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1.

図書

図書
D.Ya. Petrina, V.I. Gerasimenko and P.V. Malyshev ; translated from the Russian by P.V. Malyshev and D.V. Malyshev
出版情報: London : Taylor & Francis, 2002  ix, 338 p. ; 24 cm
シリーズ名: Advanced studies in contemporary mathematics ; v. 8
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Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
Grand Canonical Ensemble
Thermodynamic Limit for Non-equilibrium Systems
Stationary Solutions of the BBGKY Hierarchy of Equations / Appendix 1:
Existence of the Hamiltonian Dynamics of Infinitely Many Particles / Appendix 2:
References
Index
Problem for the BBGKY Hierarchy
Equilibrium States
Canonical Ensemble
2.

図書

図書
Jan Cnops
出版情報: Boston : Birkhäuser, c2002  x, 211 p. ; 24 cm
シリーズ名: Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser ; v. 24
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Introduction
Clifford Algebras
Manifolds
Dirac Operators
Conformal Maps
Unique Continuation and the Cauchy Kernel
Boundary Values
Appendix
General Manifolds
The Additional Canterbury Tales
List of Symbols
Bibliography
Index
Introduction
Clifford Algebras
Manifolds
3.

図書

図書
Franz J. Vesely
出版情報: New York : Kluwer Academic/Plenum Publishers, c2001  xvi, 259 p. ; 26 cm
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The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
NGF Interpolation / 1.1.1:
NGB Interpolation / 1.1.2:
ST Interpolation / 1.1.3:
Difference Quotients / 1.2:
DNGF Formulae / 1.2.1:
DNGB Formulae / 1.2.2:
DST Formulae / 1.2.3:
Finite Differences in Two Dimensions / 1.3:
Sample Applications / 1.4:
Classical Point Mechanics / 1.4.1:
Diffusion and Thermal Conduction / 1.4.2:
Linear Algebra / 2:
Exact Methods / 2.1:
Gauss Elimination and Back Substitution / 2.1.1:
Simplifying Matrices: The Householder Transformation / 2.1.2:
LU Decomposition / 2.1.3:
Tridiagonal Matrices: Recursion Method / 2.1.4:
Iterative Methods / 2.2:
Jacobi Relaxation / 2.2.1:
Gauss-Seidel Relaxation (GSR) / 2.2.2:
Successive Over-Relaxation (SOR) / 2.2.3:
Alternating Direction Implicit Method (ADI) / 2.2.4:
Conjugate Gradient Method (CG) / 2.2.5:
Eigenvalues and Eigenvectors / 2.3:
Largest Eigenvalue and Related Eigenvector / 2.3.1:
Arbitrary Eigenvalue/-vector: Inverse Iteration / 2.3.2:
Potential Equation / 2.4:
Electronic Orbitals / 2.4.3:
Stochastics / 3:
Equidistributed Random Variates / 3.1:
Linear Congruential Generators / 3.1.1:
Shift Register Generators / 3.1.2:
Other Distributions / 3.2:
Fundamentals / 3.2.1:
Transformation Method / 3.2.2:
Generalized Transformation Method / 3.2.3:
Rejection Method / 3.2.4:
Multivariate Gaussian Distribution / 3.2.5:
Equidistribution in Orientation Space / 3.2.6:
Random Sequences / 3.3:
Markov Processes / 3.3.1:
Autoregressive Processes / 3.3.3:
Wiener-Levy Process / 3.3.4:
