Mathematical / Computational / Theoretical physics Books
MP-AMM American Mathematical Continuous Symmetries and Integrability of
Book SynopsisFocuses on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices.Table of Contents Introduction Integrability and symmetries of nonlinear differential and difference equations in two independent variables Symmetries as integrability criteria Construction of lattice equations and their Lax pair Transformation groups for quad lattice equations Algebraic entropy of the nonautonomous Boll equations Translation from Russian of R. I. Yamilov, ''On the classification of discrete eqautions'', reference [841] No quad-graph equation can have a generalized symmetry given by the narita-Itoh-Bogoyavlensky equation Bibliography Subject Index
£99.90
Springer Statistical and Nonlinear Physics
Book SynopsisThis volume of the Encyclopedia of Complexity and Systems Science, Second Edition, focuses on current challenges in the field from materials and mechanics to applications of statistical and nonlinear physics in the life sciences.Table of ContentsStatistical and Non-linear Physics: IntroductionComplex Systems and Emergent PhenomenaPolymer PhysicsChaotic Dynamics in Nonequilibrium Statistical MechanicsMonte Carlo Simulations in Statistical PhysicsNonlinear Fluid Flow, Pattern Formation, Mixing, and TurbulenceFluid Dynamics in CloudsCollective Transport and DepinningDisordered Elastic MediaPhysics of Jerky Motion in Slowly Driven Magnetic and Earthquake Fault SystemsFlexible mechanical structures and their topologically protected deformationsA Statistical Mechanics Perspective on Glasses and AgingStress Localization in Soft Particulate GelsNonlinear Mechanics of Colloidal Gels: Creep, Fatigue, and Shear-Induced YieldingStatistical physics of the yielding transitionGranular FlowsStatistical Mechanics of CloggingJamming of Granular MatterRigidity Percolation and Frictional JammingCell Biology: Networks , Regulation and PathwaysFluctuation Theorems, Brownian Motors and Thermodynamics of Small SystemsNeuronal DynamicsDense Active MatterUltracold Atomic Gases: Novel States of MatterQuantum ChaosNetworks: Structure and DynamicsCentralities in complex networksOptimization Problems and Algorithms from Computer ScienceStatistical Mechanics Approach to Econophysics
£306.69
Springer Solitons
Book SynopsisDifferent linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM).Table of ContentsNonlinear Water Waves and Nonlinear Evolution Equations with ApplicationsInverse Scattering Transform and the Theory of SolitonsKorteweg-de Vries Equation (KdV), Different Analytical Methods for Solving theKorteweg-de Vries Equation (KdV), History, Exact N-Soliton Solutions and Further Properties of theSemi-analytical Methods for Solving the KdV and mKdV EquationsKorteweg-de Vries Equation (KdV), Some Numerical Methods for Solving theNonlinear Internal WavesPartial Differential Equations that Lead to SolitonsShallow Water Waves and Solitary WavesSoliton PerturbationSolitons and CompactonsSolitons: Historical and Physical IntroductionSolitons InteractionsSolitons, Introduction toSolitons, Tsunamis and Oceanographical Applications ofWater Waves and the Korteweg-de Vries EquationSoliton Solutions for Some Nonlinear Water Wave Dynamical ModelsAnalytical Soliton Solutions for Some Nonlinear Dynamical Water Waves ModelsSoliton Propagation in Solids: Advances and ApplicationsApplications of lump and interaction soliton solutions to the model of liquid crystals and nerve fibersPeriodic cross-kink, rogue-waves, and lump interaction soliton solutions with kink and periodic waves for fractional Bogoyavlenskii equationDouble Tchebyshev spectral tau algorithm for solving KdV equation, with soliton application
£249.73
John Wiley & Sons Inc Quantum Information and Computation for Chemistry
Book SynopsisExamines the intersection of quantum information and chemical physics The Advances in Chemical Physics series is dedicated to reviewing new and emerging topics as well as the latest developments in traditional areas of study in the field of chemical physics. Each volume features detailed comprehensive analyses coupled with individual points of view that integrate the many disciplines of science that are needed for a full understanding of chemical physics. This volume of the series explores the latest research findings, applications, and new research paths from the quantum information science community. It examines topics in quantum computation and quantum information that are related to or intersect with key topics in chemical physics. The reviews address both what chemistry can contribute to quantum information and what quantum information can contribute to the study of chemical systems, surveying both theoretical and experimental quantum information research wTable of ContentsCONTRIBUTORS TO VOLUME 154 v FOREWORD ix PREFACE TO THE SERIES xiii INTRODUCTION TO QUANTUM INFORMATION AND COMPUTATION FOR CHEMISTRY 1 By Sabre Kais BACK TO THE FUTURE: A ROADMAP FOR QUANTUM SIMULATION FROM VINTAGE QUANTUM CHEMISTRY 39 By Peter J. Love INTRODUCTION TO QUANTUM ALGORITHMS FOR PHYSICS AND CHEMISTRY 67 By Man-Hong Yung, James D. Whitfield, Sergio Boixo, David G. Tempel, and Alan Aspuru-Guzik QUANTUM COMPUTING APPROACH TO NONRELATIVISTIC AND RELATIVISTIC MOLECULAR ENERGY CALCULATIONS 107 By Libor Veis and Jiri Pittner DENSITY FUNCTIONAL THEORY AND QUANTUM COMPUTATION 137 By Frank Gaitan and Franco Nori QUANTUM ALGORITHMS FOR CONTINUOUS PROBLEMS AND THEIR APPLICATIONS 151 By A. Papageorgiou and J. F. Traub ANALYTIC TIME EVOLUTION, RANDOM PHASE APPROXIMATION, AND GREEN FUNCTIONS FOR MATRIX PRODUCT STATES 179 By Jesse M. Kinder, Claire C. Ralph, and Garnet Kin-Lic Chan FEW-QUBIT MAGNETIC RESONANCE QUANTUM INFORMATION PROCESSORS: SIMULATING CHEMISTRY AND PHYSICS 193 By Ben Criger, Daniel Park, and Jonathan Baugh PHOTONIC TOOLBOX FOR QUANTUM SIMULATION 229 By Xiao-Song Ma, Borivoje Daki´c, and Philip Walther PROGRESS IN COMPENSATING PULSE SEQUENCES FOR QUANTUM COMPUTATION 241 By J. True Merrill and Kenneth R. Brown REVIEW OF DECOHERENCE-FREE SUBSPACES, NOISELESS SUBSYSTEMS, AND DYNAMICAL DECOUPLING 295 By Daniel A. Lidar FUNCTIONAL SUBSYSTEMS AND STRONG CORRELATION IN PHOTOSYNTHETIC LIGHT HARVESTING 355 By David A. Mazziotti and Nolan Skochdopole VIBRATIONAL ENERGY TRANSFER THROUGH MOLECULAR CHAINS: AN APPROACH TOWARD SCALABLE INFORMATION PROCESSING 371 By C. Gollub, P. von den Hoff, M. Kowalewski, U. Troppmann, and R. de Vivie-Riedle ULTRACOLD MOLECULES: THEIR FORMATION AND APPLICATION TO QUANTUM COMPUTING 403 By Robin Cote DYNAMICS OF ENTANGLEMENT IN ONE- AND TWO-DIMENSIONAL SPIN SYSTEMS 449 By Gehad Sadiek, Qing Xu, and Sabre Kais FROM TOPOLOGICAL QUANTUM FIELD THEORY TO TOPOLOGICAL MATERIALS 509 By Paul Watts, Graham Kells, and Jiri Vala TENSOR NETWORKS FOR ENTANGLEMENT EVOLUTION 567 By Sebastian Meznaric and Jacob Biamonte AUTHOR INDEX 581 SUBJECT INDEX 615
£161.95
John Wiley & Sons Inc Advances in Chemical Physics Volume 155
Book SynopsisDiscusses aspects of the state of diverse subjects in chemical physics and related fields, with chapters written by top researchers in the field. This title provides the space needed for readers to grasp the topic, including fundamentals, discoveries, applications, and emerging avenues of research.Table of ContentsCONTRIBUTORS TO VOLUME 155 v PREFACE TO THE SERIES vii MODELING VIRAL CAPSID ASSEMBLY 1 By Michael F. Hagan CHARGES AT AQUEOUS INTERFACES: DEVELOPMENT OF COMPUTATIONAL APPROACHES IN DIRECT CONTACT WITH EXPERIMENT 69 By Robert Vácha, Frank Uhlig, and Pavel Jungwirth SOLUTE PRECIPITATE NUCLEATION: A REVIEW OF THEORY AND SIMULATION ADVANCES 97 By Vishal Agarwal and Baron Peters WATER IN THE LIQUID STATE: A COMPUTATIONAL VIEWPOINT 161 By Toshiko Ichiye CONSTRUCTION OF ENERGY FUNCTIONS FOR LATTICE HETEROPOLYMER MODELS: EFFICIENT ENCODINGS FOR CONSTRAINT SATISFACTION PROGRAMMING AND QUANTUM ANNEALING 201 By Ryan Babbush, Alejandro Perdomo-Ortiz, Bryan O’Gorman, William Macready, and Alan Aspuru-Guzik AUTHOR INDEX 245 SUBJECT INDEX 271
