915.5 Relativity of Simultaneity . . . . . . . . . . . . . . . . . . . . 925.6 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.6.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . 975.6.2 Proper Time . . . . . . . . . . . . . . . . . . . . . . . . 995.6.3 Experimental Conrmation . . . . . . . . . . . . . . . 1015.6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 1025.7 Lorentz Contraction . . . . . . . . . . . . . . . . . . . . . . . 1045.7.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.3 Proper Length and Proper Distance. . . . . . . . . . . 1045.7.4 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 1056 Special Relativity II: In Depth 1106.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . 1106.2.1 Derivation of general form . . . . . . . . . . . . . . . . 1106.2.2 Properties of Lorentz Transformations . . . . . . . . . 1136.2.3 Lorentzian Geometry . . . . . . . . . . . . . . . . . . . 1166.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.4 Proper time revisited . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Relativistic Addition of Velocities . . . . . . . . . . . . . . . . 1226.6 Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . 1246.6.1 Non-relativistic Doppler Shift Review . . . . . . . . . . 1246.6.2 Relativistic Doppler Shift . . . . . . . . . . . . . . . . 1246.7 Relativistic Energy and Momentum . . . . . . . . . . . . . . . 1276.7.1 Relativistic Energy Momentum Conservation . . . . . . 1276.7.2 Relativistic Inertia . . . . . . . . . . . . . . . . . . . . 1286.7.3 Relativistic Energy . . . . . . . . . . . . . . . . . . . . 1296.7.4 Relativistic Three-Momentum . . . . . . . . . . . . . . 1296.7.5 Relationship Between Relativistic Energy and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.7.6 Kinetic energy: . . . . . . . . . . . . . . . . . . . . . . 1306.7.7 Massless particles . . . . . . . . . . . . . . . . . . . . 1316.8 Space-time Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1336.8.1 Position Four-Vector: . . . . . . . . . . . . . . . . . . . 1346.8.2 Four-momentum: . . . . . . . . . . . . . . . . . . . . . 1356.8.3 Null four-vectors . . . . . . . . . . . . . . . . . . . . . 1376.8.4 Relativistic Scattering . . . . . . . . . . . . . . . . . . 1376.8.5 More Examples . . . . . . . . . . . . . . . . . . . . . . 1386.9 Relativistic Units . . . . . . . . . . . . . . . . . . . . . . . . . 1396.10 Symmetry Redux . . . . . . . . . . . . . . . . . . . . . . . . . 1406.10.1 Matrix form of Lorentz Transformations . . . . . . . . 1406.10.2 Lorentz Transformations as a Symmetry Group . . . . 1426.11 Supplementary: Four vectors and tensors in covariant form . . 1437 General Relativity 1497.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Problems with Newtonian Gravity . . . . . . . . . . . . . . . . 1497.2.1 Review of Newtonian Gravity . . . . . . . . . . . . . . 1497.2.2 Perihelion Shift of Mercury . . . . . . . . . . . . . . . 1517.2.3 Action at a Distance . . . . . . . . . . . . . . . . . . . 1527.2.4 The Puzzle of Inertial vs Gravitational Mass . . . . . . 1537.3 Einstein's Thinking: the Strong Principle of Equivalence . . . 1537.4 Geometry of Spacetime . . . . . . . . . . . . . . . . . . . . . . 1557.5 Some Consequences of General Relativity: . . . . . . . . . . . 1587.6 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . 1597.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1597.6.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . 1607.6.3 Recent Observations . . . . . . . . . . . . . . . . . . . 1617.7 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1647.7.4 Further Information . . . . . . . . . . . . . . . . . . . 1667.8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668 Introduction to the Quantum 1708.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1708.2 Light as particles . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2.1 Review: Light as Waves . . . . . . . . . . . . . . . . . 1718.2.2 Photoelectric Eect . . . . . . . . . . . . . . . . . . . . 1718.2.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 1758.3 Blackbody Radiation and the Ultraviolet Catastrophe . . . . . 