Computational physics : (Record no. 24700)

MARC details
000 -LEADER
fixed length control field 23614pam a2200409 i 4500
003 - CONTROL NUMBER IDENTIFIER
control field CUTN
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20180412145951.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 150624s2015 gw a b 001 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783527413157
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783527413157 (pbk.) :
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 9783527684663 (ePDF)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 9783527684694 (ePub)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN 9783527684670 (Mobi)
041 ## - LANGUAGE CODE
Language English
042 ## - AUTHENTICATION CODE
Authentication code ukblcatcopy
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 530.0113
Edition number 23
Item number LAN
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Landau, Rubin H.,
245 10 - TITLE STATEMENT
Title Computational physics :
Remainder of title problem solving with Python /
Statement of responsibility, etc Rubin H. Landau, Manuel J. Páez, Cristian C. Bordeianu.
250 ## - EDITION STATEMENT
Edition statement 3rd completely revised edition.
300 ## - PHYSICAL DESCRIPTION
Extent xxii, 622 pages :
Other physical details illustrations ;
Dimensions 25 cm
500 ## - GENERAL NOTE
General note The use of computation and simulation has become an essential part of the scientific process. Being able to transform a theory into an algorithm requires significant theoretical insight, detailed physical and mathematical understanding, and a working level of competency in programming. <br/><br/><br/><br/>This upper-division text provides an unusually broad survey of the topics of modern computational physics from a multidisciplinary, computational science point of view. Its philosophy is rooted in learning by doing (assisted by many model programs), with new scientific materials as well as with the Python programming language. Python has become very popular, particularly for physics education and large scientific projects. It is probably the easiest programming language to learn for beginners, yet is also used for mainstream scientific computing, and has packages for excellent graphics and even symbolic manipulations.<br/><br/><br/><br/>The text is designed for an upper-level undergraduate or beginning graduate course and provides the reader with the essential knowledge to understand computational tools and mathematical methods well enough to be successful. As part of the teaching of using computers to solve scientific problems, the reader is encouraged to work through a sample problem stated at the beginning of each chapter or unit, which involves studying the text, writing, debugging and running programs, visualizing the results, and the expressing in words what has been done and what can be concluded. Then there are exercises and problems at the end of each chapter for the reader to work on their own (with model programs given for that purpose).
505 ## - FORMATTED CONTENTS NOTE
Contents Dedication V<br/><br/><br/>Preface XIX<br/><br/><br/>1 Introduction 1<br/><br/><br/>1.1 Computational Physics and Computational Science 1<br/><br/><br/>1.2 This Book s Subjects 3<br/><br/><br/>1.3 This Book s Problems 4<br/><br/><br/>1.4 This Book s Language: The Python Ecosystem 8<br/><br/><br/>1.4.1 Python Packages (Libraries) 9<br/><br/><br/>1.4.2 This Book s Packages 10<br/><br/><br/>1.4.3 The EasyWay: Python Distributions (Package Collections) 12<br/><br/><br/>1.5 Python s Visualization Tools 13<br/><br/><br/>1.5.1 Visual (VPython) s 2D Plots 14<br/><br/><br/>1.5.2 