£157.45
John Wiley & Sons Inc Statistical Physics
Book SynopsisThis undergraduate textbook provides students with a statistical mechanical foundation to the classical laws of thermodynamics through a comprehensive treatment of the basics of classical thermodynamics, equilibrium statistical mechanics, irreversible thermodynamics, and statistical mechanics of non-equilibrium phenomena.Trade Review“Summing Up: Recommended. Upper-division undergraduates.” (Choice, 1 March 2014) “The best choice is finally that the entropy is uncertainty commodified". The reviewer believes that the aim of the book is evident and it is worthwhile to make a detailed study of it from time to time.” (Zentralblatt MATH, 1 October 2013)Table of ContentsPreface xiii 1. Disorder or Uncertainty? 1 2. Classical Thermodynamics 5 2.1 The Classical Laws of Thermodynamics 5 2.2 Macroscopic State Variables and Thermodynamic Processes 6 2.3 Properties of the Ideal Classical Gas 8 2.4 Thermodynamic Processing of the Ideal Gas 10 2.5 Entropy of the Ideal Gas 13 2.6 Entropy Change in Free Expansion of an Ideal Gas 15 2.7 Entropy Change due to Nonquasistatic Heat Transfer 17 2.8 Cyclic Thermodynamic Processes, the Clausius Inequality and Carnot’s Theorem 19 2.9 Generality of the Clausius Expression for Entropy Change 21 2.10 Entropy Change due to Nonquasistatic Work 23 2.11 Fundamental Relation of Thermodynamics 25 2.12 Entropy Change due to Nonquasistatic Particle Transfer 28 2.13 Entropy Change due to Nonquasistatic Volume Exchange 30 2.14 General Thermodynamic Driving 31 2.15 Reversible and Irreversible Processes 32 2.16 Statements of the Second Law 33 2.17 Classical Thermodynamics: the Salient Points 35 Exercises 35 3. Applications of Classical Thermodynamics 37 3.1 Fluid Flow and Throttling Processes 37 3.2 Thermodynamic Potentials and Availability 39 3.2.1 Helmholtz Free Energy 40 3.2.2 Why Free Energy? 43 3.2.3 Contrast between Equilibria 43 3.2.4 Gibbs Free Energy 44 3.2.5 Grand Potential 46 3.3 Maxwell Relations 47 3.4 Nonideal Classical Gas 48 3.5 Relationship between Heat Capacities 49 3.6 General Expression for an Adiabat 50 3.7 Determination of Entropy from a Heat Capacity 50 3.8 Determination of Entropy from an Equation of State 51 3.9 Phase Transitions and Phase Diagrams 52 3.9.1 Conditions for Coexistence 53 3.9.2 Clausius–Clapeyron Equation 55 3.9.3 The Maxwell Equal Areas Construction 57 3.9.4 Metastability and Nucleation 59 3.10 Work Processes without Volume Change 59 3.11 Consequences of the Third Law 60 3.12 Limitations of Classical Thermodynamics 61 Exercises 62 4. Core Ideas of Statistical Thermodynamics 65 4.1 The Nature of Probability 65 4.2 Dynamics of Complex Systems 68 4.2.1 The Principle of Equal a Priori Probabilities 68 4.2.2 Microstate Enumeration 71 4.3 Microstates and Macrostates 72 4.4 Boltzmann’s Principle and the Second Law 75 4.5 Statistical Ensembles 77 4.6 Statistical Thermodynamics: the Salient Points 78 Exercises 79 5. Statistical Thermodynamics of a System of Harmonic Oscillators 81 5.1 Microstate Enumeration 81 5.2 Microcanonical Ensemble 83 5.3 Canonical Ensemble 84 5.4 The Thermodynamic Limit 88 5.5 Temperature and the Zeroth Law of Thermodynamics 91 5.6 Generalisation 91 Exercises 92 6. The Boltzmann Factor and the Canonical Partition Function 95 6.1 Simple Applications of the Boltzmann Factor 95 6.1.1 Maxwell–Boltzmann Distribution 95 6.1.2 Single Classical Oscillator and the Equipartition Theorem 97 6.1.3 Isothermal Atmosphere Model 98 6.1.4 Escape Problems and Reaction Rates 99 6.2 Mathematical Properties of the Canonical Partition Function 99 6.3 Two-Level Paramagnet 101 6.4 Single Quantum Oscillator 103 6.5 Heat Capacity of a Diatomic Molecular Gas 104 6.6 Einstein Model of the Heat Capacity of Solids 105 6.7 Vacancies in Crystals 106 Exercises 108 7. The Grand Canonical Ensemble and Grand Partition Function 111 7.1 System of Harmonic Oscillators 111 7.2 Grand Canonical Ensemble for a General System 115 7.3 Vacancies in Crystals Revisited 116 Exercises 117 8. Statistical Models of Entropy 119 8.1 Boltzmann Entropy 119 8.1.1 The Second Law of Thermodynamics 120 8.1.2 The Maximum Entropy Macrostate of Oscillator Spikiness 122 8.1.3 The Maximum Entropy Macrostate of Oscillator Populations 122 8.1.4 The Third Law of Thermodynamics 126 8.2 Gibbs Entropy 127 8.2.1 Fundamental Relation of Thermodynamics and Thermodynamic Work 129 8.2.2 Relationship to Boltzmann Entropy 130 8.2.3 Third Law Revisited 131 8.3 Shannon Entropy 131 8.4 Fine and Coarse Grained Entropy 132 8.5 Entropy at the Nanoscale 133 8.6 Disorder and Uncertainty 134 Exercises 135 9. Statistical Thermodynamics of the Classical Ideal Gas 137 9.1 Quantum Mechanics of a Particle in a Box 137 9.2 Densities of States 138 9.3 Partition Function of a One-Particle Gas 140 9.4 Distinguishable and Indistinguishable Particles 141 9.5 Partition Function of an N -Particle Gas 145 9.6 Thermal Properties and Consistency with Classical Thermodynamics 146 9.7 Condition for Classical Behaviour 147 Exercises 149 10. Quantum Gases 151 10.1 Spin and Wavefunction Symmetry 151 10.2 Pauli Exclusion Principle 152 10.3 Phenomenology of Quantum Gases 153 Exercises 154 11. Boson Gas 155 11.1 Grand Partition Function for Bosons in a Single Particle State 155 11.2 Bose–Einstein Statistics 156 11.3 Thermal Properties of a Boson Gas 158 11.4 Bose–Einstein Condensation 161 11.5 Cooper Pairs and Superconductivity 166 Exercises 167 12. Fermion Gas 169 12.1 Grand Partition Function for Fermions in a Single Particle State 169 12.2 Fermi–Dirac Statistics 170 12.3 Thermal Properties of a Fermion Gas 171 12.4 Maxwell–Boltzmann Statistics 173 12.5 The Degenerate Fermion Gas 176 12.6 Electron Gas in Metals 177 12.7 White Dwarfs and the Chandrasekhar Limit 179 12.8 Neutron Stars 182 12.9 Entropy of a Black Hole 183 Exercises 184 13. Photon Gas 187 13.1 Electromagnetic Waves in a Box 187 13.2 Partition Function of the Electromagnetic Field 189 13.3 Thermal Properties of a Photon Gas 191 13.3.1 Planck Energy Spectrum of Black-Body Radiation 191 13.3.2 Photon Energy Density and Flux 193 13.3.3 Photon Pressure 193 13.3.4 Photon Entropy 194 13.4 The Global Radiation Budget and Climate Change 195 13.5 Cosmic Background Radiation 197 Exercises 198 14. Statistical Thermodynamics of Interacting Particles 201 14.1 Classical Phase Space 201 14.2 Virial Expansion 203 14.3 Harmonic Structures 206 14.3.1 Triatomic Molecule 207 14.3.2 Einstein Solid 208 14.3.3 Debye Solid 209 Exercises 211 15. Thermodynamics away from Equilibrium 213 15.1 Nonequilibrium Classical Thermodynamics 213 15.1.1 Energy and Particle Currents and their Conjugate Thermodynamic Driving Forces 213 15.1.2 Entropy Production in Constrained and Evolving Systems 218 15.2 Nonequilibrium Statistical Thermodynamics 220 15.2.1 Probability Flow and the Principle of Equal a Priori Probabilities 220 15.2.2 The Dynamical Basis of the Principle of Entropy Maximisation 222 Exercises 223 16. The Dynamics of Probability 225 16.1 The Discrete Random Walk 225 16.2 Master Equations 226 16.2.1 Solution to the Random Walk 228 16.2.2 Entropy Production during a Random Walk 229 16.3 The Continuous Random Walk and the Fokker–Planck Equation 230 16.3.1 Wiener Process 232 16.3.2 Entropy Production in the Wiener Process 233 16.4 Brownian Motion 235 16.5 Transition Probability Density for a Harmonic Oscillator 236 Exercises 238 17. Fluctuation Relations 241 17.1 Forward and Backward Path Probabilities: a Criterion for Equilibrium 241 17.2 Time Asymmetry of Behaviour and a Definition of Entropy Production 243 17.3 The Relaxing Harmonic Oscillator 245 17.4 Entropy Production Arising from a Single Random Walk 247 17.5 Further Fluctuation Relations 249 17.6 The Fundamental Basis of the Second Law 253 Exercises 253 18. Final Remarks 255 Further Reading 261 Index 263