Markov Chains and the Monte Carlo method / 3.3.5:
Stochastic Optimization / 3.4:
Simulated Annealing / 3.4.1:
Genetic Algorithms / 3.4.2:
Everything Flows / II:
Ordinary Differential Equations / 4:
Initial Value Problems of First Order / 4.1:
Euler-Cauchy Algorithm / 4.1.1:
Stability and Accuracy of Difference Schemes / 4.1.2:
Explicit Methods / 4.1.3:
Implicit Methods / 4.1.4:
Predictor-Corrector Method / 4.1.5:
Runge-Kutta Method / 4.1.6:
Extrapolation Method / 4.1.7:
Initial Value Problems of Second Order / 4.2:
Verlet Method / 4.2.1:
Nordsieck Formulation of the PC Method / 4.2.2:
Symplectic Algorithms / 4.2.4:
Numerov's Method / 4.2.6:
Boundary Value Problems / 4.3:
Shooting Method / 4.3.1:
Relaxation Method / 4.3.2:
Partial Differential Equations / 5:
Initial Value Problems I (Hyperbolic) / 5.1:
FTCS Scheme; Stability Analysis / 5.1.1:
Lax Scheme / 5.1.2:
Leapfrog Scheme (LF) / 5.1.3:
Lax-Wendroff Scheme (LW) / 5.1.4:
Lax and Lax-Wendroff in Two Dimensions / 5.1.5:
Initial Value Problems II (Parabolic) / 5.2:
FTCS Scheme / 5.2.1:
Implicit Scheme of First Order / 5.2.2:
Crank-Nicholson Scheme (CN) / 5.2.3:
Dufort-Frankel Scheme (DF) / 5.2.4:
Boundary Value Problems: Elliptic DE / 5.3:
Relaxation and Multigrid Techniques / 5.3.1:
ADI Method for the Potential Equation / 5.3.2:
Fourier Transform Method (FT) / 5.3.3:
Cyclic Reduction (CR) / 5.3.4:
Anchors Aweigh / III:
Simulation and Statistical Mechanics / 6:
Model Systems of Statistical Mechanics / 6.1:
A Nutshellfull of Fluids and Solids / 6.1.1:
Tricks of the Trade / 6.1.2:
Monte Carlo Method / 6.2:
Molecular Dynamics Simulation / 6.3:
Hard Spheres / 6.3.1:
Continuous Potentials / 6.3.2:
Beyond Basic Molecular Dynamics / 6.3.3:
Evaluation of Simulation Experiments / 6.4:
Pair Correlation Function / 6.4.1:
Autocorrelation Functions / 6.4.2:
Particles and Fields / 6.5:
Ewald summation / 6.5.1:
Particle-Mesh Methods (PM and P3M) / 6.5.2:
Stochastic Dynamics / 6.6:
Quantum Mechanical Simulation / 7:
Diffusion Monte Carlo (DMC) / 7.1:
Path Integral Monte Carlo (PIMC) / 7.2:
Wave Packet Dynamics (WPD) / 7.3:
Density Functional Molecular Dynamics (DFMD) / 7.4:
Hydrodynamics / 8:
Compressible Flow without Viscosity / 8.1:
Explicit Eulerian Methods / 8.1.1:
Particle-in-Cell Method (PIC) / 8.1.2:
Smoothed Particle Hydrodynamics (SPH) / 8.1.3:
Incompressible Flow with Viscosity / 8.2:
Vorticity Method / 8.2.1:
Pressure Method / 8.2.2:
Free Surfaces: Marker-and-Cell Method (MAC) / 8.2.3:
Lattice Gas Models for Hydrodynamics / 8.3:
Lattice Gas Cellular Automata / 8.3.1:
The Lattice Boltzmann Method / 8.3.2:
Direct Simulation Monte Carlo / Bird method / 8.4:
Appendixes
Machine Errors / A:
Discrete Fourier Transformation / B:
Fast Fourier Transform (FFT) / B.1:
Bibliography
Index
The Three Pillars of Computational Physics / I:
Finite Differences / 1:
Interpolation Formulae / 1.1:
4.

