Mathematical / Computational / Theoretical physics Books

Book SynopsisThe application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com.Trade ReviewFrom the book reviews:“The book is carefully divided into two parts. The first part deals with modeling of statistical systems. The second part is devoted to the analysis of the respective systems. … followed by a section that offers helpful hints and solutions to problems throughout the text, making it easier for students to deepen their understanding and confidence in their newfound knowledge. … topics in each chapter are carefully selected and are well presented, making it a reliable reference for ‘statistical physics.’” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsStatistical Physics is more than Statistical Mechanics.- Part I: Modeling of Statistical Systems.- Random Variables: Fundamentals of Probability Theory and Statistics.- Random Variables in State Space: Classical Statistical Mechanics of Fluids.- Random Fields: Textures and Classical Statistical Mechanics of Spin Systems.- Time-Dependent Random Variables: Classical Stochastic Processes.- Quantum Random Systems.- Changes of External Conditions.- Part II: Analysis of Statistical Systems.- Estimation of Parameters.- Signal Analysis: Estimation of Spectra.- Estimators Based on a Probability Distribution for the Parameters.- Identification of Stochastic Models from Observations.- Estimating the Parameters of a Hidden Stochastic Model.- Statistical Tests and Classification Methods.- Appendix: Random Number Generation for Simulating Realizations of Random Variables.- Problems.- Hints and Solutions.

Read more less

Book SynopsisOne of the driving forces behind much of modern science and technology is the desire to foresee and thereby control the future. In recent years, however, it has become clear that, even in a deterministic world, there is alimit to the accuracy with which we can predict the future. This book details, in a largely nontechnical style, the extent to which we can predict the future development of various physical, biological and socio-economic processes.Table of Contents1. Introduction.- References.- 2. Forecasting Weather and Climate.- 2.1 Weather and Climate.- 2.2 Dynamical Systems and Their Properties.- 2.3 Weather Predictability.- 2.4 Elements of Stationary Random Process Prediction Theory.- 2.5 Predictability of Climatic Processes.- 2.6 Ways to Improve Statistical Forecasting.- 2.7 Utilization of Forecasting Results.- 2.8 Conclusion.- References.- 3. How an Active Autowave Medium Can Be Used to Predict the Future.- 3.1 Prediction.- 3.2 Active Autowave Media.- 3.3 Autowave Propagation in Energy-Restoring Active Media.- 3.4 Dynamics of Autowave Interaction.- 3.5 The External Medium Model and Its Fourier Image.- 3.6 Non-isochronism of Cyclic Processes.- 3.7 Harmonious Modulation and Modulation of Harmonics.- 3.8 The Fourier Image Cleared by the Active Autowave Medium.- References.- 4. Synergetics, Predictability and Deterministic Chaos.- 4.1 Dynamical Chaos.- 4.2 Nonlinearity and Open Systems Behavior.- 4.3 Synergetics and Order Parameters.- 4.4 Strangeness of the Strange Attractors.- 4.5 Dynamical Chaos and Reality.- 4.6 Dynamical Chaos. Gates of Fairyland.- References.- 5. The Information-Theoretic Approach to Assessing Reliability of Forecasts.- 5.1 Assessing Forecasts.- 5.2 Forecasting as the Subject Matter of Information Theory.- 5.3 An Example.- 5.4 Optimization of Forecasting Methods.- 5.5 Properties Shared by Prediction Methods.- 5.6 The Connection Between Discounting and Non-stationarity.- 5.7 Conclusion.- References.- 6. Prediction of Time Series.- 6.1 The Problem.- 6.2 Genesis of Random Phenomena.- 6.3 Time Series Prediction Based on Dynamical Chaos Theory.- 6.4 Prediction of Point Processes.- 6.5 The Nature of Errors Hindering Prediction.- 6.6 Prediction of Strong Earthquakes.- References.- 7. Fundamental and Practical Limits of Predictability.- 7.1 Predictability.- 7.2 Real, Observed, and Model Processes.- 7.3 Degree of Predictability. The Predictability Horizon.- 7.4 Searching for Prediction Models.- 7.5 Limits to Predictability.- 7.6 Dynamical Analogs to Social and Economic Phenomena.- 7.7 Conclusion.- References.- 8. The Future is Foreseeable but not Predictable: The ‘Oedipus Effect’ in Social Forecasting.- 8.1 Historical Background.- 8.2 The ‘Oedipus Effect’ in Social Forecasting.- 8.3 The Problem of Foresight and Prediction in Globalistics.- 8.4 The Problem of Foreseeing and Predicting the Development of the Former Soviet Society.- References.- Appendix A: Looking Back on the August 1991 Coup.- Appendix B: Looking Ahead.- 9. The Self-Organization of American Society in Presidential and Senatorial Elections.- 9.1 Historical Background.- 9.2 The American Presidential Election: Formal Analysis.- 9.3 Midterm Senatorial Elections: Formal Analysis.- 9.4 Discussion.- References.- 10. Problems of Predictability in Ethnogenic Studies.- References.