£43.65
John Wiley & Sons Inc Numerical Calculations in Clifford Algebra
Book SynopsisNUMERICAL CALCULATIONS IN CLIFFORD ALGEBRA An intuitive combination of the theory of Clifford algebra with numerous worked and computed examples and calculations Numerical Calculations in Clifford Algebra: A Practical Guide for Engineers and Scientists is an accessible and practical introduction to Clifford algebra, with comprehensive coverage of the theory and calculations. The book offers many worked and computed examples at a variety of levels of complexity and over a range of different applications making extensive use of diagrams to maintain clarity. The author introduces and documents the Clifford Numerical Suite, developed to overcome the limitations of existing computational packages and to enable the rapid creation and deployment of sophisticated and efficient code. Applications of the suite include Fourier transforms for arrays of any types of Clifford numbers and the solution of linear systems in which the coefficients are Clifford numbers of paTable of ContentsList of Figures xv List of Tables xix Preface xxi Part I Entities and Operations 1 1 Introduction 3 1.1 Operations 3 1.2 History 4 1.3 Alternative Forms 5 1.4 Naming 6 1.5 Structure 7 1.5.1 Algebraic 7 1.5.2 Numeric 8 1.6 Entities 11 References 12 2 Input 13 2.1 Syntax 13 2.2 Constants 14 2.2.1 Specific Types 14 2.2.2 General 16 2.3 Variables 19 2.3.1 Checking and Converting 19 Reference 23 3 Output 25 3.1 Tree Format 26 3.2 Numeric Formats 29 3.2.1 Default Format 29 3.2.2 Defined Format 31 3.3 Extended Formats 32 3.3.1 Rounding 32 3.3.2 Parts of Coefficients 33 3.4 Selected Components 35 3.5 Primitive Formats 36 3.6 Recovered Values 38 4 Unary Operations 41 4.1 Theory 41 4.1.1 Negation 41 4.1.2 Involution 41 4.1.3 Pair Exchange 42 4.1.4 Reversion 43 4.1.5 Clifford Conjugation 44 4.1.6 Supplementation and Pseudo-scalar 44 4.2 Practice 45 4.2.1 Example Code 45 4.2.2 Example Output 47 5 Binary Operations 49 5.1 Geometric Origins 49 5.1.1 Outer Multiplication 49 5.1.2 Orthogonal Components 52 5.1.3 Inner Multiplication 53 5.1.4 Names 54 5.2 Multiplication of Units 55 5.2.1 Progressive and Regressive Multiplication 55 5.2.2 Outer, Inner, and Central Multiplication 57 5.2.3 Multiplication By Scalars 58 5.3 Central Multiplication 59 5.3.1 Primal Units 60 5.3.2 Evolved and Other Units 61 5.3.3 Numbers 62 5.4 Practice 63 5.4.1 Example Code 63 5.4.2 Example Output 65 5.4.3 Multiplication Tables 65 References 70 6 Vectors and Geometry 71 6.1 Theory 71 6.1.1 Magnitude 71 6.1.2 Inverse 72 6.1.3 Reflection 72 6.1.4 Projection 73 6.1.5 Rotation 73 6.2 Practice 74 6.2.1 Example Code 74 6.2.2 Example Output 76 7 Quaternions 79 7.1 Theory 79 7.1.1 Magnitude 80 7.1.2 Inverse 80 7.1.3 Reflection and Projection 80 7.1.4 Rotation 81 7.1.5 Intersection 82 7.1.6 Factorisation 82 7.2 Practice 83 7.2.1 Example Code 83 7.2.2 Example Output 86 References 87 8 Pauli Matrices 89 8.1 Theory 89 8.1.1 Recovery of Components 90 8.1.2 Magnitude 90 8.1.3 Inverse 91 8.1.4 Reflection, Projection, and Rotation 91 8.2 Practice 91 8.2.1 Example Code 91 8.2.2 Example Output 94 Reference 95 9 Bicomplex Numbers 97 9.1 Theory 97 9.1.1 Conjugate 98 9.1.2 Magnitude 98 9.1.3 Inverse 98 9.1.4 Reflection, Projection, and Rotation 99 9.2 Practice 99 9.2.1 Example Code 99 9.2.2 Example Output 101 Reference 102 10 Electromagnetic Fields 103 10.1 Theory 103 10.1.1 Time and Frequency 103 10.1.2 Electromagnetic Entities 104 10.1.3 Dirac Operators 105 10.1.4 Maxwell’s Equations 105 10.1.5 Simplified Notation 105 10.1.6 Magnitude 106 10.1.7 Inverse 106 10.1.8 Reflection 107 10.1.9 Projection 107 10.1.10 Rotation 107 10.2 Practice 107 10.2.1 Example Code 107 10.2.2 Example Output 110 10.3 Field Arithmetic 112 10.3.1 Extensions Based on Quaternions 112 10.3.2 Inverses 113 10.3.3 Example Code 115 10.3.4 Example Output 117 References 118 11 Arrays of Clifford Numbers 119 11.1 Theory 119 11.2 Practice 120 11.2.1 Example Code 120 11.2.2 Example Output 123 Reference 125 12 Power Series 127 12.1 Theory 127 12.1.1 User Defined 127 12.1.2 Predefined 128 12.1.3 Convergence 129 12.1.4 Factorisation 130 12.1.5 Squaring 131 12.2 Practice 131 12.2.1 User Defined 131 12.2.2 Predefined 133 12.2.2.1 Standard Convergence 136 12.2.2.2 Extended Convergence 141 12.2.2.3 Doubly Extended Convergence 146 References 148 13 Matrices of Clifford Numbers 149 13.1 Background 149 13.2 Inversion 150 13.3 Practice 152 13.3.1 Example Code 152 13.3.2 Example Output 155 Reference 159 Part II Customisation 161 14 Memory 163 14.1 Memory Usage 163 14.2 Examples 165 14.2.1 Memory Tree Sparsity 165 14.2.2 Memory Expansion 170 14.2.3 Memory Recycling 171 14.2.3.1 Explicit and Implicit 171 14.2.3.2 Implicit and Nested 173 Reference 175 15 Errors 177 15.1 User Errors 177 15.1.1 Syntax Errors and Messages 180 15.2 System Errors 181 15.3 Recovery 182 15.4 Beneficial Usage 185 Reference 191 16 Extension 193 16.1 Accumulation 193 16.2 Multiplication 195 16.3 Transformation 197 16.4 Filtration 198 Part III Application 203 17 Verification 205 17.1 Identities 205 17.2 Tests 205 17.2.1 Example Code 205 17.2.2 Example Output 208 Reference 214 18 Lines Not Parallel 215 18.1 Theory 215 18.1.1 Common Plane 215 18.1.1.1 Inner Product 216 18.1.1.2 Outer Product 217 18.1.1.3 Geometrical Interpretation 217 18.1.2 No Plane in Common 218 18.1.2.1 Inner Product 219 18.1.2.2 Solution 219 18.2 Practice 220 18.2.1 Example Code 220 18.2.2 Example Output 223 Reference 224 19 Perspective Projection 225 19.1 Theory 225 19.2 Practice 225 19.2.1 Example Code 225 19.2.2 Example Output 229 Reference 230 20 Linear Systems 231 20.1 Theory 231 20.2 Practice 233 20.2.1 Example Code 233 20.2.2 Example Output 235 References 235 21 Fast Fourier Transform 237 21.1 Theory 237 21.2 Practice 238 21.2.1 Example Code 238 21.2.2 Example Output 243 References 244 22 Hertzian Dipole 245 22.1 Theory 245 22.2 Practice 246 22.2.1 Example Code 246 22.2.2 Example Output 251 Reference 253 23 Finite Difference Time Domain 255 23.1 Theory 255 23.1.1 Analytical Solution 255 23.1.2 Series Solution 256 23.1.3 Analytical Example 257 23.1.4 Numerical Derivatives 257 23.2 Practice 259 23.2.1 Example Code 259 23.2.2 Example Output 265 References 270 24 Cauchy Extension 271 24.1 Background 271 24.2 Theory 272 24.2.1 Two Dimensions 272 24.2.2 Three Dimensions 272 24.2.3 Singularity 273 24.2.4 The Taming Function 273 24.2.5 Construction 274 24.3 Practice 276 24.3.1 Example Code 276 24.3.2 Example Output 281 References 284 25 Electromagnetic Scattering 285 25.1 Background 285 25.2 Theory 286 25.3 Practice 288 25.3.1 Example Code 288 25.3.2 Example Output 289 References 293 Part IV Programming 295 26 Interfaces 297 26.1 Configuration and Observation 297 26.1.1 Management 297 26.1.2 Printing 298 26.2 Simple Entities 300 26.2.1 Units 300 26.2.2 Components 300 26.2.3 Numbers 302 26.2.3.1 Establishing and Recovering Values 302 26.2.3.2 Functions 303 26.2.3.3 Addition and Subtraction 304 26.2.3.4 Multiplication 304 26.2.3.5 Geometric 305 26.2.3.6 Filtering 305 26.3 Higher Entities 306 26.3.1 Vectors 306 26.3.2 Bicomplex Numbers 307 26.3.3 Quaternions 307 26.3.4 Pauli Matrices 308 26.3.5 Electromagnetic Fields 308 26.4 Multiple Entities 309 26.4.1 Arrays 309 26.4.2 Fast Fourier Transforms 309 26.4.3 Series 310 26.4.4 Matrices 310 Reference 311 27 Descriptions 313 27.1 Arguments 313 27.2 Data types 313 27.3 Formats 315 27.4 Manual Pages 316 27.4.1 A–e 316 27.4.2 F–j 342 27.4.3 K–o 369 27.4.4 P–t 387 27.4.5 U–z 468 27.5 Quick Reference 477 Reference 487 A Key to Example Code and Results 489 Index 493
