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E-grāmata: From Newton to Mandelbrot: A Primer in Theoretical Physics

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  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 24-Jan-2017
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662536858
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From Newton to Mandelbrot: A Primer in Theoretical PhysicsPalielināt
  • Formāts: EPUB+DRM
  • Sērija : Graduate Texts in Physics
  • Izdošanas datums: 24-Jan-2017
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Valoda: eng
  • ISBN-13: 9783662536858
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This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, presenting all the central concepts and equations at an accessible level. Chapters 1 to 4 contain the standard material of courses in theoretical physics and are supposed to accompany lectures at the university; thus they are rather condensed. They are supposed to fill one year of teaching. Chapters 5 and 6, in contrast, are written less condensed since this material may not be part of standard lectures and thus could be studied without the help of a university teacher. An appendix on elementary particles lies somewhere in between: It could be a summary of a much more detailed course, or studied without such a course. Illustrations and numerous problems round off this unusual textbook. It will ideally accompany the students all along their course in theoretical physics and prove indispensable in preparing and revising the exams. It is also suited as a reference for teachers or scientists from other disciplines who are interested in the topic.

1 Mechanics
1(60)
1.1 Point Mechanics
1(16)
1.1.1 Basic Concepts of Mechanics and Kinematics
1(2)
1.1.2 Newton's Law of Motion
3(3)
1.1.3 Simple Applications of Newton's Law
6(7)
1.1.4 Harmonic Oscillator in One Dimension
13(4)
1.2 Mechanics of Point Mass Systems
17(7)
1.2.1 The Ten Laws of Conservation
17(2)
1.2.2 The Two-Body Problem
19(1)
1.2.3 Constraining Forces and d'Alembert's Principle
20(4)
1.3 Analytical Mechanics
24(9)
1.3.1 The Lagrange Function
24(2)
1.3.2 The Hamilton Function
26(2)
1.3.3 Harmonic Approximation for Small Oscillations
28(5)
1.4 Mechanics of Rigid Bodies
33(9)
1.4.1 Kinematics and Inertia Tensor
33(3)
1.4.2 Equations of Motion
36(6)
1.5 Continuum Mechanics
42(19)
1.5.1 Basic Concepts
42(5)
1.5.2 Stress, Strain and Hooke's Law
47(2)
1.5.3 Waves in Isotropic Continua
49(1)
1.5.4 Hydrodynamics
50(11)
2 Electricity and Magnetism
61(32)
2.1 Vacuum Electrodynamics
61(15)
2.1.1 Steady Electric and Magnetic Fields
61(5)
2.1.2 Maxwell's Equations and Vector Potential
66(2)
2.1.3 Energy Density of the Field
68(1)
2.1.4 Electromagnetic Waves
68(1)
2.1.5 Fourier Transformation
69(1)
2.1.6 Inhomogeneous Wave Equation
70(1)
2.1.7 Applications
71(5)
2.2 Electrodynamics in Matter
76(7)
2.2.1 Maxwell's Equations in Matter
76(1)
2.2.2 Properties of Matter
77(2)
2.2.3 Wave Equation in Matter
79(1)
2.2.4 Electrostatics at Surfaces
80(3)
2.3 Theory of Relativity
83(10)
2.3.1 Lorentz Transformation
84(3)
2.3.2 Relativistic Electrodynamics
87(2)
2.3.3 Energy, Mass and Momentum
89(4)
3 Quantum Mechanics
93(36)
3.1 Basic Concepts
93(8)
3.1.1 Introduction
93(1)
3.1.2 Mathematical Foundations
94(2)
3.1.3 Basic Axioms of Quantum Theory
96(2)
3.1.4 Operators
98(2)
3.1.5 Heisenberg's Uncertainty Principle
100(1)
3.2 Schrodinger's Equation
101(9)
3.2.1 The Basic Equation
101(1)
3.2.2 Penetration
102(2)
3.2.3 Tunnel Effect
104(1)
3.2.4 Quasi-classical WKB Approximation
105(1)
3.2.5 Free and Bound States in the Potential Well
106(1)
3.2.6 Harmonic Oscillators
107(3)
3.3 Angular Momentum and the Structure of the Atom
110(10)
3.3.1 Angular Momentum Operator
110(1)
3.3.2 Eigenfunctions of L2 and Lz
111(1)
3.3.3 Hydrogen Atom
112(3)
3.3.4 Atomic Structure and the Periodic System
115(1)