Read more less

Table of Contents18 Elementary Group Theory.- 18.1 The group axioms; examples.- 18.2 Elementary consequences of the axioms; further definitions.- 18.3 Isomorphism.- 18.4 Permutation groups.- 18.5 Homomorphisms; normal subgroups.- 18.6 Cosets.- 18.7 Factor groups.- 18.8 The Law of Homomorphism.- 18.9 The structure of cyclic groups.- 18.10 Translations, inner automorphisms.- 18.11 The subgroups of ?4.- 18.12 Generators and relations; free groups.- 18.13 Multiply periodic functions and crystals.- 18.14 The space and point groups.- 18.15 Direct and semidirect products of groups; symmorphic space groups.- 19 Continuous Groups.- 19.1 Orthogonal and rotation groups.- 19.2 The rotation group SO(3); Euler’s theorem.- 19.3 Unitary groups.- 19.4 The Lorentz groups.- 19.5 Group manifolds.- 19.6 Intrinsic coordinates in the manifold of the rotation group.- 19.7 The homomorphism of SU(2) onto SO(3).- 19.8 The homomorphism of SL(2, ?) onto the proper Lorentz group ? p.- 19.9 Simplicity of the rotation and Lorentz groups.- 20 Group Representations I: Rotations and Spherical Harmonics.- 20.1 Finite-dimensional representations of a group.- 20.2 Vector and tensor transformation laws.- 20.3 Other group representations in physics.- 20.4 Infinite-dimensional representations.- 20.5 A simple case: SO(2).- 20.6 Representations of matrix groups on X?.- 20.7 Homogeneous spaces.- 20.8 Regular representations.- 20.9 Representations of the rotation group SO(3).- 20.10 Tesseral harmonics; Legendre functions.- 20.11 Associated Legendre functions.- 20.12 Matrices of the irreducible representations of SO(3); the Euler angles.- 20.13 The addition theorem for tesseral harmonics.- 20.14 Completeness of the tesseral harmonics.- 21 Group Representations II: General; Rigid Motions; Bessel Functions.- 21.1 Equivalence; unitary representations.- 21.2 The reduction of representations.- 21.3 Schur’s Lemma and its corollaries.- 21.4 Compact and noncompact groups.- 21.5 Invariant integration; Haar measure.- 21.6 Complete system of representations of a compact group.- 21.7 Homogeneous spaces as configuration spaces in physics.- 21.8 M2 and related groups.- 21.9 Representations of M2.- 21.10 Some irreducible representations.- 21.11 Bessel functions.- 21.12 Matrices of the representations.- 21.13 Characters.- 22 Group Representations and Quantum Mechanics.- 22.1 Representations in quantum mechanics.- 22.2 Rotations of the axes.- 22.3 Ray representations.- 22.4 A finite-dimensional case.- 22.5 Local representations.- 22.6 Origin of the two-valued representations.- 22.7 Representations of SU(2) and SL(2, ?).- 22.8 Irreducible representations of SU(2).- 22.9 The characters of SU(2).- 22.10 Functions of z and z?.- 22.11 The finite-dimensional representations of SL(2, ?).- 22.12 The irreducible invariant subspaces of X? for SL(2, ?).- 22.13 Spinors.- 23 Elementary Theory of Manifolds.- 23.1 Examples of manifolds; method of identification.- 23.2 Coordinate systems or charts; compatibility; smoothness.- 23.3 Induced topology.- 23.4 Definition of manifold; Hausdorff separation axiom.- 23.5 Curves and functions in a manifold.- 23.6 Connectedness; components of a manifold.- 23.7 Global topology; homotopic curves; fundamental group.- 23.8 Mechanical linkages: Cartesian products.- 24 Covering Manifolds.- 24.1 Definition and examples.- 24.2 Principles of lifting.- 24.3 Universal covering manifold.- 24.4 Comments on the construction of mathematical models.- 24.5 Construction of the universal covering.- 24.6 Manifolds covered by a given manifold.- 25 Lie Groups.- 25.1 Definitions and statement of objectives.- 25.2 The expansions of m(·, ·) and l(·, ·).- 25.3 The Lie algebra of a Lie group.- 25.4 Abstract Lie algebras.- 25.5 The Lie algebras of linear groups.- 25.6 The exponential mapping; logarithmic coordinates.- 25.7 An auxiliary lemma on inner automorphisms; the mappings Ad?.- 25.8 Auxiliary lemmas on formal derivatives.- 25.9 An auxiliary lemma on the differentiation of exponentials.- 25.10 The Campbell-Baker-Hausdorf (CBH) formula.- 25.11 Translation of charts; compatibility; G as an analytic manifold.- 25.12 Lie algebra homomorphisms.- 25.13 Lie group homomorphisms.- 25.14 Law of homomorphism for Lie groups.- 25.15 Direct and semidirect sums of Lie algebras.- 25.16 Classification of the simple complex Lie algebras.- 25.17 Models of the simple complex Lie algebras.- 25.18 Note on Lie groups and Lie algebras in physics.- Appendix to Chapter 25—Two nonlinear Lie groups.- 26 Metric and Geodesics on a Manifold.- 26.1 Scalar and vector fields on a manifold.- 26.2 Tensor fields.- 26.3 Metric in Euclidean space.- 26.4 Riemannian and pseudo-Riemannian manifolds.- 26.5 Raising and lowering of indices.- 26.6 Geodesies in a Riemannian manifold.- 26.7 Geodesies in a pseudo-Riamannian manifold M.- 26.8 Geodesies; the initial-value problem; the Lipschitz condition.- 26.9 The integral equation; Picard iterations.- 26.10 Geodesies; the two-point problem.- 26.11 Continuation of geodesies.- 26.12 Affmely connected manifolds.- 26.13 Riemannian and pseudo-Riemannian covering manifolds.- 27 Riemannian, Pseudo-Riemannian, and Affinely Connected Manifolds.- 27.1 Topology and metric.- 27.2 Geodesic or Riemannian coordinates.- 27.3 Normal coordinates in Riemannian and pseudo-Riemannian manifolds.- 27.4 Geometric concepts; principle of equivalence.- 27.5 Covariant differentiation.- 27.6 Absolute differentiation along a curve.- 27.7 Parallel transport.- 27.8 Orientability.- 27.9 The Riemann tensor, general; Laplacian and d’Alembertian.- 27.10 The Riemann tensor in a Riemannian or pseudo-Riemannian manifold.- 27.11 The Riemann tensor and the intrinsic curvature of a manifold.- 27.12 Flatness and the vanishing of the Riemann tensor.- 27.13 Eisenhart’s analysis of the Stäckel systems.- 28 The Extension of Einstein Manifolds.- 28.1 Special relativity.- 28.2 The Einstein gravitational field equations.- 28.3 The Schwarzschild charts.- 28.4 The Finkelstein extensions of the Schwarzschild charts.- 28.5 The Kruskal extension.- 28.6 Maximal extensions; geodesic completeness.- 28.7 Other extensions of the Schwarzschild manifolds.- 28.8 The Kerr manifolds.- 28.9 The Cauchy problem.- 28.10 Concluding remarks.- 29 Bifurcations in Hydrodynamic Stability Problems.- 29.1 The classical problems of hydrodynamic stability.- 29.2 Examples of bifurcations in hydrodynamics.- 29.3 The Navier-Stokes equations.- 29.4 Hilbert space formulation.- 29.5 The initial-value problem; the semiflow in ?.- 29.6 The normal modes.- 29.7 Reduction to a finite-dimensional dynamical system.- 29.8 Bifurcation to a new steady state.- 29.9 Bifurcation to a periodic orbit.- 29.10 Bifurcation from a periodic orbit to an invariant torus.- 29.11 Subharmonic bifurcation.- Appendix to Chapter 29—Computational details for the invariant torus.- 30 Invariant Manifolds in the Taylor Problem.- 30.1 Survey of the Taylor problem to 1968.- 30.2 Calculation of invariant manifolds.- 30.3 Cylindrical coordinates.- 30.4 The Hilbert space.- 30.5 Separation of variables in cylindrical coordinates.- 30.6 Results to date for the Taylor problem.- Appendix to Chapter 30—The matrices in Eagles’ formulation.- 31 The Early Onset of Turbulence.- 31.1 The Landau-Hopf model.- 31.2 The Hopf example.- 31.3 The Ruelle-Takens model.- 31.4 The co-limit set of a motion.- 31.5 Attractors.- 31.6 The power spectrum for motions in ?n.- 31.7 Almost periodic and aperiodic motions.- 31.8 Lyapounov stability.- 31.9 The Lorenz system; the bifurcations.- 31.10 The Lorenz attractor; general description.- 31.11 The Lorenz attractor; aperiodic motions.- 31.12 Statistics of the mapping f and g.- 31.13 The Lorenz attractor; detailed structure I.- 31.14 The symbols [i, j] of Williams.- 31.15 Prehistories.- 31.16 The Lorenz attractor; detailed structure II.- 31.17 Existence of 1-cells in F.- 31.18 Bifurcation to a strange attractor.- 31.19 The Feigenbaum model.- Appendix to Chapter 31 (Parts A-H)—Generic properties of systems:.- 31.A Spaces of systems.- 31.B Absence of Lebesgue measure in a Hilbert space.- 31.C Generic properties of systems.- 31.D Strongly generic; physical interpretation.- 31.E Peixoto’s theorem.- 31.F Other examples of generic and nongeneric properties.- 31.G Lack of correspondence between genericity and Lebesgue measure 308 31.H Probability and physics.- References.

Read more less

Book SynopsisAt the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory.Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications.The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.Trade Review“Aimed at the advanced graduate student or a practitioner of high energy theory interested in the subject, the book begins with a review of non-abelian gauge theory and its conventional Feynman methods before immediately delving into on-shell recursion relations of BCFW (Britto-Cachazo-Feng-Witten) and factorization properties. … Of particular usefulness to the student are the exercises and an entire appendix dedicated to their detailed solutions.” (Yang-Hui He, zbMATH 1315.81005, 2015)Table of ContentsIntroduction and Basics.- Tree-Level Techniques.- Loop-Level Structure.- Advanced Topics.- Renormalization Properties of Wilson Loops.- Conventions and Useful Formulae.- Solutions to the Exercises.- References.

Read more less

Book SynopsisThis book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.Table of ContentsErgodicity – A Basic Concept.- Large Deviations in Statistical Mechanics: Rigorous and Non-Rigorous.- Large Deviation Techniques for Long-Range Interactions.- Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium Phenomena and Back.- Stochastic Fluctuations in Deterministic Systems.- Large Deviation and Disordered Systems.- Large Deviations in Turbulence.- Ergodicity Breaking Challenges Monte Carlo Methods.- Anomalous Diffusion: Deterministic and Stochastic Perspectives.- The Use of Fluctuation Relations for the Analysis of Free-Energy Landscapes.

Read more less

Book SynopsisThis monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem.This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra.Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.Table of ContentsPreface.- Conventions.- List of Symbols.- 1 Symmetric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravariant spinors.- 5 Enveloping algebras.- 6 Weil algebras.- 7 Quantum Weil algebras.- 8 Applications to reductive Lie algebras.- 9 D(g; k) as a geometric Dirac operator.- 10 The Hopf–Koszul–Samelson Theorem.- 11 The Clifford algebra of a reductive Lie algebra.- A Graded and filtered super spaces.- B Reductive Lie algebras.- C Background on Lie groups.- References.- Index.