£90.25
Springer New York Conformal Field Theory Graduate Texts in Contemporary Physics
Book SynopsisIntended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics.Table of Contents1. Introduction; 2. Quantum Field Theory; 3. Statistical Mechanics; 4. Global Conformal Invariance; 5. Conformal Invariance in Two Dimensions; 6. The Operator Formalism I; 7. The Operator Formalism II; 8. Minimal Models; 9. The Coulomb Gas Formalism; 10. Modular Invariance; 11. Finite Size Scaling; 12. The Two-Dimensional Ising Model; 13. Simple Lie Algebras; 14. Affine Lie Algebras; 15. The WZNW Model; 16. Fusion Rules; 17. Modular Invariants; 18. The Coset Construction
£134.99
Birkhauser Boston Inc Linear Integral Equations
Book SynopsisMany physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.Trade ReviewA nice introductory text... Presents the basics of linear integral equations theory in a very comprehensive way... [The] richness of examples and applications makes the book extremely useful for teachers and also researchers. —Applications of Mathematics (Review of the Second Edition) This second edition of this highly useful book continues the emphasis on applications and presents a variety of techniques with extensive examples...The book is ideal as a text for a beginning graduate course. Its excellent treatment of boundary value problems and an up-to-date bibliography make the book equally useful for researchers in many applied fields.—MathSciNet (Review of the Second Edition)Table of ContentsIntroduction.- Integral Equations with Separable Kernels.- Method Of Successive Approximations.- Classical Fredholm Theory.- Applications of Ordinary Differential Equations.- Applications of Partial Differential Equations.- Symmetric Kernels.- Singular Integral Equations.- Integral Transformation Methods.- Applications to Mixed Boundary Value Problems.- Integral Equations Perturbation Methods.- Appendix.- Bibliography.- Index.
£46.74
MP-AMM American Mathematical Hyperbolic Dynamics Fluctuations and Large
Book SynopsisThe papers in this volume cover topics in large deviations and thermodynamics formalism and limit theorems for dynamic systems. The material presented is primarily directed at researchers and graduate students in the very broad area of dynamical systems and ergodic theory, but will also be of interest to researchers in related areas.Table of Contents Hyperbolic dynamics, fluctuations and large deviations by D. Dolgopyat, Y. Pesin, M. Pollicott, and L. Stoyanov Large deviations and thermodynamical formalism: The almost Borel structure of diffeomorphisms with some hyperbolicity by J. Buzzi Lectures on large deviations in probability and dynamical systems by Y. Kifer Thermodynamic formalism for countable Markov shifts by O. M. Sarig Limit theorems for dynamical systems: Limit theorems for horocycle flows by G. Forni Limit theorems in dynamical systems using the spectral method by S. Gouezel Kinetic limits of dynamical systems by J. Marklof Additional topics: Limit theorems for toral translations by D. Dolgopyat and B. Fayad Spectral gap properties and limit theorems for some random walks and dynamical systems by Y. Guivarc'h The martingale approach after Varadhan and Dolgopyat by J. De Simoi and C. Liverani
£110.70
MP-AMM American Mathematical Nonlinear Dispersive Waves and Fluids
Book SynopsisAddresses the latest trends and perspectives in the area of nonlinear dispersive equations and fluid flows. The topics mainly focus on using state-of-the-art methods and techniques to investigate problems of depth and richness arising in quantum mechanics, general relativity, and fluid dynamics.Table of Contents N. Basharat, Y. Hu, and S. Zheng, Blowup rate for mass critical rotational nonlinear Schrodinger equations D. Cao, T. Mengesha, and T. Phan, Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients R. Denlinger, Virial estimates for hard spheres Y. Du, G. Chen, and J. Liu, The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited, I: The critical generalized KdV equation L. G. Farah, J. Holmer, and S. Roudenko, Instability of solitons-revisited, II: The supercritical Zakharov-Kuznetsov equation C. Flores, S. Oh, and D. Smith, Stabilization of dispersion-generalized Benjamin-Ono D. Garrisi and V. Georgiev, Uniqueness of standing-waves for a non-linear Schrodinger equation with three pure-power combinations in dimension one S. Gustafson and D. Roxanas, Below-threshold solutions of a focusing energy-critical heat equation in $\mathbb{R}^4$ D. Li and X. Zhang, A regularity upgrade of pressure S. Miao, On large future-global-in-time solutions to energy-supercritical nonlinear wave equation J. Murphy, The nonlinear Schrodinger equation with an inverse-square potential Y. Shao and C. Wang, The harmonic map heat flow on conic manifolds K. Yamazaki, On the global regularity issue of the two-dimensional magnetohydrodynamics system with magnetic diffusion weaker than a Laplacian J. Zhang, S. Zheng, and S. Zhu, Orbital stability of standing waves for fractional Hartree equation with unbounded potentials.
£103.50
MP-AMM American Mathematical Mathematical Theory of Scattering Resonances
Book SynopsisFocuses on the simplest case of scattering by compactly supported potentials, and provides pointers to modern literature where more general cases are studied. The book also presents an approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.Trade ReviewThis is an up to date account of modern mathematical scattering theory with an emphasis on the deep interplay between the location of the scattering poles or resonances, and the underlying dynamics and geometry. The masterful exposition reflects the authors' significant roles in shaping this very active field. A must read for researchers and students working in scattering theory or related areas." - Peter Sarnak, Institute for Advanced Study"This is a very broad treatise of the modern theory of scattering resonances, beautifully written with a wealth of important mathematical results as well as applications, motivations and numerical and experimental illustrations. For experts, it will be a basic reference and for non-experts and graduate students an appealing and quite accessible introduction to a fascinating field with multiple connections to other branches of mathematics and to physics." - Johannes Sjostrand, Universite de Bourgogne"Resonance is the Queen of the realm of waves. No other book addresses this realm so completely and compellingly, oscillating effortlessly between illustration, example, and rigorous mathematical discourse. Mathematicians will find a wonderful array of physical phenomena given a solid intuitive and mathematical foundation, linked to deep theorems. Physicists and engineers will be inspired to consider new realms and phenomena. Chapters travel between motivation, light mathematics, and deeper mathematics, passing the baton from one to the other and back in a way that these authors are uniquely qualified to do." - Eric J. Heller, Harvard UniversityTable of Contents Introduction Potential scattering: Scattering resonances in dimension one Scattering resonances in odd dimensions Geometric scattering: Black box scattering in $\mathbb{R}^n$ Scattering on hyperbolic manifolds Resonances in the semiclassical limit: Resonance-free regions Resonances and trapping Appendices: Notation Spectral theory Fredholm theory Complex analysis Semiclassical analysis Bibliography Index.