1798.3.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 1798.3.2 Derivation of Rayleigh-Jeans Law . . . . . . . . . . . . 1818.3.3 The ultraviolet catastrophe . . . . . . . . . . . . . . . 1888.3.4 Quantum resolution: . . . . . . . . . . . . . . . . . . . 1898.3.5 The Early Universe: the ultimate blackbody . . . . . . 1918.4 Particles as waves . . . . . . . . . . . . . . . . . . . . . . . . . 1968.4.1 Electron waves . . . . . . . . . . . . . . . . . . . . . . 1968.4.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . 1978.4.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1998.5 The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . 2029 The Wave Function 2049.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Quantum vs Newtonian description of physical states . . . . . 2049.2.1 Newtonian description of the state of a particle . . . . 2059.2.2 Quantum description of the state of a particle . . . . . 2059.3 Physical Consequences and Interpretation . . . . . . . . . . . 2079.4 Measurements of position . . . . . . . . . . . . . . . . . . . . 2089.5 Example: Gaussian wavefunction . . . . . . . . . . . . . . . . 2099.6 \Spooky" Action at a Distance: Non-Locality in QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6.1 The EPR \Paradox" . . . . . . . . . . . . . . . . . . . 2119.6.2 Bell's Theorem and the Experimental Repudiation ofEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410 The Schrodinger Equation 21710.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Momentum in Quantum Mechanics . . . . . . . . . . . . . . . 21810.2.1 Pure Waves . . . . . . . . . . . . . . . . . . . . . . . . 21810.2.2 The Momentum Operator . . . . . . . . . . . . . . . . 22010.3 Energy in Quantum Mechanics . . . . . . . . . . . . . . . . . 22310.4 The Time Independent Schrodinger Equation . . . . . . . . . 22410.4.1 Stationary States . . . . . . . . . . . . . . . . . . . . . 22410.4.2 The \Quantum" in Quantum Mechanics . . . . . . . . 22610.5 Examples of Stationary States . . . . . . . . . . . . . . . . . . 22610.5.1 Free particle in one dimension . . . . . . . . . . . . . . 22610.5.2 Example 2: Particle in a Box with Impenetrable Walls 22710.5.3 Example 3 : Simple Harmonic Oscillator . . . . . . . . 22910.6 Absorption and emission . . . . . . . . . . . . . . . . . . . . . 23110.7 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 Tunnelling through a potential barrier of nite width . 23310.7.2 Particle in a Box with Penetrable Walls . . . . . . . . . 23510.7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 23710.7.4 Applications of tunnelling . . . . . . . . . . . . . . . . 23810.8 The Quantum Correspondence Principle . . . . . . . . . . . . 24210.8.1 Recovering the everyday world . . . . . . . . . . . . . . 24210.8.2 The Bohr Correspondence Principle . . . . . . . . . . . 24310.9 The Time Dependent Schrodinger equation . . . . . . . . . . . 24410.9.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 24611 The Hydrogen Atom 24911.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 24911.2 Newtonian (Classical) Dynamics . . . . . . . . . . . . . . . . . 24911.3 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 25111.4 Semi-classical spectrum from the Bohr correspondence principle25411.5 Emission and Absorption Spectra . . . . . . . . . . . . . . . . 25411.6 Three Dimensional Hydrogen Atom . . . . . . . . . . . . . . . 25611.6.1 Schrodinger Equation . . . . . . . . . . . . . . . . . . . 25611.6.2 Solutions and Quantum Numbers . . . . . . . . . . . . 25811.6.3 Fermions and the spin quantum number . . . . . . . . 26211.7 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 26511.7.1 Hydrogen-like atoms . . . . . . . . . . . . . . . . . . . 26511.7.2 Chemical Properties and the Periodic Table . . . . . . 26612 Nuclear Physics 27012.1 Properties of the Nucleus . . . . . . . . . . . . . . . . . . . . . 27012.1.1 Mass of Nucleons . . . . . . . . . . . . . . . . . . . . . 27012.1.2 Structure of Nucleus . . . . . . . . . . . . . . . . . . . 27112.1.3 The Nuclear Force . . . . . . . . . . . . . . . . . . . . 