Read more less

Book SynopsisThe German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". Its aim was, to explain the fundamental notions of the Theory of Groups and their Representations, and the application of this theory to the Quantum Mechanics of Atoms and Molecules. The book was mainly written for the benefit of physicists who were supposed to be familiar with Quantum Mechanics. However, it turned out that it was also used by. mathematicians who wanted to learn Quantum Mechanics from it. Naturally, the physical parts were too difficult for mathematicians, whereas the mathematical parts were sometimes too difficult for physicists. The German language created an additional difficulty for many readers. In order to make the book more readable for physicists and mathe­ maticians alike, I have rewritten the whole volume. The changes are most notable in Chapters 1 and 6. In Chapter t, I have tried to give a mathematically rigorous exposition of the principles of Quantum Mechanics. This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932. Chapter 6, on Molecule Spectra, was too much condensed in the German edition. I hope it is now easier to understand. In Chapter 2-5 too, numerous changes were made in order to make the book more readable and more useful.Table of Contents1. Fundamental Notions of Quantum Mechanics.- § 1. Wave Functions.- § 2. Hilbert Spaces.- § 3. Linear Operators.- § 4. Hypermaximal Operators.- § 5. Separation of Variables.- § 6. One Electron in a Central Field.- § 7. Perturbation Theory.- § 8. Angular Momentum and Infinitesimal Rotations.- 2. Groups and Their Representations.- § 9. Linear Transformations.- § 10. Groups.- § 11. Equivalence and Reducibility of Representations.- § 12. Representations of Abelian Groups. Examples.- § 13. Uniqueness Theorems.- § 14. Kronecker’s Product Transformation.- § 15. The Operators Commuting with all Operators of a Given Representation.- § 16. Representations of Finite Groups.- § 17. Group Characters.- 3. Translations, Rotations and Lorentz Transformations.- § 18. Lie Groups and their Infinitesimal Transformations.- A. Lie Groups.- B. One-dimensional Lie Groups and Semi-Groups.- C. Causality and Translations in Time.- D. The Lie Algebra of a Lie Group.- E. Representations of Lie Groups.- § 19. The Unitary Groups SU(2) and the Rotation Group O3.- § 20. Representations of the Rotation Group O3.- § 21. Examples and Applications.- A. The Product Representation ?j × ?j’.- B. The Clebsch-Gordan Series.- C. Applications of (21.1).- D. The Reflection Character.- § 22. Selection and Intensity Rules.- § 23. The Representations of the Lorentz Group.- A. The Group SL(2) and the Restricted Lorentz Group.- B. Infinitesimal Transformations.- C. The Relation between World Vectors and Spinors.- IV. The Spinning Electron.- § 24. The Spin.- § 25. The Wave Function of the Spinning Electron.- A. Pauli’s Pair of Functions (?1, ?2).- B. Transformation of the Pair (?1, ?2).- C. Infinitesimal Rotations.- D. The Angular Momenta.- E. The Doublet Splitting of the Alkali Terms.- G. The Inversion s.- § 26. Dirac’s Wave Equation.- § 27. Two-Component Spinors.- A. Dirac’s Equation Rewritten.- B. Weyl’s Equation.- § 28. The Several Electron Problem. Multiplet Structure. Zeeman Effect.- V. The Group of Permutations and the Exclusion Principle.- § 29. The Resonance of Equal Particles.- § 30. The Exclusion Principle and the Periodical System.- § 31. The Eigenfunctions of the Atom.- § 32. The Calculation of the Energy Values.- § 33. Pure Spin Functions and their Transformation under Rotations and Permutations.- § 34. Representations of the Symmetric Group Sn.- VI. Molecule Spectra.- § 35. The Quantum Numbers of the Molecule.- § 36. The Rotation Levels.- § 37. The Case of Two Equal Nuclei.- Author and Subject Index.

Read more less

Book SynopsisIn structure mechanics analysis, finite element methods are now well estab­ lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap­ proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require­ ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.Table of ContentsNotations.- 1. Elliptic Equations of Order 2: Some Standard Finite Element Methods.- 1.1. A 1-Dimensional Model Problem: The Basic Notions.- 1.2. A 2-Dimensional Problem.- 1.3. The Finite Element Equations.- 1.4. Standard Examples of Finite Element Methods.- 1.4.1. Example 1: The P1-Triangle (Courant’s Triangle).- 1.4.2. Example 2: The P2-Triangle.- 1.4.3. Example 3: The Q1-Quadrangle.- 1.4.4. Example 4: The Q2-Quadrangle.- 1.4.5. A Variational Crime: The P1 Nonconforming Element.- 1.5. Mixed Formulation and Mixed Finite Element Methods for Elliptic Equations.- 1.5.1. The One Dimensional Problem.- 1.5.2. A Two Dimensional Problem.- 2. Upwind Finite Element Schemes.- 2.1. Upwind Finite Differences.- 2.2. Modified Weighted Residual (MWR).- 2.3. Reduced Integration of the Advection Term.- 2.4. Computation of Directional Derivatives at the Nodes.- 2.5. Discontinuous Finite Elements and Mixed Interpolation.- 2.6. The Method of Characteristics in Finite Elements.- 2.7. Peturbation of the Advective Term: Bredif (1980).- 2.8. Some Numerical Tests and Further Comments.- 2.8.1. One Dimensional Stationary Advection Equation (56).- 2.8.2. Two Dimensional Stationary Advection Equation.- 2.8.3. Time Dependent Advection.- 3. Numerical Solution of Stokes Equations.- 3.1. Introduction.- 3.2. Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 3.2.1. uh: P1 Nonconforming Triangle (§1-4-5); ph: Piecewise Constant.- 3.2.2. uh: P2 Triangle ph: P0 (Piecewise Constant).- 3.2.3. uh: “P2+bubble” Triangle (or Modified P2); ph: Discontinuous P1.- 3.2.4. uh: Q2 Quadrangle; ph: Q1 Discontinuous.- 3.2.5. Numerical Solution by Penalty Methods.- 3.2.6. Numerical Results and Further Comments.- 3.3. Velocity—Pressure Formulations: Continuous Approximation of the Pressure and Velocity.- 3.3.1. Introduction.- 3.3.2. Examples and Error Estimates.- 3.3.3. Decomposition of the Stokes Problem.- 3.4. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 3.5. Vorticity Stream-Function Formulation: Decompositions of the Biharmonic Problem.- 4. Navier-Stokes Equations: Accuracy Assessments and Numerical Results.- 4.1. Remarks on the Formulation.- 4.2. A review of the Different Methods.- 4.2.1 Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure.- 4.2.2. Velocity—Pressure Formulations: Continuous Approximations of the Pressure.- 4.2.3. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity.- 4.2.4. Vorticity Stream-Function Formulation.- 4.3. Some Numerical Tests.- 4.3.1. The Square Wall Driven Cavity Flow.- 4.3.2. An Engineering Problem: Unsteady 2-D Flow Around and In an Air-Intake.- 5. Computational Problems and Bookkeeping.- 5.1. Mesh Generation.- 5.2. Solution of the Nonlinear Problems.- 5.2.1. Successive Approximations (or Linearization) with Under Relaxation.- 5.2.2. Newton-Raphson Algorithm.- 5.2.3. Conjugate Gradient Method (with Scaling) for Nonlinear Problems.- 5.2.4. A Splitting Technique for the Transient Problem.- 5.3. Iterative and Direct Solvers of Linear Equations.- 5.3.1. Successive Over Relaxation.- 5.3.2. Cholesky Factorizations.- 5.3.3. Out of Core Factorizations.- 5.3.4. Preconditioned Conjugate Gradient.- Appendix 2. Numerical Illustration.- Three Dimensional Case.- References.

Read more less

Book SynopsisAnimationen im Internet veranschaulichen z. B. die Wellengleichung durch eine schwingende Membran, die Wärmeleitung durch eine abnehmende Temperaturverteilung und die Potentialgleichung durch ein von der Randbelegung aufgeprägtes Potenzial. Welche Methoden verbergen sich dahinter, wie erzeugt man diese Animationen? Darauf soll der Leser eine erschöpfende Antwort geben können. Auf ausführliche, formale Beweise wird verzichtet. Die Begriffe werden mittels Beispielen und Graphiken in ihren Grundideen veranschaulicht und motiviert. Der Leser soll Hintergrundwissen und Lösungskompetenz bekommen, damit er sich nicht mit der Formelmanipulation zufrieden geben muss. Studierende sollen in die Lage versetzt werden, Probleme, die sich aus ihrer Bachelor/Masterarbeit oder aus den Anwendungen ergeben, zu bearbeiten. Table of ContentsTensoren.- Tensorfelder.- Kurven- und Flächenintegrale.- Orthogonale Systeme von Polynomen.- Lineare Differentialgleichungen im Komplexen.- Stabilität dynamischer Systeme.- Partielle Differentialgleichungen.- Gleichungen erster Ordnung.- Gleichungen zweiter Ordnung.- Wellengleichung.- Wärmeleitungsgleichung.- Potentialgleichung.

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisA thorough introduction to the computation of celestial mechanics, covering everything from astronomical and computational theory to the construction of rapid and accurate applications programs. The book supplies the necessary knowledge and software solutions for determining and predicting positions of the Sun, Moon, planets, minor planets and comets, solar eclipses, stellar occultations by the Moon, phases of the Moon and much more. This completely revised edition takes advantage of C++, and individual applications may be efficiently realized through the use of a powerful module library. The accompanying CD-ROM contains the complete, fully documented and commented source codes as well as executable programs for Windows 98/2000/XP and LINUX.Table of Contents1 Introduction.- 2 Coordinate Systems.- 3 Calculation of Rising and Setting Times.- 4 Cometary Orbits.- 5 Special Perturbations.- 6 Planetary Orbits.- 7 Physical Ephemerides of the Planets.- 8 The Orbit of the Moon.- 9 Solar Eclipses.- 10 Stellar Occultations.- 11 Orbit Determination.- 12 Astrometry.- A.1 The Accompanying CD-ROM.- A.1.1 Contents.- A.1.2 System Requirements.- A.1.3 Executing the Programs.- A.2 Compiling and Linking the Programs.- A.2.1 General Advice on Computer-Specific Modifications.- A.2.2 Microsoft Visual C++ for Windows 98/2000/XP.- A.2.3 GNU C++ for Linux.- A.3 List of the Library Functions.- Symbols.