£106.20
MP-AMM American Mathematical The YangMills Heat Equation with Finite Action in
Book Synopsis
£67.50
MP-AMM American Mathematical Partial Compactification of Monopoles and Metric
Book SynopsisView the abstract.
£68.40
MP-AMM American Mathematical Spiral Waves Linear and Nonlinear Theory
Book Synopsis
£68.40
American Mathematical Society The Mathematical Analysis of the Incompressible
Book SynopsisProvides graduate students with exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. The book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.Table of Contents Ideal incompressible fluids: The Euler equations Existence of solutions and continuation criteria for Euler Incompressible viscous fluids: The Navier-Stokes equations Leray-Hopf weak solutions of Navier-Stokes Mild solutions of Navier-Stokes A survey of some advanced topics Appendix Bibliography Index
£67.50
MP-AMM American Mathematical Dynamics Near the Subcritical Transition of the
Book SynopsisThe second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re.
£67.50
American Mathematical Society From Representation Theory to Mathematical Physics and Back
£104.40
MP-AMM American Mathematical Recovery Methodologies Regularization and
Book SynopsisIntroduces the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. By avoiding extreme technicalities and elaborate proof techniques, this is an accessible resource for students and researchers.Table of Contents Introductory remarks: Constituents of the univariate antenna problem Regularization tools: Functional and Fourier analytic auxiliaries Regularization methodologies: Matricial methodologies of resolution Compact operator methodologies of resolution Example realizations light: Univariate differentiation Reconstruction and regularization methods Regularization examples: Regularization methodologies in geotechnology Sampling tools: Lattice point and special function theoretic auxiliaries Sampling methodologies: Sampling over continuously connected pointsets Sampling over discretely given pointsets Polyharmonic finite bandwidth sampling Polyharmonic infinite bandwidth sampling Polymetaharmonic finite bandwidth sampling Polymetaharmonic infinite bandwidth sampling Sampling examples: Sampling methodologies in technology Concluding remarks: Recovery as interconnecting whole List of symbols Bibliography Index
£103.50
Springer New York Modern Fluid Dynamics for Physics and Astrophysics
Trade Review“This hefty tome offers a comprehensive introduction to fluid dynamics, mainly with application to planetary science and astrophysics in mind. ... it is a useful resource for course development. It certainly offers a wealth of interesting insights into fluid dynamics and plasma physics for those with experience, and I found it to be an enjoyable and informative read.” (David A. Burton, The Observatory, Vol. 137 (1260), October, 2017)“Modern Fluid Dynamics for Physics and Astrophysics is a welcome addition that helps fill the gap between introductory and advanced books. … The textbook is especially suited for graduate courses, but I believe that it can also be easily used for senior undergraduate courses. … Modern Fluid Dynamics for Physics and Astrophysics to be a very good resource, not just for astrophysics and geophysics courses but for any physics course that covers the fundamental topic of fluid dynamics.” (Giuseppe Lodato, Physics Today, May, 2017)Table of Contents
£71.99
Society for Industrial and Applied Mathematics (SIAM) The Defocusing Nonlinear Schrödinger Equation
Book Synopsis
£90.95
Society for Industrial & Applied Mathematics,U.S. Tensor Analysis: Spectral Theory and Special
Book SynopsisTensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory – some of which are nontrivial – have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors.Tensor Analysis is unique in that it is the first book on the spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors, which is covered in a chapter.Table of Contents List of Figures. List of Algorithms. Preface. Chapter 1: Introduction. Chapter 2: Eigenvalues of Tensors. Chapter 3: Nonnegative Tensors. Chapter 4: Spectral Hypergraph Theory via Tensors. Chapter 5: Positive Semidefinite Tensors. Chapter 6: Completely Positive Tensors and Copositive Tensors. Bibliography. Index.
£76.50
John Wiley & Sons Consensus and Synchronization
£44.65
Springer London Ltd Geometry, Spinors and Applications
Book SynopsisThis text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.Table of ContentsPreface.- Part I Preliminaries and Algebraic Aspects of Spinors: General Vector Spaces. Vector Spaces with a Metric.- Part II Preliminaries and Geometrical Aspects of Spinors: Manifolds in General. Lie Groups as Special Manifolds. Fibre Bundles as Special Manifolds.- Part III General Spinorial Differentiation: Geometrical Definition of C31 (R) Spinors. Differentiation of Spinor Fields. Interplay between Differentiations. The Invariant Formalism.- Part IV Illustrations and Applications: Newtonian Mechanics and C30 (R). Electro-Magnetism. Cartan Formalism. Geometrical Gravitational Theories.- A: Infeld-van der Waerden Symbols.- B: Maxwells's Equations: Complements.
£80.99
Springer Nature Switzerland AG Close Encounters of Art and Physics: An Artist's
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
£25.19
Springer Nature Switzerland AG Powers of Two: The Information Universe —
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.
£40.49
Springer Nature Switzerland AG Recent Advances in Kinetic Equations and
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.
£127.99
Springer Nature Switzerland AG Proceedings of the 2020 Conference of The
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?
£125.99
Springer Nature Switzerland AG Geometry and Invariance in Stochastic Dynamics:
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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Springer Nature Switzerland AG Advances in Social Simulation: Proceedings of the
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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Springer Nature Switzerland AG Periodic Monopoles and Difference Modules
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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Springer Nature Switzerland AG Luminescence Signal Analysis Using Python
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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Springer International Publishing AG Marcelo Viana - Selected Works
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.
£143.99
Springer International Publishing AG Jost Functions in Quantum Mechanics: A Unified
Book SynopsisBased on Jost function theory this book presents an approach useful for different types of quantum mechanical problems. These include the description of scattering, bound, and resonant states, in a unified way. The reader finds here all that is known about Jost functions as well as what is needed to fill the gap between the pure mathematical theory and numerical calculations. Some of the topics covered are: quantum resonances, Regge poles, multichannel scattering, Coulomb interaction, Riemann surfaces, multichannel analog of the effective range theory, one- and two-dimensional problems, many-body problems within the hyperspherical approach, just to mention few of them. These topics are relevant in the fields of quantum few-body theory, nuclear reactions, atomic collisions, and low-dimensional semiconductor nanostructures. In light of this, the book is meant for students, who study quantum mechanics, scattering theory, or nuclear reactions at the advanced level as well as for post-graduate students and researchers in the fields of nuclear and atomic physics. Many of the arguments that are traditional for textbooks on quantum mechanics and scattering theory, are covered here in a different way, using the Jost functions. This gives the reader a new insight into the subject, revealing new features of various mathematical objects and quantum phenomena.Trade Review“This book has to be recommended to graduate students and to young researchers as well who want to enter the difficult field of modern scattering theory.” (Giorgio Cattapan, Mathematical Reviews, July, 2023)Table of ContentsChapter 1: The Basic Concepts.- Part I: Single-Channel Problems.- Chapter 2: Schr¨Odinger Equation and its Solutions.- Chapter 3: Riemann Surface and the Spectral Points.- Chapter 4: Scattering States and the S-Matrix.- Chapter 5: Complex Angular Momentum.- Chapter 6: Green’s Functions.- Chapter 7: Short-Range Potential Extending to Infinity.- Chapter 8: Single-Channel Potential with Coulombic Tail.- Part II: Multi-Channel Problems.- Chapter 9: Non-Central Potential.- Chapter 10: Systems with Non-Zero Spin.- Chapter 11: Multi-Channel Schr Odinger Equation.- Chapter 12: Multi-Channel Jost Matrix.- Chapter 13: Riemann Surfaces for Multi-Channel Systems.- Chapter 14: Multi-Channel Problems of Charged Particles.- Chapter 15: Effective-Range Expansion and its Generalizations.- Part III: Special Issues.- Chapter 16: Singular and Low-Dimensional Potentials.- Chapter 17: Miscellaneous Extensions of the Jost Function Approach.- Chapter 18: Some Exactly Solvable Potential Models.- Appendices.- References and Index.