VPython s Animations 17<br/><br/><br/>1.5.3 Matplotlib s 2D Plots 17<br/><br/><br/>1.5.4 Matplotlib s 3D Surface Plots 22<br/><br/><br/>1.5.5 Matplotlib s Animations 24<br/><br/><br/>1.5.6 Mayavi s Visualizations Beyond Plotting 26<br/><br/><br/>1.6 Plotting Exercises 30<br/><br/><br/>1.7 Python s Algebraic Tools 31<br/><br/><br/>2 Computing Software Basics 33<br/><br/><br/>2.1 Making Computers Obey 33<br/><br/><br/>2.2 ProgrammingWarmup 35<br/><br/><br/>2.2.1 Structured and Reproducible Program Design 36<br/><br/><br/>2.2.2 Shells, Editors, and Execution 37<br/><br/><br/>2.3 Python I/O 39<br/><br/><br/>2.4 Computer Number Representations (Theory) 40<br/><br/><br/>2.4.1 IEEE Floating-Point Numbers 41<br/><br/><br/>2.4.2 Python and the IEEE 754 Standard 47<br/><br/><br/>2.4.3 Over and Underflow Exercises 48<br/><br/><br/>2.4.4 Machine Precision (Model) 49<br/><br/><br/>2.4.5 Experiment: Your Machine s Precision 50<br/><br/><br/>2.5 Problem: Summing Series 51<br/><br/><br/>2.5.1 Numerical Summation (Method) 51<br/><br/><br/>2.5.2 Implementation and Assessment 52<br/><br/><br/>3 Errors and Uncertainties in Computations 53<br/><br/><br/>3.1 Types of Errors (Theory) 53<br/><br/><br/>3.1.1 Model for Disaster: Subtractive Cancelation 55<br/><br/><br/>3.1.2 Subtractive Cancelation Exercises 56<br/><br/><br/>3.1.3 Round-off Errors 57<br/><br/><br/>3.1.4 Round-off Error Accumulation 58<br/><br/><br/>3.2 Error in Bessel Functions (Problem) 58<br/><br/><br/>3.2.1 Numerical Recursion (Method) 59<br/><br/><br/>3.2.2 Implementation and Assessment: Recursion Relations 61<br/><br/><br/>3.3 Experimental Error Investigation 62<br/><br/><br/>3.3.1 Error Assessment 65<br/><br/><br/>4 Monte Carlo: Randomness, Walks, and Decays 69<br/><br/><br/>4.1 Deterministic Randomness 69<br/><br/><br/>4.2 Random Sequences (Theory) 69<br/><br/><br/>4.2.1 Random-Number Generation (Algorithm) 70<br/><br/><br/>4.2.2 Implementation: Random Sequences 72<br/><br/><br/>4.2.3 Assessing Randomness and Uniformity 73<br/><br/><br/>4.3 RandomWalks (Problem) 75<br/><br/><br/>4.3.1 Random-Walk Simulation 76<br/><br/><br/>4.3.2 Implementation: RandomWalk 77<br/><br/><br/>4.4 Extension: Protein Folding and Self-Avoiding RandomWalks 79<br/><br/><br/>4.5 Spontaneous Decay (Problem) 80<br/><br/><br/>4.5.1 Discrete Decay (Model) 81<br/><br/><br/>4.5.2 Continuous Decay (Model) 82<br/><br/><br/>4.5.3 Decay Simulation with Geiger Counter Sound 82<br/><br/><br/>4.6 Decay Implementation and Visualization 84<br/><br/><br/>5 Differentiation and Integration 85<br/><br/><br/>5.1 Differentiation 85<br/><br/><br/>5.2 Forward Difference (Algorithm) 86<br/><br/><br/>5.3 Central Difference (Algorithm) 87<br/><br/><br/>5.4 Extrapolated Difference (Algorithm) 87<br/><br/><br/>5.5 Error Assessment 88<br/><br/><br/>5.6 Second Derivatives (Problem) 90<br/><br/><br/>5.6.1 Second-Derivative Assessment 90<br/><br/><br/>5.7 Integration 91<br/><br/><br/>5.8 Quadrature as Box Counting (Math) 91<br/><br/><br/>5.9 Algorithm: Trapezoid Rule 93<br/><br/><br/>5.10 Algorithm: Simpson s Rule 94<br/><br/><br/>5.11 Integration Error (Assessment) 96<br/><br/><br/>5.12 Algorithm: Gaussian Quadrature 97<br/><br/><br/>5.12.1 Mapping Integration Points 98<br/><br/><br/>5.12.2 Gaussian Points Derivation 99<br/><br/><br/>5.12.3 Integration Error Assessment 100<br/><br/><br/>5.13 Higher Order Rules (Algorithm) 103<br/><br/><br/>5.14 Monte Carlo Integration by Stone Throwing (Problem) 104<br/><br/><br/>5.14.1 Stone Throwing Implementation 104<br/><br/><br/>5.15 Mean Value Integration (Theory and Math) 105<br/><br/><br/>5.16 Integration Exercises 106<br/><br/><br/>5.17 Multidimensional Monte Carlo