Read more less

Book SynopsisQuantum effects may be modelled by means of stochastic perturbation of non-linear partial differential (field) equations. Contributions to this field of research are collected in this volume. Finite dimensional stochastically perturbed Hamiltonian systems and infinite dimensional white noise analysis are treated. The main part concerns problems encountered in deterministic equations. Papers treat the existence of solutions for given initial data, the existence of non-linear bound states or solitary waves including a thorough discussion of various approaches to stability, and global properties (e.g. time decay properties) for non-linear wave equations. This volume provides a good survey of present-day research in non-linear problems of quantum theory for researchers and graduate students.Table of ContentsSome remarks on stochastically perturbed (Hamiltonian) systems.- Stability of ground states for nonlinear classical field theories.- A note on solutions of two-dimensional semilinear elliptic vector-field equations with strong nonlinearity.- Some remarks on the nonlinear Schrödinger equation in the subcritical case.- The Cauchy problem for the Dirac equation with cubic nonlinearity in three space dimensions.- The Cauchy problem for the non-linear Klein-Cordon equation.- Conformal invariance and time decay for nonlinear wave equations.- Energy forms and white noise analysis.- Principles of solitary wave stability.

Read more less

Book SynopsisDer beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für das Bachelor-/Master- oder Diplomstudium maßgeblichen Gebiete ab. Jeder Band vermittelt gut durchdacht das im jeweiligen Semester nötige theoretisch-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes. Der zweite Teil des fünften Bandes befasst sich mit Anwendungen und mit dem Ausbau der im ersten Teil entwickelten Konzepte der Quantenmechanik.Die vorliegende neue Auflage enthält einige neue Aufgaben, wurde grundlegend überarbeitet und durch einige Zusatzkapitel zur Streutheorie ergänzt. Sie ermöglicht durch die zweifarbige Darstellung einen sehr übersichtlichen und schnellen Zugriff auf den Lehrstoff.Table of ContentsQuantentheorie des Drehimpulses.- Zentralpotential.- Näherungsmethoden.- Mehr-Teilchen-Systeme.- Streutheorie.- Lösungen der Übungsaufgaben.

Read more less

Book SynopsisThis guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and new paragraphs, new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.Trade Review“Russian scholars Bronshtein and Semendyayev created a math classic over seven decades ago. … This new Springer edition details over 1,500 entries in its table of contents, including new entries for analytical geometry, Lie groups and Lie algebra, nonlinear optimization, and computer algebra systems. … Summing Up: Recommended. All mathematics library collections.” (K. L. Swetland, Choice, Vol. 53 (11), July, 2016)Table of ContentsArithmetics.- Functions.- Geometry.- Linear Algebra.- Algebra and Discrete Mathematics.- Differentiation.- Infinite Series.- Integral Calculus.- Differential Equations.- Calculus of Variations.- Linear Integral Equations.- Functional Analysis.- Vector Analysis and Vector Fields.- Function Theory.- Integral Transformations.- Probability Theory and Mathematical Statistics.- Dynamical Systems and Chaos.- Optimization.- Numerical Analysis.- Computer Algebra Systems-Example Mathematica.

Read more less

Book SynopsisThis second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.The main difference between the second and first English editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.Table of Contents9 Continuous Mappings (General Theory).- 10 Differential Calculus from a General Viewpoint.- 11 Multiple Integrals.- 12 Surfaces and Differential Forms in Rn.- 13 Line and Surface Integrals.- 14 Elements of Vector Analysis and Field Theory.- 15 Integration of Differential Forms on Manifolds.- 16 Uniform Convergence and Basic Operations of Analysis.- 17 Integrals Depending on a Parameter.- 18 Fourier Series and the Fourier Transform.- 19 Asymptotic Expansions.- Topics and Questions for Midterm Examinations.- Examination Topics.- Examination Problems (Series and Integrals Depending on a Parameter).- Intermediate Problems (Integral Calculus of Several Variables).- Appendices: A Series as a Tool (Introductory Lecture).- B Change of Variables in Multiple Integrals.- C Multidimensional Geometry and Functions of a Very Large Number of Variables.- D Operators of Field Theory in Curvilinear Coordinates.- E Modern Formula of Newton–Leibniz.- References.- Index of Basic Notation.- Subject Index.- Name Index.

Read more less

Book SynopsisThis text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.Trade Review“This volume of Lecture Notes in Physics presents in three parts the topics of Grassmann algebra and its applications and the subject of supermathematics, where commuting and anticommuting variables are treated on equal footing, and its applications. … it may be of interest to those already in the field who want to expand their knowledge in both the underlying mathematics and its applications in physics.” (Moorad Alexanian, Mathematical Reviews, January, 2017)“Each chapter contains a set of illustrating problems supplied with answers in the book's end. Thus, this monograph can be used for practical teaching as well.” (Eugene Postnikov, zbMATH 1345.81003, 2016)Table of ContentsPart I Grassmann Variables and Applications.- Part II Supermathematics.- Part III Supersymmetry in Statistical Physics.- Summary and Additional Remarks.- References.- Solutions.- Index.

Read more less

Book SynopsisThis new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.Trade ReviewFrom the reviews: "We find here a book where the theory is developed with rigours in parallel with a strong physical intuition. Comparison with experiments and simulations are always proposed and carefully analysed. The book contains at the end a very rich and complete bibliography ... I warmly encourage everyone interested in boundary-layer theory to have this book in his bookcase." Physicalia "... I do recommend the book highly, especially for its long historical perspective, including all the diagrams comparing theory and experiment that remind us that engineering is practical ..." SIAM ReviewsTable of ContentsPart I. Fundamentals of Viscous Flows.- 1. Some Features of Viscous Flows.- 2. Fundamentals of Boundary–Layer Theory.- 3. Field Equations for Flows of Newtonian Fluids.- 4. General Properties of the Equations of Motion.- 5. Exact Solutions of the Navier–Stokes Equations.- Part II. Laminar Boundary Layers.- 6 Boundary–Layer Equations in Plane Flow; Plate Boundary Layer.- 7 General Properties and Exact Solutions of the Boundary–Layer Equations for Plane Flows.- 8 Approximate Methods for Solving the Boundary–Layer Equations for Steady Plane Flows.- 9 Thermal Boundary Layers Without Coupling of the Velocity Field to the Temperature Field.- 10 Thermal Boundary Layers with Coupling of the Velocity Field to the Temperature Field.- 11. Boundary–Layer Control (Suction/Blowing).- 12. Axisymmetric and Three–Dimensional Boundary Layers.- 13. Unsteady Boundary Layers.- 14. Extensions to the Prandtl Boundary–Layer Theory.- Part III. Laminar–Turbulent Transition.- 15. Onset of Turbulence (Stability Theory).- Part IV. Turbulent Boundary Layers.- 16. Fundamentals of Turbulent Flows.- 17. Internal Flows.- 18. Turbulent Boundary Layers Without Coupling of the Velocity Field to the Temperature Field.- 19. Turbulent Boundary Layers with Coupling of the Velocity Field to the Temperature Field.- 20. Axisymmetric and Three–Dimensional Turbulent Boundary Layers.- 21. Unsteady Turbulent Boundary Layers.- 22. Turbulent Free Shear Flows.- Part V. Numerical Methods in Boundary–Layer Theory.- 23. Numerical Integration of the Boundary–Layer Equations.

Read more less

Book SynopsisAs a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.Table of ContentsRemarks on Mathematial Physics.- 1 Introduction.- 2 Dynamical Systems.- 3 Ordinary Differential Equations.- 4 Linear Dynamics.- 5 Classification of Linear Flows.- 6 Hamiltonian Equations and Symplectic Group.- 7 Stability Theory.- 8 Variational Principles.- 9 Ergodic Theory.- 10 Symplectic Geometry.- 11 Motion in a Potential.- 12 Scattering Theory.- 13 Integrable Systems and Symmetries.- 14 Rigid and Non-Rigid Bodies.- 15 Perturbation Theory.- 16 Relativistic Mechanics.- 17 Symplectic Topology.- A Topological Spaces and Manifolds.- B Differential Forms.- C Convexity and Legendre Transform.- D Fixed Point Theorems, and Results about Inverse Images.- E Group Theory.- F Bundles, Connection, Curvature.- G Morse Theory.- H Solutions of the Exercises.- Bibiography.- Index of Proper Names.- Table of Symbols.- Image Credits.- Index.

Read more less

Book SynopsisThis textbook introduces modern techniques based on computer simulation to study materials science. It starts from first principles calculations enabling to calculate the physical and chemical properties by solving a many-body Schroedinger equation with Coulomb forces. For the exchange-correlation term, the local density approximation is usually applied. After the introduction of the first principles treatment, tight-binding and classical potential methods are briefly introduced to indicate how one can increase the number of atoms in the system. In the second half of the book, Monte Carlo simulation is discussed in detail. Problems and solutions are provided to facilitate understanding. Readers will gain sufficient knowledge to begin theoretical studies in modern materials research. This second edition includes a lot of recent theoretical techniques in materials research. With the computers power now available, it is possible to use these numerical techniques to study various physical and chemical properties of complex materials from first principles. The new edition also covers empirical methods, such as tight-binding and molecular dynamics.Table of ContentsAb-Initio Methods.- Tight-Binding Methods.- Empirical Methods and Coarse-Graining.- Monte Carlo Methods.- Quantum Monte Carlo (QMC) Methods.