27112.2 Binding Energy and Stability . . . . . . . . . . . . . . . . . . 27412.2.1 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 27412.2.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . 27512.2.3 Binding Energy per Nucleon . . . . . . . . . . . . . . . 27512.3 Formation of Elements: A Brief History of the Universe . . . . 27612.4 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27912.4.1 Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . 27912.4.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 28112.4.3 Beta decay . . . . . . . . . . . . . . . . . . . . . . . . . 28212.4.4 Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . 28312.4.5 Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . 28312.4.6 Carbon Dating . . . . . . . . . . . . . . . . . . . . . . 28513 Supplementary: Advanced Topics 28713.1 Quantum Information and Quantum Computation . . . . . . . 28713.2 Relativity and quantum mechanics . . . . . . . . . . . . . . . 28714 Conclusions 28815 Appendix: Mathematical Background 28915.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 Probabilities and expectation values . . . . . . . . . . . . . . . 29115.2.1 Discrete Distributions . . . . . . . . . . . . . . . . . . 29115.2.2 Continuous probability distributions . . . . . . . . . . 29215.2.3 Dirac Delta Function . . . . . . . . . . . . . . . . . . . 29615.3 Supplementary: Fourier Series and Transforms . . . . . . . . . 29815.3.1 Fourier series . . . . . . . . . . . . . . . . . . . . . . . 29815.3.2 Fourier Transforms . . . . . . . . . . . . . . . . . . . . 30015.3.3 The mathematical uncertainty principle . . . . . . . . . 30215.3.4 Dirac Delta Function Revisited . . . . . . . . . . . . . 30315.3.5 Parseval's Theorem . . . . . . . . . . . . . . . . . . . . 30315.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30415.4.1 Moving pure waves . . . . . . . . . . . . . . . . . . . . 30415.4.2 Complex Waves . . . . . . . . . . . . . . . . . . . . . . 30515.4.3 Group velocity and phase velocity . . . . . . . . . . . 30515.4.4 Wave packets . . . . . . . . . . . . . . . . . . . . . . . 30715.4.5 Wave number and momentum . . . . . . . . . . . . . . 30915.5 Derivation of Hydrogen Wave Functions . . . . . . . . . . . . 312

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Book SynopsisThis book covers the latest advances in applying agent-based modelling in social sciences. The Social Simulation Conference is the major global conference devoted to this topic. It is aimed at promoting social simulation and computational social science. This year’s special theme is “Social Simulation geared towards Post-Pandemic times”, focused not only on questions raised by the current pandemic but also on future challenges related to economic recovery, such as localization, globalization, inequality, sustainable growth and social changes induced by progressive digitalization, data availability and artificial intelligence. The primary audience of this book are scholars and practitioners in computational social sciences including economics, business, sociology, politics, psychology and urban studies.Table of ContentsThis year’s special theme will be “Social Simulation geared towards Post-Pandemic times”, focused not only on questions raised by the current pandemic but also on future challenges related to economic recovery, such as localisation, globalization, inequality, sustainable growth and social changes induced by progressive digitalisation, data availability and artificial intelligence.

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Book SynopsisThis book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.Table of Contents. - Introduction. - Preliminaries. - Formal Difference Modules and Good Parabolic Structure. - Filtered Bundles. - Basic Examples of Monopoles Around Infinity. - Asymptotic Behaviour of Periodic Monopoles Around Infinity. - The Filtered Bundles Associated with Periodic Monopoles. - Global Periodic Monopoles of Rank One. - Global Periodic Monopoles and Filtered Difference Modules. - Asymptotic Harmonic Bundles and Asymptotic Doubly Periodic Instantons (Appendix).