Integration (Problem) 108<br/><br/><br/>5.17.1 Multi Dimension Integration Error Assessment 109<br/><br/><br/>5.17.2 Implementation: 10D Monte Carlo Integration 110<br/><br/><br/>5.18 Integrating Rapidly Varying Functions (Problem) 110<br/><br/><br/>5.19 Variance Reduction (Method) 110<br/><br/><br/>5.20 Importance Sampling (Method) 111<br/><br/><br/>5.21 von Neumann Rejection (Method) 111<br/><br/><br/>5.21.1 Simple Random Gaussian Distribution 113<br/><br/><br/>5.22 Nonuniform Assessment !N 113<br/><br/><br/>5.22.1 Implementation !N 114<br/><br/><br/>6 Matrix Computing 117<br/><br/><br/>6.1 Problem 3: N D Newton Raphson; Two Masses on a String 117<br/><br/><br/>6.1.1 Theory: Statics 118<br/><br/><br/>6.1.2 Algorithm: Multidimensional Searching 119<br/><br/><br/>6.2 Why Matrix Computing? 122<br/><br/><br/>6.3 Classes ofMatrix Problems (Math) 122<br/><br/><br/>6.3.1 Practical Matrix Computing 124<br/><br/><br/>6.4 Python Lists as Arrays 126<br/><br/><br/>6.5 Numerical Python (NumPy) Arrays 127<br/><br/><br/>6.5.1 NumPy s linalg Package 132<br/><br/><br/>6.6 Exercise: TestingMatrix Programs 134<br/><br/><br/>6.6.1 Matrix Solution of the String Problem 137<br/><br/><br/>6.6.2 Explorations 139<br/><br/><br/>7 Trial-and-Error Searching and Data Fitting 141<br/><br/><br/>7.1 Problem 1: A Search for Quantum States in a Box 141<br/><br/><br/>7.2 Algorithm: Trial-and-Error Roots via Bisection 142<br/><br/><br/>7.2.1 Implementation: Bisection Algorithm 144<br/><br/><br/>7.3 Improved Algorithm: Newton Raphson Searching 145<br/><br/><br/>7.3.1 Newton Raphson with Backtracking 147<br/><br/><br/>7.3.2 Implementation: Newton Raphson Algorithm 148<br/><br/><br/>7.4 Problem 2: Temperature Dependence ofMagnetization 148<br/><br/><br/>7.4.1 Searching Exercise 150<br/><br/><br/>7.5 Problem 3: Fitting An Experimental Spectrum 150<br/><br/><br/>7.5.1 Lagrange Implementation, Assessment 152<br/><br/><br/>7.5.2 Cubic Spline Interpolation (Method) 153<br/><br/><br/>7.6 Problem 4: Fitting Exponential Decay 156<br/><br/><br/>7.7 Least-Squares Fitting (Theory) 158<br/><br/><br/>7.7.1 Least-Squares Fitting: Theory and Implementation 160<br/><br/><br/>7.8 Exercises: Fitting Exponential Decay,Heat Flow andHubble s Law 162<br/><br/><br/>7.8.1 Linear Quadratic Fit 164<br/><br/><br/>7.8.2 Problem 5: Nonlinear Fit to a Breit Wigner 167<br/><br/><br/>8 Solving Differential Equations: Nonlinear Oscillations 171<br/><br/><br/>8.1 Free Nonlinear Oscillations 171<br/><br/><br/>8.2 Nonlinear Oscillators (Models) 171<br/><br/><br/>8.3 Types of Differential Equations (Math) 173<br/><br/><br/>8.4 Dynamic Form for ODEs (Theory) 175<br/><br/><br/>8.5 ODE Algorithms 177<br/><br/><br/>8.5.1 Euler s Rule 177<br/><br/><br/>8.6 Runge Kutta Rule 178<br/><br/><br/>8.7 Adams Bashforth Moulton Predictor Corrector Rule 183<br/><br/><br/>8.7.1 Assessment: rk2 vs. rk4 vs. rk45 185<br/><br/><br/>8.8 Solution for Nonlinear Oscillations (Assessment) 187<br/><br/><br/>8.8.1 Precision Assessment: Energy Conservation 188<br/><br/><br/>8.9 Extensions: Nonlinear Resonances, Beats, Friction 189<br/><br/><br/>8.9.1 Friction (Model) 189<br/><br/><br/>8.9.2 Resonances and Beats: Model, Implementation 190<br/><br/><br/>8.10 Extension: Time-Dependent Forces 190<br/><br/><br/>9 ODE Applications: Eigenvalues, Scattering, and Projectiles 193<br/><br/><br/>9.1 Problem: Quantum Eigenvalues in Arbitrary Potential 193<br/><br/><br/>9.1.1 Model: Nucleon in a Box 194<br/><br/><br/>9.2 Algorithms: Eigenvalues via ODE Solver + Search 195<br/><br/><br/>9.2.1 Numerov Algorithm for Schroedinger ODE !N 197<br/><br/><br/>9.2.2 Implementation: Eigenvalues viaODESolver + BisectionAlgorithm 