£142.49
Springer International Publishing AG Black Hole Physics: From Collapse to Evaporation
Book SynopsisThis textbook gradually introduces the reader to several topics related to black hole physics with a didactic approach. It starts with the most basic black hole solution, the Schwarzschild metric, and discusses the basic classical properties of black hole solutions as seen by different probes. Then it reviews various theorems about black hole properties as solutions to Einstein gravity coupled to matter fields, conserved charges associated with black holes, and laws of black hole thermodynamics. Next, it elucidates semiclassical and quantum aspects of black holes, which are relevant in ongoing and future research. The book is enriched with many exercises and solutions to assist in the learning.The textbook is designed for physics graduate students who want to start their research career in the field of black holes; postdocs who recently changed their research focus towards black holes and want to get up-to-date on recent and current research topics; advanced researchers intending to teach (or learn) basic and advanced aspects of black hole physics and the associated mathematical tools. Besides general relativity, the reader needs to be familiar with standard undergraduate physics, like thermodynamics, quantum mechanics, and statistical mechanics. Moreover, familiarity with basic quantum field theory in Minkowski space is assumed. The book covers the rest of the needed background material in the main text or the appendices.Table of ContentsChapter I: INTRODUCTION1. A brief review on essentials of General Relativity, from basic concepts, mathematical frameworkand Einstein equations Einstein-Hilbert action and classical tests of GR;2. Brief review of history and timeline of developments from Schwarzschild solution to black holemergers and to information paradox and rewall;3. Gravitational collapse and Chandrasekhar mass bound;4. Different schools of thought on black holes: high energy oriented, GR oriented and quantuminformation theory oriented; open issue how to merge these schoolsChapter II: BASIC CONCEPTS and TOOLS1. Schwarzschild metric and some basic facts and analysis;2. Analysis of geodesics, notion of Killing horizon and near horizon Rindler geometry;3. Kruskal coordinates, maximal extensions and Carter-Penrose diagram;4. Einstein-Maxwell theory and Reisner-Nordström solution and its basic analysis;5. Kerr solution and its basic analysis;6. Black holes in (A)dS backgrounds.Chapter III: CLASSICAL ASPECTS1. Lensing and black hole shadows;2. Super-radiance, Penrose process and black hole mining;3. Gravitational wave emission in black hole mergers;4. Accretion disk physics;5. Extremal black holes, their near horizon and basic analysis.Chapter IV: ADVANCED CONCEPTS1. Mathematical defnition of black holes, notion of various different horizons, Killing, event,cosmological, isolated; trapped surface.2. Conjectures and theorems (Cosmic censorship; Penrose mass inequality, singularity, uniquenessand topology theorems)3. Raychaudhuri equation and area theorem (2nd law); energy conditions;4. Linear and nonlinear stability of black hole solutions;5. More detailed analysis of collapse, Choptuik exponents and critical exponents;6. Canonical boundary charges (1st law), ADM, Brown-York, Regge-Teitelboim, Iyer-Wald-Zoupas,Barnich-Brandt and Hajian-Sh-J charges.7. Variation principle; Gibbons-Hawking-York boundary term; Brown-York stress tensor;8. Quasi-normal modes and black hole perturbations;9. Four laws of black hole thermodynamics and their new derivations a la Wald-Hajian-Sh-J;Chapter V: SEMICLASSICAL ASPECTS1. Quantization on black hole backgrounds;2. Unruh effect;3. Hawking effect;4. Bekenstein entropy and the area law, the Bekenstein bound;5. Parikh-Wilczek tunneling;6. Black hole evaporation;7. Membrane paradigm.Chapter VI: EXPERT TOPICS1. Gravity in lower dimensions (including various asymptotic symmetry algebras)2. Gravity in higher dimensions (including a brief discussion on supergravity);3. Higher dimensional black hole/ring/brane solutions.4. Aspects of holography - holographic renormalization, correlation functions and asymptoticsymmetries5. Extremal black holes and attractor mechanism6. Kerr/CFT and related topics7. Soft hair and black hole microstates.Chapter VII: QUANTUM ASPECTS1. Black holes in string theory;2. Microstate counting;3. Microstate identification/constructions, fuzzballs, fluffballs;4. Information paradox and black hole complementarity and firewalls;5. Black holes and quantum gravity;6. Information paradox and the AdS/CFT;7. Holography, Quantum information (entanglement entropy, Bousso bound, QNEC etc.) andgeneralized laws of black hole thermodynamics.Chapter VIII: OUTLOOK1. Summary;2. Outlook and open issues; - Experimental/observational prospects - Black holes as a window to Quantum Gravity - gravity may be emergent | what does it emerge from?Chapter IX: SOLUTIONS TO EXERCISESWe present numerous exercises throughout the book and in this chapter we give solutions to aselected subset of them.AppendicesWe intend to have some appendices in which we present some details of crucial mathematicalframeworks and formulations not fitting into the main text, in particular - Cartan formulation - Basics of QFT in curved spacetime - Covariant phase space method
£66.49
Springer International Publishing AG New Frontiers of Celestial Mechanics: Theory and
Book SynopsisThis volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.Table of Contents1) The contribution by Ugo Locatelli focuses on the explicit construction of invariant tori exploiting suitable Hamiltonian normal forms, with particular emphasis on applications to Celestial Mechanics. First, the algorithm constructing the Kolmogorov normal form is described in detail. Then the extension to lowerdimensional elliptic tori is provided. Both algorithms are then combined so as to accurately approximate the long-term dynamics of the HD 4732 extrasolar system. 2) The contribution by Gabriella Pinzari presents a review of some results of their research group, regarding the relation between some particular motions of the Three–Body problem (3BP) and the motions of the so–called Euler (or two–centre) problem, which is integrable. For the analysis of such relation, the authors make use of two novel results: on one hand, the two–centre problem (2CP) bears a remarkable property, here called renormalizable integrability, which states that the simple averaged potential of the 2CP and the Euler integral are one function of the other; on the other hand, the motions of the Euler integral are at least qualitatively explicit, and the averaged Newtonian potential is a prominent part of the 3BP Hamiltonian.3) The contribution by Alessandra Celletti deals with dissipative systems, a key topic in Celestial Mechanics. In particular the problem of the existence of invariant tori for conformally symplectic systems, which have the property to transform the symplectic form into a multiple of itself, is studied. Two different models are presented: a discrete system known as the standard map and a continuous system known as the spin–orbit problem. In both cases, both the conservative and dissipative versions are considered, in order to highlight the differences between the symplectic and conformally symplectic dynamics. 4) The contribution by Gwenael Boué provides basic tools to understand the rotational dynamics of extended bodies which could be either rigid or deformable by tides. The problem is described in a Lagrangian formalism as it was developed by H. Poincar´e in 1901. The case of rigid body is also presented in the corresponding Hamiltonian formalism. The mathematical description of the deformation of the extended body follows the approach used by C. Ragazzo and L. Ruiz in their two papers of 2015, 2017 due to the compactness and clarity of their formalism. In this Chapter, many applications to the rotation and the libration of celestial bodies are illustrated. 5) The contribution by Christos Efthymiopoulos concerns the phenomenon of Arnold diffusion. The authors begin with the famous example given by Arnold to describe the slow diffusion taking place in the action–space in Hamiltonian nonlinear dynamical systems with three or more degrees of freedom. The text introduces basic concepts related to our current understanding of the mechanisms leading to Arnold diffusion and at the same time performed a qualitative investigation of the phenomenon of Arnold diffusion with many examples. The problem of the speed of diffusion is investigated using methods of perturbation theory, with particular emphasis on Nekhoroshevs theorem. 6) The contribution by Giovanni F. Gronchi deals with the problem of initial orbit determination of a solar system body, i.e. the determination of a preliminary orbit from observations collected for example by a telescope. The two methods that are presented, named Link2 and Link3, try to link together two and three, respectively, short arcs of optical observations of the same object which can possibly be quite far apart in time. The conservation laws of Kepler’s problem are used to derive a polynomial equation of degree 9 (Link2) and 8 (Link3) for the distance of the body from the observer. 7) The contribution by Catalin Gales provides an overview of some recent developments in the study of dynamics of space debris with focus on specific resonant interactions, in particular those related to the tesseral resonances. After an historical introduction to the topic, the authors provide a long–term picture of the dynamics that can help in the modeling and mitigation of the space debris problem, both in term of Cartesian coordinates and in the Hamiltonian framework. Some key terms in the perturbing functions are classified, while the effect of the dissipative force of the atmospheric drag is also formulated. 8) The contribution by Massimiliano Guzzo presents the use of the Fast Lyapunov Indicators (FLI) in the Three–Body problem, with the eventual aim of computing transit orbits. The FLI belong to the family of the finite time indicators, which are able to extract the information of the solutions of the variational equations on short time intervals. First, the FLI are applied to two model problems: the standard map and the double gyre. Then, it is described a modification of the FLI which was originally introduced to improve the computation of stable and unstable manifolds in model systems and the Three–Body problem. 9) The contribution by Antonio Giorgilli provides an answer to a simple question, how did Kepler discover his celebrated laws?. The answer however is not that simple and the present paper guides the reader by a short walk along the main works of Kepler, notably the Astronomia Nova, trying to follow his search of the perfection of the World till the discovery of his celebrated laws. At the end of the road, the consciousness that the finish line had not yet been reached.