図書

図書
Louis H. Kauffman
出版情報: Singapore : World Scientific, c2001  xvi, 770 p. ; 23 cm
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Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
A Short Course of Knots and Physics / Part I.:
Physical Knots / 1.:
Diagrams and Moves / 2.:
States and the Bracket Polynomial / 3.:
Alternating Links and Checkerboard Surfaces / 4.:
The Jones Polynomial and its Generalizations / 5.:
An Oriented State Model for V[subscript K](t) / 6.:
Braids and the Jones Polynomial / 7.:
Abstract Tensors and the Yang-Baxter Equation / 8.:
Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)[subscript q] / 9.:
The Form of the Universal R-matrix / 10.:
Yang-Baxter Models for Specializations of the Homfly Polynomial / 11.:
The Alexander Polynomial / 12.:
Knot-Crystals - Classical Knot Theory in a Modern Guise / 13.:
The Kauffman Polynomial / 14.:
Oriented Models and Piecewise Linear Models / 15.:
Three Manifold Invariants from the Jones Polynomial / 16.:
Integral Heuristics and Witten's Invariants / 17.:
Appendix - Solutions to the Yang-Baxter Equation / 18.:
Knots and Physics--Miscellany / Part II.:
Theory of Hitches
The Rubber Band and Twisted Tube
On a Crossing
Slide Equivalence
Unoriented Diagrams and Linking Numbers
The Penrose Chromatic Recursion
The Chromatic Polynomial
The Potts Model and the Dichromatic Polynomial
Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum
Quaternions, Cayley Numbers and the Belt Trick
The Quaternion Demonstrator
The Penrose Theory of Spin Networks
Q-Spin Networks and the Magic Weave
Knots and Strings - Knotted Strings
DNA and Quantum Field Theory
Knots in Dynamical Systems - The Lorenz Attractor
Coda
References
Index
Appendix
Introduction
Gauss Codes, Quantum Groups and Ribbon Hopf Algebras
Spin Networks, Topology and Discrete Physics
Link Polynomials and a Graphical Calculus / P. Vogel
Knots, Tangles, and Electrical Networks / J. R. Goldman
Knot Theory and Functional Integration
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
5.

図書

図書
Roger Moser
出版情報: New Jersey : World Scientific, c2005  viii, 184 p. ; 24 cm
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6.

図書

図書
by R. Courant and D. Hilbert
出版情報: New York : Interscience Publishers, 1953  xv, 561 p. ; 24 cm
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7.

図書

図書
Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily
出版情報: Singapore : World Scientific, c2011  xi, 392 p. ; 24 cm
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8.

図書

図書
edited by Silvio Levy
出版情報: Cambridge [England] : Cambridge University Press, 1999  x, 331 p., [4] p. of col. plates ; 25 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 35
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9.

図書

図書
Jean Piquet
出版情報: Berlin : Springer-Verlag, c1999  x, 761 p. ; 24 cm
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The Equations of Motion / Chapter 1:
Introduction, the Equations / 1:
Some General Properties of Navier-Stokes Equations / 2:
References
Principles of Turbulent Flow Modeling / Chapter 2:
Introduction and Averaging Procedures
The Reynolds-Averaged Mean-Flow Equations
The Closure Problem / 3:
Homogeneous and Inhomogeneous Flows / 4:
The Eddy-Viscosity Concept / 5:
Two-Point Homogeneous Turbulence / Chapter 3:
Introduction
Homogeneous Turbulence ; Correlations and Spectra
The Dynamics of Second-Order Correlations
Theory of Homogeneous Isotropic Turbulence
Rapid Distorsion Theory
Second-Order Turbulence Modeling / Chapter 4:
Reynolds-Stress Modeling
The Transfer Term
Inhomogeneous Flow
Non Linear Ev and Ars Models
Intermittency Modeling
Definition of Turbulence Models / Appendix A:
Turbulent Two-Dimensional Shear Flows / Chapter 5:
Thin Free Shear Layers, Classification
Asymptotics of Wall Shear Layers
Channel and Pipe Flows
Zero-Pressure-Gradient Boundary Layers
Jets / 6:
Wakes / 7:
Complex Effects in Turbulent Flows / Chapter 6:
2D Boundary Layers in Pressure Gradients
Two-Dimensional Turbulent Separation
Classification of Three-Dimensional Flows
Three-Dimensional Turbulent Boundary Layers
Curvature Effects
Rotation Effects
Lateral Straining
Imposition of Sudden Strains / 8:
Roughness Effects / 9:
Freestream Turbulence / 10:
Three-Dimensional Duct Flow / 11:
Geometry Concepts
Subject Index
List of Symbols and Page of First Occurrence
The Equations of Motion / Chapter 1:
Introduction, the Equations / 1:
Some General Properties of Navier-Stokes Equations / 2:
10.

図書

図書
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
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