Read more less

Book SynopsisThis second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis. The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics. The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.Trade Review“This is a thorough and easy-to-follow text for a beginning course in real analysis … . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. … Will be popular with students because of the detailed explanations and the worked examples.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)Table of Contents1 Some General Mathematical Concepts and Notation: 1.1 Logical Symbolism.- 1.2 Sets and Elementary Operations on them.- 1.3 Functions.- 1.4 Supplementary Material.- 2 The Real Numbers: 2.1 Axioms and Properties of Real Numbers.- 2.2 Classes of Real Numbers and Computations.- 2.3 Basic Lemmas on Completeness.- 2.4 Countable and Uncountable Sets.- 3 Limits: 3.1 The Limit of a Sequence.- 3.2 The Limit of a Function.- 4 Continuous Functions: 4.1 Basic Definitions and Examples.- 4.2 Properties of Continuous Functions.- 5 Differential Calculus: 5.1 Differentiable Functions.- 5.2 The Basic Rules of Differentiation.- 5.3 The Basic Theorems of Differential Calculus.- 5.4 Differential Calculus Used to Study Functions.- 5.5 Complex Numbers and Elementary Functions.- 5.6 Examples of Differential Calculus in Natural Science.- 5.7 Primitives.- 6 Integration: 6.1 Definition of the Integral.- 6.2 Linearity, Additivity and Monotonicity of the Integral.- 6.3 The Integral and the Derivative.- 6.4 Some Applications of Integration.- 6.5 Improper Integrals.- 7 Functions of Several Variables: 7.1 The Space Rm and its Subsets.- 7.2 Limits and Continuity of Functions of Several Variables.- 8 Differential Calculus in Several Variables: 8.1 The Linear Structure on Rm.- 8.2 The Differential of a Function of Several Variables.- 8.3 The Basic Laws of Differentiation.- 8.4 Real-valued Functions of Several Variables.- 8.5 The Implicit Function Theorem.- 8.6 Some Corollaries of the Implicit Function Theorem.- 8.7 Surfaces in Rn and Constrained Extrema.- Some Problems from the Midterm Examinations: 1. Introduction to Analysis (Numbers, Functions, Limits).- 2. One-variable Differential Calculus.- 3. Integration. Introduction to Several Variables.- 4. Differential Calculus of Several Variables.- Examination Topics: 1. First Semester: 1.1. Introduction and One-variable Differential Calculus.- 2. Second Semester: 2.1. Integration. Multivariable Differential Calculus.- Appendices: A Mathematical Analysis (Introductory Lecture).- B Numerical Methods for Solving Equations (An Introduction).- C The Legendre Transform (First Discussion).- D The Euler–Maclaurin Formula.- E Riemann–Stieltjes Integral, Delta Function, and Generalized Functions.- F The Implicit Function Theorem (An Alternative Presentation).- References.- Subject Index.- Name Index.

Read more less

Book SynopsisDieses Übungsbuch enthält zahlreiche Aufgaben zum Inhalt einer Einführungsvorlesung Physik. Mithilfe von ausführlichen Lösungen und Erklärungen lernen und üben Studierende die Anwendung physikalischer Rechenmethoden und die hierfür erforderliche Mathematik. Vor allem in Kombination mit dem Lehrbuch Physik für Studierende der Biowissenschaften, Chemie und Medizin bildet es eine ideale Basis für die Klausurvorbereitung und weiterführende Vorlesungen.Der erste Teil des Buches bietet Übungsserien mit Aufgaben, die entsprechend dem Inhalt typischer Physikvorlesungen strukturiert sind und dabei Themen von der klassischen Mechanik bis hin zur Atom- und Quantenphysik abdecken. Jede Übungsserie besteht aus einem Verständnisteil und einem Übungsteil, der durch anwendungsorientierte Aufgaben aus Biowissenschaften, Chemie und Medizin ergänzt wird.Das Gelernte kann dann anhand des zweiten Teils überprüft werden, der aus verschiedenen Testserien besteht: Hier sind gemischte Aufgaben aus den jeweiligen Inhalten der zwei Semester enthalten, wie sie auch in Physikklausuren zu finden sind.Table of ContentsMathematische Grundlagen.- Klassische Mechanik.- Zustandsformen der Materie.- Thermodynamik.- Schwingungen.- Wellen.- Optik.- Klassische Elektrodynamik.- Atom- und Quantenphysik.- Testserien Physik I.- Testserien Physik II.

Read more less

Book SynopsisThis book is the second edition of an excellent undergraduate-level overview of classical and modern physics, intended for students of physics and related subjects, and also perfectly suited for the education of physics teachers. The twelve-chapter book begins with Newton’s laws of motion and subsequently covers topics such as thermodynamics and statistical physics, electrodynamics, special and general relativity, quantum mechanics and cosmology , the standard model and quantum chromodynamics. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with standard mathematics.An important addition in this second edition is a set of exercises and problems, distributed throughout the book. Some of the problems aim to complement the text, others to provide readers with additional useful tools for tackling new or more advanced topics. Furthermore, new topics have been added in several chapters; for example, the discovery of extra-solar planets from the wobble of their mother stars, a discussion of the Landauer principle relating information erasure to an increase of entropy, quantum logic, first order quantum corrections to the ideal gas equation of state due to the Fermi-Dirac and Bose-Einstein statistics. Both gravitational lensing and the time-correction in geo-positioning satellites are explained as theoretical applications of special and general relativity. The discovery of gravitational waves, one of the most important achievements of physical sciences, is presented as well. Professional scientists, teachers, and researchers will also want to have this book on their bookshelves, as it provides an excellent refresher on a wide range of topics and serves as an ideal starting point for expanding one’s knowledge of new or unfamiliar fields. Readers of this book will not only learn much about physics, they will also learn to love it.Trade ReviewFrom the reviews of the first edition:Selected by Choice magazine as an "Outstanding Academic Title" for 2014“This is a very high-quality presentation. The writing is lucid, and the theoretical discussions are easy to follow for anyone comfortable with the mathematics. … the work is a valuable addition to college libraries. Professionals and researchers will also want it on their bookshelves; it provides an excellent refresher on a wide range of topics and can serve as a good starting point for expanding knowledge of new or unfamiliar subjects. Summing Up: Highly recommended. Lower-division undergraduates and above.” (A. Spero, Choice, Vol. 51 (9), May, 2014)“It describes all the major developments and theories regarding the description of the universe we live on, from the very small to the very large. … I highly recommend this book to any physicist. It will not only be a fun and an easy read but also a useful revision of all the main concepts in physics. Undergraduate and graduate physics students definitely should read it. … appropriate for scientists in other fields who have a genuine interest for physics.” (Monica Pierri-Galvao, Contemporary Physics, April, 2014)Table of ContentsGravitation and Newton Laws.- Entropy, Statistical Physics and Information.- Electromagnetism and Maxwell's Equations.- Electromagnetic Waves.- Special Theory of Relativity.- Atoms and Quantum Theory.- Quantum Electrodynamics.- Fermi-Dirac and Bose-Einstein Statistics.- Four Fundamental Forces.- General Relativity and Cosmology.- Unification of the Forces of Nature.- Physics and Life.