£103.99
Springer International Publishing AG Space Group Representations: Theory, Tables and
Book SynopsisThis book is devoted to the construction of space group representations, their tabulation, and illustration of their use. Representation theory of space groups has a wide range of applications in modern physics and chemistry, including studies of electron and phonon spectra, structural and magnetic phase transitions, spectroscopy, neutron scattering, and superconductivity. The book presents a clear and practical method of deducing the matrices of all irreducible representations, including double-valued, and tabulates the matrices of irreducible projective representations for all 32 crystallographic point groups. One obtains the irreducible representations of all 230 space groups by multiplying the matrices presented in these compact and convenient to use tables by easily computed factors. A number of applications to the electronic band structure calculations are illustrated through real-life examples of different crystal structures. The book's content is accessible to both graduate and advanced undergraduate students with elementary knowledge of group theory and is useful to a wide range of experimentalists and theorists in materials and solid-state physics.Table of ContentsScope and Overview.- Mathematical Preliminaries.- Induced Representations.- Projective Representations.- Representations of the Space Groups.- Tables.- Group Theory and Quantum Mechanics.
£123.49
Springer International Publishing AG Dialogues Between Physics and Mathematics: C. N.
Book SynopsisThis volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.Table of Contents1 Frank Yang at Stony Brook and the Beginning of Supergravity.- 2. A Stacky Approach to Crystals.- 3 The Potts Model, the Jones Polynomial and Link Homology.- 4 The Penrose–Onsager–Yang Approach to Superconductivity and Superfluidity.- 5 Quantum Operads.- 6 Quantum computational complexity withphotons and linear optics.- 7 Quantized Twistors, G2*, and the Split Octonions.- 8 Kronecker Anomalies and Gravitational Striction.- 9 Projecting Local and Global Symmetries to the Planck Scale.- 10 Gauge Symmetry in Shape Dynamics.- 11 Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.- 12 Quantum Anomalous Hall Effect.- 13 Magic Superconducting States in Cuprates.
£87.99
Springer International Publishing AG High Performance Computing in Science and
Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2021. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart I Physics.- Part II Molecules, Interfaces, and Solids.- Part III Reactive Flows.- Part IV Computational Fluid Dynamics.- Part V Transport and Climate.- Part VI Computer Science.- Part VII Miscellaneous Topics.
£159.99
Springer International Publishing AG An Introduction to Anomalous Diffusion and Relaxation
Book SynopsisThis book provides a contemporary treatment of the problems related to anomalous diffusion and anomalous relaxation. It collects and promotes unprecedented applications dealing with diffusion problems and surface effects, adsorption-desorption phenomena, memory effects, reaction-diffusion equations, and relaxation in constrained structures of classical and quantum processes. The topics covered by the book are of current interest and comprehensive range, including concepts in diffusion and stochastic physics, random walks, and elements of fractional calculus. They are accompanied by a detailed exposition of the mathematical techniques intended to serve the reader as a tool to handle modern boundary value problems. This self-contained text can be used as a reference source for graduates and researchers working in applied mathematics, physics of complex systems and fluids, condensed matter physics, statistical physics, chemistry, chemical and electrical engineering, biology, and many others.Table of ContentsPreface.- Integral Transforms and Special Functions.- Concepts in Diffusion and Stochastic Processes.- Random Walks.- Elements of Fractional Calculus.- Fractional Anomalous Diffusion.- Adsorption Phenomena and Anomalous Behavior.- Reaction-Diffusion Problems.- Relaxation under Geometric Constraints I: Classical Processes.- Relaxation under Geometric Constraints II: Quantum Processes.- Index.
£49.49
Springer International Publishing AG Statistical Methods for Data Analysis: With
Book SynopsisThis third edition expands on the original material. Large portions of the text have been reviewed and clarified. More emphasis is devoted to machine learning including more modern concepts and examples. This book provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP).It starts with an introduction to probability theory and basic statistics, mainly intended as a refresher from readers’ advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. Following, the author discusses Monte Carlo methods with emphasis on techniques like Markov Chain Monte Carlo, and the combination of measurements, introducing the best linear unbiased estimator. More advanced concepts and applications are gradually presented, including unfolding and regularization procedures, culminating in the chapter devoted to discoveries and upper limits.The reader learns through many applications in HEP where the hypothesis testing plays a major role and calculations of look-elsewhere effect are also presented. Many worked-out examples help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data.Trade Review“The book is important because, as AI and data science continue to shape the future, much interdisciplinary work is being done in many different domains. It is a very good example of interdisciplinary physics research using AI and data science. ... Graduate students are often expected to apply theoretical knowledge. This book will be an invaluable resource for them, to jumpstart their research by getting equipped with the right statistical and data analysis toolsets.” (Gulustan Dogan, Computing Reviews, August 8, 2023)Table of ContentsPreface to the third edition Preface to previous edition/s 1 Probability Theory 1.1 Why Probability Matters to a Physicist 1.2 The Concept of Probability 1.3 Repeatable and Non-Repeatable Cases 1.4 Different Approaches to Probability 1.5 Classical Probability 1.6 Generalization to the Continuum 1.7 Axiomatic Probability Definition 1.8 Probability Distributions 1.9 Conditional Probability 1.10 Independent Events 1.11 Law of Total Probability 1.12 Statistical Indicators: Average, Variance and Covariance 1.13 Statistical Indicators for a Finite Sample 1.14 Transformations of Variables 1.15 The Law of Large Numbers 1.16 Frequentist Definition of Probability References 2 Discrete Probability Distributions 2.1 The Bernoulli Distribution 2.2 The Binomial Distribution 2.3 The Multinomial Distribution 2.4 The Poisson Distribution References 3 Probability Distribution Functions 3.1 Introduction 3.2 Definition of Probability Distribution Function 3.3 Average and Variance in the Continuous Case 3.4 Mode, Median, Quantiles 3.5 Cumulative Distribution 3.6 Continuous Transformations of Variables 3.7 Uniform Distribution 3.8 Gaussian Distribution 3.9 X^2 Distribution 3.10 Log Normal Distribution 3.11 Exponential Distribution3.12 Other Distributions Useful in Physics 3.13 Central Limit Theorem 3.14 Probability Distribution Functions in More than One Dimension 3.15 Gaussian Distributions in Two or More Dimensions References 4 Bayesian Approach to Probability 4.1 Introduction 4.2 Bayes’ Theorem 4.3 Bayesian Probability Definition 4.4 Bayesian Probability and Likelihood Functions 4.5 Bayesian Inference 4.6 Bayes Factors 4.7 Subjectiveness and Prior Choice 4.8 Jeffreys’ Prior 4.9 Reference priors 4.10 Improper Priors 4.11 Transformations of Variables and Error Propagation References 5 Random Numbers and Monte Carlo Methods 5.1 Pseudorandom Numbers 5.2 Pseudorandom Generators Properties 5.3 Uniform Random Number Generators 5.4 Discrete Random Number Generators 5.5 Nonuniform Random Number Generators 5.6 Monte Carlo Sampling 5.7 Numerical Integration with Monte Carlo Methods 5.8 Markov Chain Monte Carlo References 6 Parameter Estimate 6.1 Introduction 6.2 Inference 6.3 Parameters of Interest 6.4 Nuisance Parameters 6.5 Measurements and Their Uncertainties 6.6 Frequentist vs Bayesian Inference 6.7 Estimators 6.8 Properties of Estimators 6.9 Binomial Distribution for Efficiency