3.3.5 Indistinguishability
116(2)
3.3.6 Exchange Reactions and Homopolar Binding
118(2)
3.4 Perturbation Theory and Scattering
120(9)
3.4.1 Steady Perturbation Theory
120(2)
3.4.2 Unsteady Perturbation Theory
122(2)
3.4.3 Scattering and Born's First Approximation
124(5)
4 Statistical Physics
129(60)
4.1 Probability and Entropy
129(6)
4.1.1 Canonical Distribution
129(3)
4.1.2 Entropy, Axioms and Free Energy
132(3)
4.2 Thermodynamics of the Equilibrium
135(15)
4.2.1 Energy and Other Thermodynamic Potentials
135(3)
4.2.2 Thermodynamic Relations
138(2)
4.2.3 Alternatives to the Canonical Probability Distribution
140(1)
4.2.4 Efficiency and the Carnot Cycle
141(2)
4.2.5 Phase Equilibrium and the Clausius-Clapeyron Equation
143(3)
4.2.6 Mass Action Law for Gases
146(1)
4.2.7 The Laws of Henry, Raoult and van't Hoff
147(2)
4.2.8 Joule-Thomson Effect
149(1)
4.3 Statistical Mechanics of Ideal and Real Systems
150(39)
4.3.1 Fermi and Bose Distributions
150(2)
4.3.2 Classical Limiting Case βμ → -∞
152(3)
4.3.3 Classical Equidistribution Law
155(1)
4.3.4 Ideal Fermi-Gas at Low Temperatures βμ → +∞
156(1)
4.3.5 Ideal Bose-Gas at Low Temperatures βμ → 0
157(3)
4.3.6 Vibrations
160(1)
4.3.7 Virial Expansion of Real Gases
161(1)
4.3.8 Van der Waals' Equation
162(2)
4.3.9 Magnetism of Localised Spins
164(5)
4.3.10 Scaling Theory
169(20)
5 Fractals in Theoretical Physics
189(26)
5.1 Non-random Fractals
190(2)
5.2 Random Fractals: The Unbiased Random Walk
192(2)
5.3 `A Single Length'
194(2)
5.3.1 The Concept of a Characteristic Length
194(1)
5.3.2 Higher Dimensions
195(1)
5.3.3 Additional Lengths that Scale with √t
195(1)
5.4 Functional Equations and Scaling: One Variable
196(1)
5.5 Fractal Dimension of the Unbiased Random Walk
197(1)
5.6 Universality Classes and Active Parameters
197(3)
5.6.1 Biased Random Walk
197(1)
5.6.2 Scaling of the Characteristic Length
198(2)
5.7 Functional Equations and Scaling: Two Variables
200(1)
5.8 Fractals and the Critical Dimension
201(6)
5.9 Fractal Aggregates
207(3)
5.10 Fractals in Nature
210(5)
6 Dynamical Systems and Chaos
215(38)
6.1 Basic Notions and Framework
215(6)
6.1.1 Phase Space
215(1)
6.1.2 Continuous-Time Dynamical Systems
216(1)
6.1.3 Flows and Phase Portraits
217(1)
6.1.4 Insights from Dynamical Systems Theory
217(1)
6.1.5 Some Examples
218(3)
6.2 Fixed Points and Linear Stability Analysis
221(10)
6.2.1 Fixed Points and Stability Matrix
221(1)
6.2.2 Flow Linearization Theorem
222(1)
6.2.3 The Different Types of Fixed Points
223(2)
6.2.4 Constructing the Phase Portrait
225(2)
6.2.5 Application: Anharmonic Oscillators
227(3)
6.2.6 The Origin of Bifurcations
230(1)
6.3 Attractors, Bifurcations and Normal Forms
231(4)
6.3.1 Attractors
231(1)
6.3.2 Conservative Versus Dissipative Systems
232(1)
6.3.3 The Different Types of Bifurcations
233(2)
6.3.4 Normal Forms and Structural Stability
235(1)
6.4 Discrete-Time Dynamical Systems
235(4)
6.4.1 Discrete-Time Evolution Equations
235(1)
6.4.2 Linear Stability Analysis
236(1)
6.4.3 Attractors and Bifurcations
237(1)
6.4.4 Discretization by Poincare Sections
237(2)
6.5 Lyapunov Exponents and Deterministic Chaos
239(4)
6.5.1 Lyapunov Exponents
239(1)
6.5.2 Deterministic Chaos
240(2)
6.5.3 Ergodic Theory
242(1)
6.6 Routes to Chaos
243(5)
6.6.1 Period Doubling and Subharmonic Cascade
243(2)
6.6.2 Intermittency
245(1)
6.6.3 Ruelle-Takens Scenario
246(1)
6.6.4 Hamiltonian Systems and KAM Theorem
246(2)
6.7 Conclusion
248(1)
6.8 Problems
249(1)
6.9 Further Reading
250(3)
Appendix A Elementary Particles 253(10)
Appendix B Answers to Questions 263(4)
Index 267
CV of D. Stauffer 1980/81 Guest Professor in Marseille, France 1985 Humboldt Prize for French-German Scientific Cooperation 1987 James Chair Professor; Canada 1988-90 first manager of many-body research group at German Supercomputer Center HLRZ Julich 1993/94 first Canada-Germany Research Awardee; spends one year in Antigonish