200<br/><br/><br/>9.3 Explorations 203<br/><br/><br/>9.4 Problem: Classical Chaotic Scattering 203<br/><br/><br/>9.4.1 Model and Theory 204<br/><br/><br/>9.4.2 Implementation 206<br/><br/><br/>9.4.3 Assessment 207<br/><br/><br/>9.5 Problem: Balls Falling Out of the Sky 208<br/><br/><br/>9.6 Theory: Projectile Motion with Drag 208<br/><br/><br/>9.6.1 Simultaneous Second-Order ODEs 209<br/><br/><br/>9.6.2 Assessment 210<br/><br/><br/>9.7 Exercises: 2- and 3-Body Planet Orbits and ChaoticWeather 211<br/><br/><br/>10 High-Performance Hardware and Parallel Computers 215<br/><br/><br/>10.1 High-Performance Computers 215<br/><br/><br/>10.2 Memory Hierarchy 216<br/><br/><br/>10.3 The Central Processing Unit 219<br/><br/><br/>10.4 CPU Design: Reduced Instruction Set Processors 220<br/><br/><br/>10.5 CPU Design:Multiple-Core Processors 221<br/><br/><br/>10.6 CPU Design: Vector Processors 222<br/><br/><br/>10.7 Introduction to Parallel Computing 223<br/><br/><br/>10.8 Parallel Semantics (Theory) 224<br/><br/><br/>10.9 Distributed Memory Programming 226<br/><br/><br/>10.10 Parallel Performance 227<br/><br/><br/>10.10.1 Communication Overhead 229<br/><br/><br/>10.11 Parallelization Strategies 230<br/><br/><br/>10.12 Practical Aspects of MIMD Message Passing 231<br/><br/><br/>10.12.1 High-Level View ofMessage Passing 233<br/><br/><br/>10.12.2 Message Passing Example and Exercise 234<br/><br/><br/>10.13 Scalability 236<br/><br/><br/>10.13.1 Scalability Exercises 238<br/><br/><br/>10.14 Data Parallelism and Domain Decomposition 239<br/><br/><br/>10.14.1 Domain Decomposition Exercises 242<br/><br/><br/>10.15 Example: The IBM Blue Gene Supercomputers 243<br/><br/><br/>10.16 Exascale Computing via Multinode-Multicore GPUs 245<br/><br/><br/>11 Applied HPC: Optimization, Tuning, and GPU Programming 247<br/><br/><br/>11.1 General Program Optimization 247<br/><br/><br/>11.1.1 Programming for Virtual Memory (Method) 248<br/><br/><br/>11.1.2 Optimization Exercises 249<br/><br/><br/>11.2 Optimized Matrix Programming with NumPy 251<br/><br/><br/>11.2.1 NumPy Optimization Exercises 254<br/><br/><br/>11.3 Empirical Performance of Hardware 254<br/><br/><br/>11.3.1 Racing Python vs. Fortran/C 255<br/><br/><br/>11.4 Programming for the Data Cache (Method) 262<br/><br/><br/>11.4.1 Exercise 1: Cache Misses 264<br/><br/><br/>11.4.2 Exercise 2: Cache Flow 264<br/><br/><br/>11.4.3 Exercise 3: Large-Matrix Multiplication 265<br/><br/><br/>11.5 Graphical Processing Units for High Performance Computing 266<br/><br/><br/>11.5.1 The GPU Card 267<br/><br/><br/>11.6 Practical Tips forMulticore and GPU Programming !N 267<br/><br/><br/>11.6.1 CUDA Memory Usage 270<br/><br/><br/>11.6.2 CUDA Programming !N 271<br/><br/><br/>12 Fourier Analysis: Signals and Filters 275<br/><br/><br/>12.1 Fourier Analysis of Nonlinear Oscillations 275<br/><br/><br/>12.2 Fourier Series (Math) 276<br/><br/><br/>12.2.1 Examples: Sawtooth and Half-Wave Functions 278<br/><br/><br/>12.3 Exercise: Summation of Fourier Series 279<br/><br/><br/>12.4 Fourier Transforms (Theory) 279<br/><br/><br/>12.5 The Discrete Fourier Transform 281<br/><br/><br/>12.5.1 Aliasing (Assessment) 285<br/><br/><br/>12.5.2 Fourier Series DFT (Example) 287<br/><br/><br/>12.5.3 Assessments 288<br/><br/><br/>12.5.4 Nonperiodic Function DFT (Exploration) 290<br/><br/><br/>12.6 Filtering Noisy Signals 290<br/><br/><br/>12.7 Noise Reduction via Autocorrelation (Theory) 290<br/><br/><br/>12.7.1 Autocorrelation Function Exercises 293<br/><br/><br/>12.8 Filtering with Transforms (Theory) 294<br/><br/><br/>12.8.1 Digital Filters:Windowed Sinc Filters (Exploration) !N 296<br/><br/><br/>12.9 The Fast