Estimate 6.10 Maximum Likelihood Method 6.11 Errors with the Maximum Likelihood Method 6.12 Minimum X^2 and Least-Squares Methods 6.13 Binned Data Samples 6.14 Error Propagation 6.15 Treatment of Asymmetric Errors References7 Combining Measurements7.1 Introduction7.2 Simultaneous Fits and Control Regions7.3 Weighted Average7.4 X^2 in n Dimensions7.5 The Best Linear Unbiased EstimatorReferences 8 Confidence Intervals8.1 Introduction8.2 Neyman Confidence Intervals8.3 Binomial Intervals8.4 The Flip-Flopping Problem8.5 The Unified Feldman–Cousins ApproachReferences 9 Convolution and Unfolding9.1 Introduction9.2 Convolution9.3 Unfolding by Inversion of the Response Matrix9.4 Bin-by-Bin Correction Factors9.5 Regularized Unfolding9.6 Iterative Unfolding9.7 Other Unfolding Methods9.8 Software Implementations9.9 Unfolding in More DimensionsReferences10 Hypothesis Tests10.1 Introduction10.2 Test Statistic10.3 Type I and Type II Errors10.4 Fisher’s Linear Discriminant10.5 The Neyman–Pearson Lemma10.6 Projective Likelihood Ratio Discriminant10.7 Kolmogorov–Smirnov Test10.8 Wilks’ Theorem10.9 Likelihood Ratio in the Search for a New SignalReferences 11 Machine Learning11.1 Supervised and Unsupervised Learning11.2 Terminology11.3 Machine Learning Classification from a Statistical Point of View11.4 Bias-Variance tradeo11.5 Overtraining11.6 Artificial Neural Networks 11.7 Deep Learning11.8 Convolutional Neural Networks11.9 Boosted Decision Trees11.10 Multivariate Analysis ImplementationsReferences 12 Discoveries and Upper Limits12.1 Searches for New Phenomena: Discovery and Upper Limits12.2 Claiming a Discovery12.3 Excluding a Signal Hypothesis12.4 Combined Measurements and Likelihood Ratio12.5 Definitions of Upper Limit12.6 Bayesian Approach12.7 Frequentist Upper Limits12.8 Modified Frequentist Approach: the CLs Method12.9 Presenting Upper Limits: the Brazil Plot12.10 Nuisance Parameters and Systematic Uncertainties12.11 Upper Limits Using the Profile Likelihood12.12 Variations of the Profile-Likelihood Test Statistic12.13 The Look Elsewhere EffectReferences Index
£55.96
Springer International Publishing AG Introduction to String Theory
Book SynopsisGraduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts. Table of ContentsChapter 1. The Polyakov path integral. Chapter 2. Introduction to 2d conformal field theories. Chapter 3. Spectrum, vertices, and BRST quantization. Chapter 4. Tree and one-loop amplitudes in the bosonic string. Chapter 5. Consistent 10d superstring, modular invariance, and all that. Chapter 6. The Heterotic string: part I. Chapter 7. Toroidal compactifications and T-duality (bosonic string). Chapter 8. The Heterotic string: part II. Chapter 9. Superstring interactions and anomalies. Chapter 10. Superstring D-branes. Chapter 11. Strings at strong coupling. Chapter 12. Calabi-Yau compactifications. Appendix.
£98.99
Springer International Publishing AG Cosmic Rays: Multimessenger Astrophysics and
Book SynopsisIn recent years, cosmic rays have become the protagonists of a new scientific revolution. We are able today to film the Universe with telescopes of completely novel conception, recording information from many different messengers and accessing previously unknown cosmic regions.Written by a recognized authority in physics, this book takes readers on a captivating journey through the world of cosmic rays, their role in the revolutionary field of multi-messenger astronomy, their production from powerful accelerators close to the surfaces of black holes and compact objects, reaching the highest levels of energy observed in nature, and the implications this has for our understanding of the Universe. Through the stories of pioneering scientists, explorations of cutting-edge technologies, and simple explanations related to particle physics, quantum mechanics, and astrophysics, the book provides an illuminating state-of-the-art introduction to the current state of high-energy astrophysics. The book was written in straightforward yet rigorous language, so as to be accessible to the greater public. For those curious about the cosmos and cosmic gamma rays, nuclei, neutrinos, and gravitational waves, from casual observers to professional astronomers and physicists, the book is a must-read, offering a thrilling adventure into the future of astronomy and particle physics.Table of ContentsIntroduction 1 The Largest Energies in the Universe 1.1 The Universe around us 1.2 Particles and fields 1.3 Cosmic rays 2 The Mystery of Cosmic Rays 2.1 The discovery of natural radioactivity 2.2 Is natural radioactivity of extraterrestrial origin? 2.3 Father Wulf, a true experimental physicist 2.4 Pacini’s attenuation measures in water 2.5 Hess and balloon measurements 2.6 First developments and the tragedy of the first world war 3 Cosmic-Ray Research after the First World War 3.1 Research in Europe and the Pacini-Hess controversy 3.2 Research in the United States 3.3 Are cosmic rays predominantly charged or neutral? 3.4 Bruno Rossi and the discoveries after 1930 3.5 At the origins of elementary particle physics 3.6 The recognition of the scientific community 3.7 Hypothesis on the origin of cosmic rays: Tesla, Zwicky, Fermi 4 Cosmic Rays and the Physics of Elementary Particles 4.1 Leptons and mesons 4.2 The neutral pion 4.3 The discovery of strangeness 4.4 Laboratories on the mountains 4.5 Hunters become shepherds: particle accelerators 5 Fire Under the Ashes: the Discoveries at the End of the 20th Century and at the Beginning of the 21st Century 5.1 Cosmic rays of very-high-energy 5.2 Anomalous events 5.3 X-rays 5.4 Neutrinos from the Sun and the cosmos 6 Cosmic Ray Research Today: Multi-Messenger Astrophysics and the New Astronomy 6.1 Very-high-energy cosmic rays 6.2 Search for antimatter 6.3 Gamma rays 6.4 Cosmic neutrinos 6.5 Gravitational waves 6.6 Multi-messenger astronomy 7 Cosmic Rays and Climate 7.1 Cosmic rays and thunderstorms 7.2 Variations in the flux of cosmic rays 7.3 A correlation between cosmic rays and earthquakes? 8 Cosmic Rays and Life 8.1 Ionization and chemistry of the atmosphere 8.2 The Miller-Urey experiment 8.3 Biological effects of cosmic rays 8.4 Implications on evolution 9 Cosmic Rays and the Exploration of the Universe 10 Cosmic Rays and Archaeology 10.1 Dating techniques 10.2 Muon tomography 11 The Future
£26.59
Springer International Publishing AG Instabilities in Field Theory: A Primer with Applications in Modified Gravity
Book SynopsisThis book presents the most common types of instabilities arising in classical field theories, namely tachyonic, Laplacian, ghost-like or strong coupling instabilities, also commenting on their quantum implications. The authors provide a detailed account on the Ostrogradski theorem and its implications for higher-order time-derivative field theories. After presenting the general concepts and formalism, they dive into its applications to particular field theories, using mainly modified gravity theories as examples. The book is intended for advanced undergraduate/graduate students, but can also be useful for researchers, for having a unified exposition of general results on instabilities in field theory and examples of their applications.Table of ContentsIntroduction to instabilities and some relevant examples.- Ostrogradski theorem and ghosts.- Examples of instabilities in gravity theories.- References.- Solutions.
£33.24
Springer Analytical Mechanics
Book Synopsis
£67.49
Springer Nonlinear FokkerPlanck Flows and their
Book Synopsis- Introduction.- Existence of nonlinear FokkerPlanck flows.- Time dependent FokkerPlanck equations.- Convergence to equilibrium of nonlinear FokkerPlanck flows.- Markov processes associated with nonlinear FokkerPlanck equations.- Appendix.
£41.24
Springer Geometry Topology and Operator Algebras
Book SynopsisGeometric structures, invariants and their uses in physics by A. Cardona and A.F. Reyes-Lega.- . Lectures on the Euler characteristic of affine manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez.- Elliptic Curves by Philip Candelas.- The arithmetic of Calabi-Yau varieties, by Xenia de la Ossa.- Foliations and operator algebras by Georges Skandalis.- Pseudo-differential operators on groups and nonharmonic analysis, by Michael Ruzhansky.- Mathematical Foundations of Topological Matter, by Manuel Asorey.
£62.99
Walter de Gruyter Gravitation und Relativität
Book Synopsis
£33.20