Read more less

Book Synopsis Das vorliegende Lehrbuch zur Mechanik und Wärmelehre richtet sich an Studierende der Physik im ersten Semester. Die Vorlesungsinhalte werden hier anschaulich, übersichtlich und leicht verständlich in zwölf Kapiteln dargestellt: Das Buch beginnt mit der Mechanik des Massenpunktes, Bezugssystemen und spezielle Relativitätstheorie. Es werden Systeme von Massenpunkten und die Dynamik starrer ausgedehnter Körper behandelt. Anschließend wird das Verhalten von festen und flüssigen realen Körpern und Gasen diskutiert. Strömende Flüssigkeiten und Gase, Auftrieb und die Physik des Fliegens werden im nächsten Kapitel besprochen. Nach der Vakuum-Physik wird die Wärmelehre eingeführt. Das Buch endet mit mechanischen Schwingungen und Wellen, nichtlinearer Dynamik und Chaos. Für das Verständnis notwendige Teilaspekte der Mathematik werden im Anhang aufgeführt. Ganz im Stil der bekannten Reihe zur Experimentalphysik von Professor Demtröder wird auch die Mechanik und Wärmelehre möglichst quantitativ präsentiert. Wichtige Formeln und Merksätze sind hervorgehoben und der Lernstoff direkt anhand von Beispielen verständlich gemacht. Über 160 Übungsaufgaben werden ausführlich gelöst und Zusammenfassungen unterstützen Studierende beim strukturierten Lernen. In der neunten Auflage des beliebten Lehrbuches erwartet Leserinnen und Leser jetzt zusätzlich: o Wichtige und grundlegende Aufgaben werden in Videos klar und verständlich besprochen und ausführlich an der Tafel gelöst. o Kurze Fragen am Anfang der Kapitel stimmen auf das jeweilige Themengebiet ein und machen neugierig, beispielsweise: Woher wissen wir, dass die Lichtgeschwindigkeit konstant und unabhängig von der Bewegung des Beobachters ist? Was ist ein Trägheitsmoment eines Körpers und wie unterscheidet es sich von der Masse des Körpers? Wovon hängt es ab, ob Materie fest, flüssig oder gasförmig ist? Wie kommt eine Seifenblase zustande? o Ein neues Layout präsentiert den Inhalt noch übersichtlicher. o Ausgesuchte Abbildungen stehen als Vorlesungsfolien für Dozentinnen und Dozenten zur Verfügung. Der Autor Wolfgang Demtröder studierte an den -Universitäten in Münster, Tübingen und Bonn die Fächer Physik, Mathematik und Musikwissenschaft. Dort promovierte er bei dem späteren Nobelpreisträger Prof. Wolfgang Paul. Er arbeitete an der Universität Freiburg als wissenschaftlicher Mitarbeiter, wo er auch habilitiert wurde und forschte als Visiting Fellow am Joint Institute for Astrophysics in Boulder, Colorado und erhielt 1970 einen Ruf als ordentlicher Professor an die Universität Kaiserslautern. Er forschte unter anderem auf dem Gebiet der hochauflösenden Laserspektroskopie kleiner Moleküle. Bekannt ist der Autor vor allem für sein Standardwerk über Laserspektroskopie und seine beliebte und bekannte Lehrbuchreihe Experimentalphysik I-IV.Table of ContentsEinführung und Überblick.- Mechanik eines Massenpunktes.- Bewegte Bezugssysteme und spezielle Relativitätstheorie.- Systeme von Massenpunkten. Stöße.- Dynamik starrer ausgedehnter Körper.- Reale feste und flüssige Körper.- Gase.- Strömende Flüssigkeiten und Gase.- Vakuum-Physik.- Wärmelehre.- Mechanische Schwingungen und Wellen.- Nichtlineare Dynamik und Chaos.- Anhang.- Lösungen der Übungsaufgaben.

Read more less

Book SynopsisThis book is about supergravity, which combines the principles of general relativity and local gauge invariance with the idea of supersymmetries between bosonic and fermionic degrees of freedom. The authors give a thorough and pedagogical introduction to the subject suitable for beginning graduate or advanced undergraduate students in theoretical high energy physics or mathematical physics. Interested researchers working in these or related areas are also addressed. The level of the presentation assumes a working knowledge of general relativity and basic notions of differential geometry as well as some familiarity with global supersymmetry in relativistic field theories. Bypassing curved superspace and other more technical approaches, the book starts from the simple idea of supersymmetry as a local gauge symmetry and derives the mathematical and physical properties of supergravity in a direct and “minimalistic” way, using a combination of explicit computations and geometrical reasoning. Key topics include spinors in curved spacetime, pure supergravity with and without a cosmological constant, matter couplings in global and local supersymmetry, phenomenological and cosmological implications, extended supergravity, gauged supergravity and supergravity in higher spacetime dimensions.Table of ContentsIntroduction.- From Global to Local SUSY.- Gravity and spinors.- D=4 N=1 SUGRA.- Matter couplings in global SUSY.- Matter couplings in SUGRA.- SUGRA phenomenology.- Extended supergravities.- Gauged supergravity.- SUGRA in any dimension.

Read more less

Book SynopsisThis lecture note provides a tutorial review of non-Abelian discrete groups and presents applications to particle physics where discrete symmetries constitute an important principle for model building. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics—particularly model building beyond the standard model—non-Abelian discrete symmetries have been applied particularly to understand the three-generation flavor structure. The non-Abelian discrete symmetries are indeed considered to be the most attractive choice for a flavor sector: Model builders have tried to derive experimental values of quark and lepton masses, mixing angles and CP phases on the assumption of non-Abelian discrete flavor symmetries of quarks and leptons, yet lepton mixing has already been intensively discussed in this context as well. Possible origins of the non-Abelian discrete symmetry for flavors are another topic of interest, as they can arise from an underlying theory, e.g., the string theory or compactification via orbifolding as geometrical symmetries such as modular symmetries, thereby providing a possible bridge between the underlying theory and corresponding low-energy sector of particle physics. The book offers explicit introduction to the group theoretical aspects of many concrete groups, and readers learn how to derive conjugacy classes, characters, representations, tensor products, and automorphisms for these groups (with a finite number) when algebraic relations are given, thereby enabling readers to apply this to other groups of interest. Further, CP symmetry and modular symmetry are also presented.Table of ContentsIntroduction.- Basics of Finite Groups.- SN.- AN.- 5 T ′.- DN.- QN.- QD2N.- Σ(2N ).- Δ (3N2).- TN.- Σ(3N3).- Δ(6N2).- Subgroups and Decompositions of Multiplets.- Anomalies.- Non-Abelian Discrete Symmetry in Quark/Lepton Flavor Models.- Modular Group.- CP Symmetry.- Appendices.

Read more less

Book SynopsisThis book introduces the scattering theory of nonrelativistic systems, a standard tool for interpreting collision experiments with quantum particles at energies not too high. The goal is to explore the interaction between particles and their properties. The authors cover the basics of the theory through a detailed discussion of elastic scattering using the stationary Schrödinger equation and the Lippmann-Schwinger equation. These remarks are supplemented by a consideration of the time-dependent formulation of scattering theory. Selection rules for effective cross sections due to symmetries conditioned by the structure of the interparticle forces and the scattering of spin-polarized particles are discussed. The foundations for the treatment of inelastic processes are laid and explained by application to three-body and nucleotransfer processes.In all chapters, the more technical, mathematical aspect and the more physics-oriented explanations are separated as far as possible. The explanations are well comprehensible and suitable to introduce the reader to the physics of impact processes.This book is a translation of the original German 1st edition Streutheorie in der nichtrelativistischen Quantenmechanik by Reiner M. Dreizler, Tom Kirchner & Cora S. Lüdde, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). The present version has been revised extensively with respect to technical and linguistic aspects by the authors. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.Table of Contents1 Elastic scattering: stationary formulation - differential equations.- 2 Elastic scattering: stationary formulation - integral equations.- 3 Elastic scattering: time-dependent formulation.- 4 Conservation laws in scattering theory.- 5 Elastic scattering: the analytical structure of the S-matrix.- 6 Elastic scattering with spin-polarized particles.- 7 Remarks on multichannel problems.- Bibliography.

Read more less

Book SynopsisDieses Lehrbuch führt Sie anhand von physikalischen Fragestellungen aus der Mechanik in die Programmiersprache Python ein. Neben der reinen Simulation von physikalischen Systemen wird besonderes Augenmerk auf die Visualisierung von Ergebnissen und das Erstellen von Animationen gelegt. Mit zahlreichen Beispielen und Übungsaufgaben ermöglicht dieses Buch so den praktischen Einstieg in das wissenschaftliche Rechnen. Sie lernen Kurvenanpassungen durchzuführen sowie lineare und nicht-lineare Gleichungssysteme zu lösen, die bei der Behandlung von statischen Problemen auftreten. Auch die Lösung von Differentialgleichungen, die dynamische Systeme beschreiben, sowie Themen wie Fourier-Transformationen und Eigenwertprobleme kommen nicht zu kurz. Mithilfe der in diesem Buch vorgestellten Simulationsbeispiele vertiefen Sie darüber hinaus Ihr Verständnis der zugrundeliegenden Physik, indem Sie die physikalischen Gesetze algorithmisch umsetzen und physikalische Aufgaben simulieren, die weitaus komplexer sind als die üblichen mit Papier und Bleistift lösbaren Aufgaben. Alle im Buch vorgestellten Programme, die fertigen Animationen sowie die Lösungen zu den Übungsaufgaben werden online bereitgestellt.Die vorliegende zweite Auflage enthält zahlreiche Ergänzungen, Korrekturen und Anpassungen an die aktuellen Versionen von Python, NumPy, SciPy und Matplotlib. Darüber hinaus erwartet Sie ein zusätzliches Kapitel über objektorientierte Programmiermethoden. Ob Sie also Physik oder eine Ingenieurwissenschaft mit hohem physikalischem Anteil studieren, oder ob Sie unterrichten und Ihre Lehre durch Simulationen und Animationen anreichern möchten – dieses Buch ist dabei Ihr optimaler Begleiter!Table of ContentsEinleitung.- Einführung in Python.- NumPy und Matplotlib.- Physikalische Größen und Messungen.- Kinematik des Massenpunkts.- Statik von Massenpunkten.- Dynamik des Massenpunkts.- Mehrteilchensysteme und Erhaltungssätze.- Zwangsbedingungen.- Schwingungen.- Wellen.- Grafische Benutzeroberflächen.- Objektorientierte Simulationen.- Ausblick.