Fourier Transform Algorithm !N 299<br/><br/><br/>12.9.1 Bit Reversal 301<br/><br/><br/>12.10 FFT Implementation 303<br/><br/><br/>12.11 FFT Assessment 304<br/><br/><br/>13 Wavelet and Principal Components Analyses: Nonstationary Signals and Data Compression 307<br/><br/><br/>13.1 Problem: Spectral Analysis of Nonstationary Signals 307<br/><br/><br/>13.2 Wavelet Basics 307<br/><br/><br/>13.3 Wave Packets and Uncertainty Principle (Theory) 309<br/><br/><br/>13.3.1 Wave Packet Assessment 311<br/><br/><br/>13.4 Short-Time Fourier Transforms (Math) 311<br/><br/><br/>13.5 TheWavelet Transform 313<br/><br/><br/>13.5.1 GeneratingWavelet Basis Functions 313<br/><br/><br/>13.5.2 ContinuousWavelet Transform Implementation 316<br/><br/><br/>13.6 DiscreteWavelet Transforms,Multiresolution Analysis !N 317<br/><br/><br/>13.6.1 Pyramid Scheme Implementation !N 323<br/><br/><br/>13.6.2 DaubechiesWavelets via Filtering 327<br/><br/><br/>13.6.3 DWT Implementation and Exercise 330<br/><br/><br/>13.7 Principal Components Analysis 332<br/><br/><br/>13.7.1 Demonstration of Principal Component Analysis 334<br/><br/><br/>13.7.2 PCA Exercises 337<br/><br/><br/>14 Nonlinear Population Dynamics 339<br/><br/><br/>14.1 Bug Population Dynamics 339<br/><br/><br/>14.2 The Logistic Map (Model) 339<br/><br/><br/>14.3 Properties of NonlinearMaps (Theory and Exercise) 341<br/><br/><br/>14.3.1 Fixed Points 342<br/><br/><br/>14.3.2 Period Doubling, Attractors 343<br/><br/><br/>14.4 Mapping Implementation 344<br/><br/><br/>14.5 Bifurcation Diagram (Assessment) 345<br/><br/><br/>14.5.1 Bifurcation Diagram Implementation 346<br/><br/><br/>14.5.2 Visualization Algorithm: Binning 347<br/><br/><br/>14.5.3 Feigenbaum Constants (Exploration) 348<br/><br/><br/>14.6 Logistic Map Random Numbers (Exploration) !N 348<br/><br/><br/>14.7 Other Maps (Exploration) 348<br/><br/><br/>14.8 Signals of Chaos: Lyapunov Coefficient and Shannon Entropy !N 349<br/><br/><br/>14.9 Coupled Predator PreyModels 353<br/><br/><br/>14.10 Lotka Volterra Model 354<br/><br/><br/>14.10.1 Lotka Volterra Assessment 356<br/><br/><br/>14.11 Predator Prey Chaos 356<br/><br/><br/>14.11.1 Exercises 359<br/><br/><br/>14.11.2 LVM with Prey Limit 359<br/><br/><br/>14.11.3 LVM with Predation Efficiency 360<br/><br/><br/>14.11.4 LVM Implementation and Assessment 361<br/><br/><br/>14.11.5 Two Predators, One Prey (Exploration) 362<br/><br/><br/>15 Continuous Nonlinear Dynamics 363<br/><br/><br/>15.1 Chaotic Pendulum 363<br/><br/><br/>15.1.1 Free Pendulum Oscillations 364<br/><br/><br/>15.1.2 Solution as Elliptic Integrals 365<br/><br/><br/>15.1.3 Implementation and Test: Free Pendulum 366<br/><br/><br/>15.2 Visualization: Phase-Space Orbits 367<br/><br/><br/>15.2.1 Chaos in Phase Space 368<br/><br/><br/>15.2.2 Assessment in Phase Space 372<br/><br/><br/>15.3 Exploration: Bifurcations of Chaotic Pendulums 374<br/><br/><br/>15.4 Alternate Problem: The Double Pendulum 375<br/><br/><br/>15.5 Assessment: Fourier/Wavelet Analysis of Chaos 377<br/><br/><br/>15.6 Exploration: Alternate Phase-Space Plots 378<br/><br/><br/>15.7 Further Explorations 379<br/><br/><br/>16 Fractals and Statistical Growth Models 383<br/><br/><br/>16.1 Fractional Dimension (Math) 383<br/><br/><br/>16.2 The Sierpi1/2ski Gasket (Problem 1) 384<br/><br/><br/>16.2.1 Sierpi1/2ski Implementation 384<br/><br/><br/>16.2.2 Assessing Fractal Dimension 385<br/><br/><br/>16.3 Growing Plants (Problem 2) 386<br/><br/><br/>16.3.1 Self-Affine Connection (Theory) 386<br/><br/><br/>16.3.2 Barnsley s Fern Implementation 387<br/><br/><br/>16.3.3 Self-Affinity in Trees Implementation 389<br/><br/><br/>16.4 Ballistic Deposition (Problem 3) 