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Book SynopsisThis book compiles and presents a complete package of open-access Python software code for luminescence signal analysis in the areas of radiation dosimetry, luminescence dosimetry, and luminescence dating. Featuring more than 90 detailed worked examples of Python code, fully integrated into the text, 16 chapters summarize the theory and equations behind the subject matter, while presenting the practical Python codes used to analyze experimental data and extract the various parameters that mathematically describe the luminescence signals. Several examples are provided of how researchers can use and modify the available codes for different practical situations. Types of luminescence signals analyzed in the book are thermoluminescence (TL), isothermal luminescence (ITL), optically stimulated luminescence (OSL), infrared stimulated luminescence (IRSL), timeresolved luminescence (TR) and dose response of dosimetric materials. The open-access Python codes are available at GitHub.The book is well suited to the broader scientific audience using the tools of luminescence dosimetry: physicists, geologists, archaeologists, solid-state physicists, medical physicists, and all scientists using luminescence dosimetry in their research. The detailed code provided allows both students and researchers to be trained quickly and efficiently on the practical aspects of their work, while also providing an overview of the theory behind the analytical equations.Table of ContentsTL Signals from Delocalized Transitions: Models.- Analysis of TL Signals from Delocalized Transitions.- TL from Quantum Tunneling Processes: Models.- Analysis of TL from Quantum Tunneling Processes.- Isothermal Luminescene (ITL) Signals: Models and Analysis.- TL Signals from Localized Transitions: Models and Analysis.- OSL from Delocalized Transitions: Models.- Analysis of OSL from Delocalized Transitions.- Infrared Stimulated Luminescene Signals: Models.- Analysis of IRSL Signals.- Time-Resolved Luminescene: Models.- Analysis of Time-Resolved Luminescene Signals L.- Dose Response of Dosimetric Materials: Models.- Analysis of Dose Response of Luminescene Signals.- Radiofluorescene Signals: Models and Analysis.- Radiophotoluminescene Signals: Models and Analysis

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Book SynopsisDynamical systems and the twin field ergodic theory have their roots in the qualitative theory of differential equations, developed by the great mathematician Henri Poincaré, and in the kinetic theory of gases built in mathematical terms by physicists James Clerk Maxwell and Ludwig Boltzmann. Together, they aim to model, explain and predict the behavior of natural and artificial phenomena which evolve in time. For more than three decades, Marcelo Viana has been making several outstanding contributions to this area of mathematics. This volume contains a selection of his research papers, covering a wide range of topics: rigorous theory of strange attractors, physical measures, bifurcation theory, homoclinic phenomena, fractal dimensions, partial hyperbolicity, thermodynamic formalism, non-uniform hyperbolicity, interval exchange maps Teichmüller flows, and the modern theory of Lyapunov exponents. Marcelo Viana, a world leader in this field, has been the object of several academic distinctions, such as the inaugural Ramanujan prize of the International Centre for Theoretical Physics, and the Louis D. Scientific Grand Prix of the Institut de France. He is also recognized for his broad contribution to the mathematical community, in his country and region as well as in the international arena.Table of ContentsModuli of continuity for the Lyapunov exponents of random GL(2)-cocycles: El Hadji Yaya Tall and Marcelo Viana.- Continuity of Lyapunov exponents in the C 0 topology: Marcelo Viana and Jiagang Yang.- Continuity of Lyapunov exponents for random two-dimensional matrices: Carlos Bocker-Neto and Marcelo Viana.- Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows: Artur Avila, Marcelo Viana and Amie Wilkinson.- Holonomy invariance: rough regularity and applications to Lyapunov exponents: Artur Avila, Jimmy Santamaria and Marcelo Viana.- Extremal Lyapunov exponents: an invariance principle and applications: Artur Avila and Marcelo Viana.- Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents: Marcelo Viana.- Simplicity of Lyapunov spectra: proof of the Zorich–Kontsevich conjecture: Artur Avila and Marcelo Viana.- The Lyapunov exponents of generic volume-preserving and symplectic maps: Jairo Bochi and Marcelo Viana.- xv Contents Généricité d’exposants de Lyapunov non-nuls pour des produits déterministes de matrices [Genericity of non-zero Lyapunov exponents for deterministic products of matrices]: Christian Bonatti, Xavier Gómez-Mont and Marcelo Viana.- Solution of the basin problem for Hénon-like attractors: Michael Benedicks and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly contracting: Christian Bonatti and Marcelo Viana.- SRB measures for partially hyperbolic systems whose central direction is mostly expanding: José F. Alves, Christian Bonatti and Marcelo Viana.- Multidimensional nonhyperbolic attractors: Marcelo Viana.- Strange attractors in saddle-node cycles: prevalence and globality: L.J. Diaz, J. Rocha and M. Viana.- High dimension diffeomorphisms displaying infinitely many periodic attractors: J. Palis and M. Viana.- Abundance of strange attractors: Leonardo Mora and Marcelo Viana.- List of Publications of Marcelo Viana.- List of Ph.D. Students of Marcelo Viana at IMPA.- Credits.

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