Read more less

Book SynopsisThe present volume 2 covers advanced topics in theoretical solid state physics and thus ties in directly with the fundamentals. Solids in external fields or more generally in non-equilibrium and deviations from the ideal 3-dimensional crystal structure (surfaces, impurities, low-dimensional structures, quantum dots, etc.) are treated. The consideration of collective phenomena such as superconductivity and magnetism complete the presentation. The reader is assumed to have the contents of Volume 1 (electrons and phonons in ideal crystals, Bloch theorem, population number representation or 2nd quantization, electron-electron and electron-phonon interaction) as well as the basic knowledge of general theoretical physics (mechanics, electrodynamics, quantum mechanics, and statistical physics) usually available after a bachelor's degree in physics. Volume 2 is thus ideally suited for students in the master's program in physics who wish to specialize in (experimental or theoretical) solid-state physics. Addressing current topics (e.g., Kondo effect, fractional quantum Hall effect, 2-dimensional crystals such as graphene, giant magnetoresistance effect, and others) provides an optimal transition to modern research.The new edition has been completely revised, expanded with numerous exercises and existing redesigned, with the associated solutions now included in the book.Table of ContentsElectronic transport in solids.- Optical (or dielectric) properties of solids.- Deviations from the ideal, three-dimensional crystal structure.- Solids in the external magnetic field.- Superconductivity.- Collective magnetism.- Solutions to the exercise problems.

Read more less

Book SynopsisDieses Lehrbuch bietet Studierenden der ersten Semester eine Einführung in die Theoretische Physik sowie die dazu erforderlichen mathematischen Werkzeuge. Parallel zu den Inhalten der Klassischen Mechanik lernen Sie die nötige Mathematik gleich mit – und auch die Denkweise in der Theoretischen Physik kennen. Unter sorgfältiger Berücksichtigung des Wissensstands von Studienanfängern wird eine ausführliche, schrittweise Darstellung von allen Herleitungen und Beispielen geboten. Dabei werden Ihnen nicht nur die analytischen Lösungsverfahren gezeigt, sondern Sie erhalten auch einen Einblick in die große Bedeutung von computergestützten, numerischen Verfahren. Das Buch beginnt mit den Leitbegriffen des Zustands und der Bewegungsgleichung, worauf aufbauend die Struktur der Newton‘schen Mechanik in leicht nachvollziehbarer Art und Weise vermittelt wird. Als dazugehörige mathematische Themen werden komplexe Zahlen, Vektoren und Matrizen, Taylor-Reihen, gewöhnliche Differenzialgleichungen, Fourier-Reihen, partielle Ableitungen und Elemente der Vektoranalysis behandelt. Ebenso finden Sie in diesem Buch eine Untersuchung elementarer Erhaltungssätze als auch deren Anwendung auf physikalische Fragestellungen wie z.B. die Begründung der Kepler‘schen Gesetze.Table of ContentsVorwort.- 1 Grundkonzepte.- 2 Beschreibung der Bewegung von Massenpunkten.- 3 Dynamische Gesetze für einen Massenpunkt.- 4 Gewöhnliche Differenzialgleichungen.- 5 Fourier-Reihen.- 6 Nichtlineare Dynamik.- 7 Systeme mit mehr als einem Teilchen.- 8 Partielle Ableitungen.- 9 Energie.- 10 Zweiteilchenproblem mit Gravitationskraft.- 11 Drehbewegungen.- 12 Spezielle Relativitätstheorie - 13 Anhänge: A Computerprogramm zu Kap. 1.- B Computerprogramm zu Kap. 6.- Index.

Read more less

Book SynopsisThis book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.Trade Review"The presentation provides significant insight into a large part of the current issues of interest in the physics of Bose systems and especially into the "kitchen" of several relevant mathematical techniques. As such, it is highly recommended to both advanced researchers and students preparing to work in this field." (Mathematical Reviews)Table of ContentsThe Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincaré Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for Trapped Bosons.- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases.- One-Dimensional Behavior of Dilute Bose Gases in Traps.- Two-Dimensional Behavior in Disc-Shaped Traps.- The Charged Bose Gas, the One- and Two-Component Cases.- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model.

Read more less

Book Synopsis"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century." --Bulletin of Symbolic Logic (Review of first edition)Trade ReviewFrom the book reviews:“The book is a thorough, deep, fascinating work. It is not only recommended, it is compulsory for anyone interested in the history of mathematical ideas.” (László I. Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 75 (1-2), 2009)Table of ContentsThe Emergence of Sets within Mathematics.- Institutional and Intellectual Contexts in German Mathematics, 1800–1870.- A New Fundamental Notion: Riemann’s Manifolds.- Dedekind and the Set-theoretical Approach to Algebra.- The Real Number System.- Origins of the Theory of Point-Sets.- Entering the Labyrinth-Toward Abstract Set Theory.- The Notion of Cardinality and the Continuum Hypothesis.- Sets and Maps as a Foundation for Mathematics.- The Transfinite Ordinals and Cantor’s Mature Theory.- In Search of an Axiom System.- Diffusion, Crisis, and Bifurcation: 1890 to 1914.- Logic and Type Theory in the Interwar Period.- Consolidation of Axiomatic Set Theory.

Read more less

Book SynopsisThis book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.Trade ReviewFrom the reviews: “It is worth pointing out that the book is mainly a text about commutative hypercomplex numbers and some of their applications to a 2-dimensional Minkowski spacetime. … This book should be interesting to anybody who is interested in applications of hypercomplex numbers … . In conclusion, I recommend this book to anyone who wants to learn about hypercomplex numbers.” (Emanuel Gallo, Mathematical Reviews, Issue 2010 d)Table of ContentsThe Mathematics of Minkowski Space-Time: 1 N-Dimensional Hypercomplex Numbers and the associated Geometries.- Commutative Hypercomplex Number Systems.- The General Two-Dimensional System.- Linear Transformations and Geometries.- The Geometries Associated with Hypercomplex Numbers.- Conclusions.- 2 Trigonometry in the Minkowski Plane.- Geometrical Representation of Hyperbolic Numbers.- Basics of Hyperbolic Trigonometry.- Geometry in Pseudo-Euclidean Cartesian Plane.- Trigonometry in the Pseudo-Euclidean Plane.- Theorems on Equilateral Hyperbolas in the Pseudo-Euclidean Plane.- Some Examples of Triangle Solutions in the Minkowski Plane.- Conclusions.- 3 Uniform and Accelerated Motions in the Minkowski Space-Time (Twin Paradox).- Inertial Motions.- Inertial and Uniformly Accelerated Motions.- Non-uniformly Accelerated Motions.- Conclusions.- 4 General Two-Dimensional Hypercomplex Numbers.-Geometrical Representation.- Geometry and Trigonometry in Two-Dimensional Algebras.- Some Properties of Fundamental Conic Section.- Numerical Examples.- 5 Functions of a Hyperbolic Variable.- Some Remarks on Functions of a Complex Variable.- Functions of Hypercomplex Variables.- The Functions of a Hyperbolic Variable.- The Elementary Functions of a Canonical Hyperbolic Variable.- H-Conformal Mappings.- Commutative Hypercomplex Systems with Three Unities.- 6 Hyperbolic Variables on Lorentz Surfaces.- Introduction.- Gauss: Conformal Mapping of Surfaces.- Extension of Gauss Theorem: Conformal Mapping of Lorentz Surfaces.- Beltrami: Complex Variables on a Surface.- Beltrami’s Integration of Geodesic Equations.- Extension of Beltrami’s Equation to Non-Definite Differential Forms.- 7 Constant Curvature Lorentz Surfaces.- Introduction.- Constant Curvature RiemannSurfaces.- Constant Curvature Lorentz Surfaces.- Geodesics and Geodesic Distances on Riemann and Lorentz Surfaces.- Conclusions.- 8 Generalization of Two-Dimensional Special Relativity (Hyperbolic Transformations and the Equivalence Principle).- Physical Meaning of Transformations by Hyperbolic Functions.- Physical Interpretation of Geodesics on Riemann and Lorentz Surfaces with Positive Constant Curvature.- Einstein’s Way to General Relativity.- Conclusions.- II An Introduction to Commutative Hypercomplex Numbers.- 9 Commutative Segre’s Quaternions.- Introduction.- Hypercomplex Systems with Four Units.- Historical Introduction of Segre’s Quaternion.- Algebraic Properties of Commutative Quaternions.- Functions of a Quaternion Variable.- Mapping by Means of Quaternion Functions.- Elementary Functions of the Quaternions.- Elliptic-Hyperbolic Quaternions.- Elliptic-Parabolic Generalized Segre’s Quaternions.- 10 Constant Curvature Segre’s Quaternion Spaces.- Introduction.- Quaternion differential geometry and geodesic equations.- Orthogonality in Segre’s Quaternion Space.- Constant Curvature Quaternion Spaces.- Geodesic Equations in Quaternion Space.- Beltrami’s Integration Method for Quaternion Spaces.- Beltrami’s Integration Method for Quaternion Spaces.- Conclusions.- 11 A Matrix Formalization for Commutative Hypercomplex Systems.- Mathematical Operations.- Properties of the Characteristic Matrix M.- Functions of Hypercomplex Variable.- Functions of a Two-Dimensional Hypercomplex Variable.- Derivatives of a Hypercomplex Function.- Characteristic Differential Equation.- A Equivalence Between the Formalizations of Hypercomplex Numbers.