390<br/><br/><br/>16.4.1 Random Deposition Algorithm 390<br/><br/><br/>16.5 Length of British Coastline (Problem 4) 391<br/><br/><br/>16.5.1 Coastlines as Fractals (Model) 392<br/><br/><br/>16.5.2 Box Counting Algorithm 392<br/><br/><br/>16.5.3 Coastline Implementation and Exercise 393<br/><br/><br/>16.6 Correlated Growth, Forests, Films (Problem 5) 395<br/><br/><br/>16.6.1 Correlated Ballistic Deposition Algorithm 395<br/><br/><br/>16.7 Globular Cluster (Problem 6) 396<br/><br/><br/>16.7.1 Diffusion-Limited Aggregation Algorithm 396<br/><br/><br/>16.7.2 Fractal Analysis of DLA or a Pollock 399<br/><br/><br/>16.8 Fractals in Bifurcation Plot (Problem 7) 400<br/><br/><br/>16.9 Fractals from Cellular Automata 400<br/><br/><br/>16.10 Perlin Noise Adds Realism !N 402<br/><br/><br/>16.10.1 Ray Tracing Algorithms 404<br/><br/><br/>16.11 Exercises 407<br/><br/><br/>17 Thermodynamic Simulations and Feynman Path Integrals 409<br/><br/><br/>17.1 Magnets via Metropolis Algorithm 409<br/><br/><br/>17.2 An IsingChain (Model) 410<br/><br/><br/>17.3 Statistical Mechanics (Theory) 412<br/><br/><br/>17.3.1 Analytic Solution 413<br/><br/><br/>17.4 Metropolis Algorithm 413<br/><br/><br/>17.4.1 Metropolis Algorithm Implementation 416<br/><br/><br/>17.4.2 Equilibration, Thermodynamic Properties (Assessment) 417<br/><br/><br/>17.4.3 Beyond Nearest Neighbors, 1D (Exploration) 419<br/><br/><br/>17.5 Magnets viaWang Landau Sampling !N 420<br/><br/><br/>17.6 Wang Landau Algorithm 423<br/><br/><br/>17.6.1 WLS IsingModel Implementation 425<br/><br/><br/>17.6.2 WLS IsingModel Assessment 428<br/><br/><br/>17.7 Feynman Path Integral Quantum Mechanics !N 429<br/><br/><br/>17.8 Feynman s Space Time Propagation (Theory) 429<br/><br/><br/>17.8.1 Bound-StateWave Function (Theory) 431<br/><br/><br/>17.8.2 Lattice Path Integration (Algorithm) 432<br/><br/><br/>17.8.3 Lattice Implementation 437<br/><br/><br/>17.8.4 Assessment and Exploration 440<br/><br/><br/>17.9 Exploration: Quantum Bouncer s Paths !N 440<br/><br/><br/>18 Molecular Dynamics Simulations 445<br/><br/><br/>18.1 Molecular Dynamics (Theory) 445<br/><br/><br/>18.1.1 Connection to Thermodynamic Variables 449<br/><br/><br/>18.1.2 Setting Initial Velocities 449<br/><br/><br/>18.1.3 Periodic Boundary Conditions and Potential Cutoff 450<br/><br/><br/>18.2 Verlet and Velocity Verlet Algorithms 451<br/><br/><br/>18.3 1D Implementation and Exercise 453<br/><br/><br/>18.4 Analysis 456<br/><br/><br/>19 PDE Reviewand Electrostatics via Finite Differences and Electrostatics via Finite Differences 461<br/><br/><br/>19.1 PDE Generalities 461<br/><br/><br/>19.2 Electrostatic Potentials 463<br/><br/><br/>19.2.1 Laplace s Elliptic PDE (Theory) 463<br/><br/><br/>19.3 Fourier Series Solution of a PDE 464<br/><br/><br/>19.3.1 Polynomial Expansion as an Algorithm 466<br/><br/><br/>19.4 Finite-Difference Algorithm 467<br/><br/><br/>19.4.1 Relaxation and Over-relaxation 469<br/><br/><br/>19.4.2 Lattice PDE Implementation 470<br/><br/><br/>19.5 Assessment via Surface Plot 471<br/><br/><br/>19.6 Alternate Capacitor Problems 471<br/><br/><br/>19.7 Implementation and Assessment 474<br/><br/><br/>19.8 Electric Field Visualization (Exploration) 475<br/><br/><br/>19.9 Review Exercise 476<br/><br/><br/>20 Heat Flow via Time Stepping 477<br/><br/><br/>20.1 Heat Flow via Time-Stepping (Leapfrog) 477<br/><br/><br/>20.2 The Parabolic Heat Equation (Theory) 478<br/><br/><br/>20.2.1 Solution: Analytic Expansion 478<br/><br/><br/>20.2.2 Solution: Time Stepping 479<br/><br/><br/>20.2.3 von Neumann Stability Assessment 481<br/><br/><br/>20.2.4 Heat Equation Implementation 483<br/><br/><br/>20.3 Assessment and Visualization 