1994 and 1996 Guest professor at UFF, Niteroi, Brazil; 2000/2001 and 2005, sabbatical there 1999 French-German Kastler-Genter physics prize 1999 Foreign member of Brazilian Academy of Sciences 1999 Prize of Polish Education Minister 2004/6 Honorary doctorate, Université de Liege, Belgium 1990-2002 Member of Senate teaching committee, Cologne University; coordinated 13 curricula in the sciences in 1994/96. 1990-96 Member of Computational Physics Board, European Physical Society Edited Annual Reviews of Computational Physics, World Scientific, Singapore Past or present member of editorial board for : J.Aerosol Sci., J.Stat.Phys., J.Phys.A., J.Physique, Physica A, Physics World, Computers in Physics, Annual Reviews Comput. Phys., Int. J. Mod.Phys. C (managing editor), Theory in Biosciences, European Physical Journal B, Quantitative Finance, Computing in Science and Engineering, Blickpunkt: Der Mann, Complex Systems and Inter-disciplinary science, Communications in Computational Physics (China),

Three books in 1980's (all translated into at least one other language, all in at least second edition), fourth book 1999, fifth book 2000, sixth 2006. 600 papers. Included in ISI list of 1000 most-cited physicists 1981-1997 (15000 citations, July 2006). About 20000 citations (ISI, cited reference index). Retirement Feb. 29, 2008 Stauffer

CV Prof. Annick LESNE Annick Lesne (54 years) is a senior researcher at CNRS (French national center of scientific research), working in the Theoretical Physics of Condensed Matter laboratory (LPTMC), at the University Pierre et Marie Curie in Paris, and in the Institute of Molecular Genetics in Montpellier.In the past years, she has been  assistant professor at this university (from 1990 to 2006)  co-director of the Paris Institute of Complex Systems (ISC-PIF, from 2003 to 2008), and visitor at the Institut des Hautes Etudes Scientifiques (IHES, Bures-sur-Yvette, from 2005 to 2012).Among her present responsibilities, she is a member of the editorial board of 'EPJ Nonlinear Biomedical Physics' (Springer) and the director of the series "Echelles" (Belin, 35 volumes). She has published 75 peer-reviewed articles, and  beyond the present book  'From Newton to Mandelbrot', she has   authored three monographs and coordinated four collective books, all published both in French and English.
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