Read more less

Book SynopsisDie Erforschung komplexer Strukturen ist gegenwärtig eines der interessantesten wissenschaftlichen Themen. Dieses Buch behandelt Möglichkeiten der Beschreibung und quantitativen Charakterisierung komplexer Strukturen mit Hilfe verschiedener Entropie- und Informationsmaße. Nach einer allgemein verständlichen Einführung der Grundbegriffe werden die für eine quantitative Analyse erforderlichen Konzepte ausführlich behandelt und an zahlreichen Beispielen, wie Zeitreihen, Biosequenzen, literarischen Texten und Musikstücken, veranschaulicht.Table of ContentsKomplexität und Entropie - Selbstorganisation und Information - Informationstheoretische Maße - Dynamisch generierte Strukturen - Entropie und Komplexität natürlicher Sequenzen - Quantitative Ästhetik

Read more less

Book SynopsisDas Buch vermittelt die Grundlagen und wichtigsten Konzepte der Theoretischen Mechanik und Speziellen Relativitätstheorie, soweit sie in Lehramts- und Bachelorstudiengängen benötigt werden. Dabei handelt es sich nicht um eine im Sinne des Master- oder des früheren Diplomstudiums "möglichst umfassend" gehaltene Darstellung, sondern um eine - im Vergleich zu anderen Lehrbuchwerken zur Theoretischen Physik schlank gehaltene - Darlegung der theoretischen Grundpfeiler der modernen Physik.Table of ContentsKlassische Mechanik - Spezielle Relativitätstheorie - Lösungen und Lösungstipps zu den Aufgaben - Mathematischer Anhang - Einheiten und Konstanten

Read more less

Book SynopsisIl testo si configura come un' introduzione alla fisica statistica rivolto in primo luogo a quei corsi di studio in ingegneria che più hanno a che fare con le proprietà fisiche dei materiali, ed ha lo scopo di fornire le basi microscopiche del comportamento termodinamico di cui si fa uso sia in molti corsi tradizionali, quali quelli di termofluidica d'interesse per l'ingegneria chimica e nucleare, che in corsi rivolti ad applicazioni avanzate nella scienza dei materiali e nelle nanotecnologie. Particolare attenzione viene quindi dedicata all'impiego di metodi di fisica statistica nella scienza dei materiali, approfondendo tematiche relative alle vibrazioni nei solidi, ai processi di nucleazione liquido/vapore, alla struttura dello stato fluido e vetroso, ai plasmi, ai materiali magnetici, al gas di Fermi e alla superfluidità. Per il suo carattere generale, e per l'accento posto sui fondamenti della meccanica quantistica, il volume si presta comunque a costituire anche un testo introduttivo alla meccanica statistica per studenti dei corsi di laurea in fisica.Trade ReviewFrom the reviews:“The book covers the main typical arguments of a course on statistical physics and thermodynamics in the Italian university system. … the author intends to transmit to the readers: the subject of statistical physics is not only useful, but is also far to be boring and can reveal an intrinsic beauty. Also, the style of writing the different chapters reveals the intention of the author to give a pleasant environment for the study of the subject.” (Francesco Salvarani, Zentralblatt MATH, Vol. 1241, 2012)

Read more less

Book SynopsisThe achievement of Bose-Einstein condensation in ultra-cold vapours of alkali atoms has given enormous impulse to the study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. High purity and easy optical access make them ideal candidates to investigate fundamental issues on interacting quantum systems. This review presents some theoretical issues which have been addressed in this area and the numerical techniques which have been developed and used to describe them, from mean-field models to classical and quantum simulations for equilibrium and dynamical properties. The attention given in this article to methods beyond standard mean-field approaches should make it a useful reference point for future advances in these areas.

Read more less

Book SynopsisThe birth of condensed matter physics in Italy is linked to a small number of very distinguished scientists. Mario Tosi, Professor of Physics of Matter at the Scuola Normale Superiore, is unquestionably among the leading figures, a true founder of the theoretical activity in the country and a true catalyst of novel research directions internationally. This volume collects the proceedings of a symposium held at Scuola Normale Superiore di Pisa, designed to show Mario Tosi's broad, deep influence in very diverse areas of the quantum theory of condensed matter. The topics covered in the volume represent the breadth of his interests and the highlights in the quantum theory of condensed matter: liquids, electronic states in complex structures, quantum degenerate gases, many-body physics.

Read more less

Book SynopsisThese are the informal notes of two seminars held at the Università di Roma “La Sapienza”, and at the Scuola Normale Superiore in Pisa in spring and autumn 1997. We discuss in detail the content of the parts of a paper by Givental dealing with mirror symmetry for projective complete intersections.

Read more less

Book SynopsisThese are the written notes of Fermi's Lectures supported by the Accademia Nazionale dei Lincei and given at the Scuola Normale Superiore of Pisa during March-April 1973. We propose to discuss here certain spectral properties of Schrödinger operators H=-D+V(x) (D the Laplacian and V a potential) which have application to scattering theory. We consider an operator H with potential V of class SR. We show that the positive point spectrum of H is a discrete set in R+. Eigenfunctions which correspond to positive eigenvalues are shown to decay rapidly. This property is shown to hold also for generalized eigenfunctions. We then establish the limiting absorbing principle, which is a basic tool in our study.

Read more less

Book SynopsisThese notes contain lectures on the theory of group representations and its applications to the physics of atoms, molecules and crystals, given at Purdue University, Scuola Normale Superiore (Pisa, Italy) and Universidad Técnica Federico Santa Maria (Valparaiso, Chile) on and off over a period of over 25 years. The topics selected reflect my special interests and their scope is limited by the time available to the students. The style is somewhat concise and will require careful attention on the part of the reader.

Read more less

Book SynopsisThese are transcripts of notes taken at (some of) the lectures given at the Mittag-Leffler Institute during the first semester of the year 1996/97 on Enumerative geometry and its interaction with theoretical physics. The first part of this collection consists of notes from talks on the basics of quantum cohomology; the second part treats more advanced topics in quantum cohomology; the third part consists of background material and related topics; an appendix gives a description of Kresch's C-program Farsta for quantum cohomology computations. These notes are meant as a series of snapshots of quantum cohomology as seen by the speakers at the time of their lectures. The reader should bear in mind that quantum cohomology is a growing and rapidly changing field. Many of the writeups have been left in the form of the original talks, which were usually more concerned with giving motivations and a point of view, rather than conveying detailed proofs or attempting to survey the considerably extensive literature on the subject.

Read more less

Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. Grid methods are the tool of the trade for the solution of ordinary and partial differential equations and consequently they represent a “must” for anyone dealing with computational science. With grid methods, a major distinction is made between methods which do not require matrix algebra and those which do.

Read more less

Book SynopsisThese volumes collect the lecture notes of the course “An introduction to computational physics” held in the academic year 2000/01 for students of the University of Pisa and Scuola Normale Superiore at the level of the last two-year undergraduates in physics and chemistry. The second part deals with various types of particle methods, both deterministic and stochastic, used in modern applications of computer simulations in physics and related disciplines.

Read more less

Book SynopsisThe main goal of these lectures is to get students acquainted with a glossary of nonlinear physics. I try to present the material of the lectures (delivered at SNS Pisa in April -- June 1999) in such a way that the students do not need to use additional literature during the first reading. The lectures focus on the following arguments: discussion of nonlinear problems in classical physics; the use of the multiple time scale expansion method to solve problems of nonlinear oscillations; description of nonlinear wave steepening and shock wave formation using the Lagrange variables; solution of nonlinear elliptic equations considering the Liouville equation; soliton solutions of the Korteweg de Vries, Sine-Gordon and Nonlinear Schrödinger equations; the use of the Backlund transformation; self-similarity of nonlinear systems.

Read more less

Book SynopsisElectron gas theory is one of the broadest fields in theoretical condensed matter physics, and even its most elementary application to the study of collective excitations and screening in the simpe metals poses interesting questions. Recent Electron Energy Loss and Inelastic X-Ray Scattering experiments have shown that traditional electron gas theories are unable to account for the measured plasmon dispersion relation. While it has become clear that neither correlation nor band structure alone can explain those results, the recently developed Time Dependent Density Functional Theory provides a general framework which can account for both.

Read more less

Book SynopsisThe experimental achievement of Bose-Einstein condensation (1995) and of Fermi degeneracy (1999) in ultra-cold, dilute gases has opened a new field in atomic physics and condensed matter physics. This thesis presents an overview of theoretical and experimental facts on ultra-cold atomic gases. A Green's function scheme is examined, and the book also applies a novel spin-density-functional approach to the study of Fermi gases inside one-dimensional optical lattices.Table of ContentsPreface.- 1. Reviews on Ultra-cold quantum gases.- 2. Theory of matter transport in quasi-1D arrays.- 3. Density-functional theory of 1D Fermi gases.- 4. Ultra-cold attractive fermions in 1D optical lattices.

Read more less