483<br/><br/><br/>20.4 Improved Heat Flow: Crank Nicolson Method 484<br/><br/><br/>20.4.1 Solution of Tridiagonal Matrix Equations !N 487<br/><br/><br/>20.4.2 Crank Nicolson Implementation, Assessment 490<br/><br/><br/>21 Wave Equations I: Strings and Membranes 491<br/><br/><br/>21.1 A Vibrating String 491<br/><br/><br/>21.2 The HyperbolicWave Equation (Theory) 491<br/><br/><br/>21.2.1 Solution via Normal-Mode Expansion 493<br/><br/><br/>21.2.2 Algorithm: Time Stepping 494<br/><br/><br/>21.2.3 Wave Equation Implementation 496<br/><br/><br/>21.2.4 Assessment, Exploration 497<br/><br/><br/>21.3 Strings with Friction (Extension) 499<br/><br/><br/>21.4 Strings with Variable Tension and Density 500<br/><br/><br/>21.4.1 Waves on Catenary 501<br/><br/><br/>21.4.2 Derivation of Catenary Shape 501<br/><br/><br/>21.4.3 Catenary and FrictionalWave Exercises 503<br/><br/><br/>21.5 Vibrating Membrane (2DWaves) 504<br/><br/><br/>21.6 Analytical Solution 505<br/><br/><br/>21.7 Numerical Solution for 2DWaves 508<br/><br/><br/>22 Wave Equations II: QuantumPackets and Electromagnetic 511<br/><br/><br/>22.1 Quantum Wave Packets 511<br/><br/><br/>22.2 Time-Dependent Schroedinger Equation (Theory) 511<br/><br/><br/>22.2.1 Finite-Difference Algorithm 513<br/><br/><br/>22.2.2 Wave Packet Implementation, Animation 514<br/><br/><br/>22.2.3 Wave Packets in OtherWells (Exploration) 516<br/><br/><br/>22.3 Algorithm for the 2D Schroedinger Equation 517<br/><br/><br/>22.3.1 Exploration: Bound and Diffracted 2D Packet 518<br/><br/><br/>22.4 Wave Packet Wave Packet Scattering 518<br/><br/><br/>22.4.1 Algorithm 520<br/><br/><br/>22.4.2 Implementation 520<br/><br/><br/>22.4.3 Results and Visualization 522<br/><br/><br/>22.5 E&MWaves via Finite-Difference Time Domain 525<br/><br/><br/>22.6 Maxwell s Equations 525<br/><br/><br/>22.7 FDTD Algorithm 526<br/><br/><br/>22.7.1 Implementation 530<br/><br/><br/>22.7.2 Assessment 530<br/><br/><br/>22.7.3 Extension: Circularly PolarizedWaves 531<br/><br/><br/>22.8 Application:Wave Plates 533<br/><br/><br/>22.9 Algorithm 534<br/><br/><br/>22.10 FDTD Exercise and Assessment 535<br/><br/><br/>23 Electrostatics via Finite Elements 537<br/><br/><br/>23.1 Finite-Element Method !N 537<br/><br/><br/>23.2 Electric Field from Charge Density (Problem) 538<br/><br/><br/>23.3 Analytic Solution 538<br/><br/><br/>23.4 Finite-Element (Not Difference) Methods, 1D 539<br/><br/><br/>23.4.1 Weak Form of PDE 539<br/><br/><br/>23.4.2 Galerkin Spectral Decomposition 540<br/><br/><br/>23.5 1D FEMImplementation and Exercises 544<br/><br/><br/>23.5.1 1D Exploration 547<br/><br/><br/>23.6 Extension to 2D Finite Elements 547<br/><br/><br/>23.6.1 Weak Form of PDE 548<br/><br/><br/>23.6.2 Galerkin s Spectral Decomposition 548<br/><br/><br/>23.6.3 Triangular Elements 549<br/><br/><br/>23.6.4 Solution as Linear Equations 551<br/><br/><br/>23.6.5 Imposing Boundary Conditions 552<br/><br/><br/>23.6.6 FEM2D Implementation and Exercise 554<br/><br/><br/>23.6.7 FEM2D Exercises 554<br/><br/><br/>24 Shocks Waves and Solitons 555<br/><br/><br/>24.1 Shocks and Solitons in ShallowWater 555<br/><br/><br/>24.2 Theory: Continuity and Advection Equations 556<br/><br/><br/>24.2.1 Advection Implementation 558<br/><br/><br/>24.3 Theory: ShockWaves via Burgers Equation 559<br/><br/><br/>24.3.1 Lax Wendroff Algorithm for Burgers Equation 560<br/><br/><br/>24.3.2 Implementation and Assessment of Burgers Shock Equation 561<br/><br/><br/>24.4 Including Dispersion 562<br/><br/><br/>24.5 Shallow-Water Solitons: The KdeV Equation 563<br/><br/><br/>24.5.1 Analytic Soliton Solution 563<br/><br/><br/>24.5.2 Algorithm for KdeV Solitons 564<br/><br/><br/>24.5.3 Implementation: KdeV Solitons 565<br/><br/><br/>24.5.4 Exploration: Solitons in Phase Space, Crossing 567<br/><br/><br/>24.6 Solitons on Pendulum Chain 567<br/><br/><br/>24.6.1 Including Dispersion 568<br/><br/><br/>24.6.2 Continuum Limit, the Sine-Gordon Equation 570<br/><br/><br/>24.6.3 Analytic SGE Solution 571<br/><br/><br/>24.6.4 Numeric Solution: 2D SGE Solitons 571<br/><br/><br/>24.6.5 2D Soliton Implementation 573<br/><br/><br/>24.6.6 SGE Soliton Visualization 574<br/><br/><br/>25 Fluid Dynamics 575<br/><br/><br/>25.1 River Hydrodynamics 575<br/><br/><br/>25.2 Navier Stokes Equation (Theory) 576<br/><br/><br/>25.2.1 Boundary Conditions for Parallel Plates 578<br/><br/><br/>25.2.2 Finite-Difference Algorithm and Overrelaxation 580<br/><br/><br/>25.2.3 Successive Overrelaxation Implementation 581<br/><br/><br/>25.3 2D Flow over a Beam 581<br/><br/><br/>25.4 Theory: Vorticity Form of Navier Stokes Equation 582<br/><br/><br/>25.4.1 Finite Differences and the SOR Algorithm 584<br/><br/><br/>25.4.2 Boundary Conditions for a Beam 585<br/><br/><br/>25.4.3 SOR on a Grid 587<br/><br/><br/>25.4.4 Flow Assessment 589<br/><br/><br/>25.4.5 Exploration 590<br/><br/><br/>26 Integral Equations of QuantumMechanics 591<br/><br/><br/>26.1 Bound States of Nonlocal Potentials 591<br/><br/><br/>26.2 Momentum Space Schroedinger Equation (Theory) 592<br/><br/><br/>26.2.1 Integral toMatrix Equations 593<br/><br/><br/>26.2.2 Delta-Shell Potential (Model) 595<br/><br/><br/>26.2.3 Binding Energies Solution 595<br/><br/><br/>26.2.4 Wave Function (Exploration) 597<br/><br/><br/>26.3 Scattering States of Nonlocal Potentials !N 597<br/><br/><br/>26.4 Lippmann Schwinger Equation (Theory) 598<br/><br/><br/>26.4.1 Singular Integrals (Math) 599<br/><br/><br/>26.4.2 Numerical Principal Values 600<br/><br/><br/>26.4.3 Reducing Integral Equations to Matrix Equations (Method) 600<br/><br/><br/>26.4.4 Solution via Inversion, Elimination 602<br/><br/><br/>26.4.5 Scattering Implementation 603<br/><br/><br/>26.4.6 ScatteringWave Function (Exploration) 604<br/><br/><br/>Appendix A Codes, Applets, and Animations 607<br/><br/><br/>Bibliography 609<br/><br/><br/>Index 615
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Physics
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Python (Computer program language)
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Páez Mejía, Manuel José,
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Bordeianu, Cristian C.,
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Dewey Decimal Classification
Koha item type General Books
100 1# - MAIN ENTRY--PERSONAL NAME
Relator term author.
500 ## - GENERAL NOTE
Institution to which field applies Uk
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE
Additional physical form available note Also issued online.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
General subdivision Computer simulation.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
General subdivision Mathematical models.
700 1# - ADDED ENTRY--PERSONAL NAME
Relator term author.
700 1# - ADDED ENTRY--PERSONAL NAME
Relator term author.
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Collection code Home library Location Shelving location Date of Cataloging Total Checkouts Full call number Barcode Checked out Date last seen Date checked out Price effective from Koha item type Public note
    Dewey Decimal Classification     Non-fiction CUTN Central Library CUTN Central Library Sciences 12/04/2018 1 530.011 LAN 31122 20/05/2020 20/05/2020 20/05/2020 12/04/2018 General Books Transferred to Dr.P.Ravindran

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