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Computer simulations with mathematica: explorations in complex physical and biological systems

Author: Gaylord, Richard J. ; Wellin, Paul R.Publisher: Springer, 1995. ; Telos Press 1995.Language: EnglishDescription: 297 p. : Graphs/Ill. ; 25 cm. includes CD-ROM / DVDISBN: 0387942742Type of document: BookBibliography/Index: Includes bibliographical references and indexContents Note: CD available inside back cover
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA76.9 .C65 G39 1995
(Browse shelf)
Available 001257335
Total holds: 0

Includes bibliographical references and index

CD available inside back cover


Computer Simulations with Mathematica® Explorations in Complex Physical and Biological Systems Contents Preface How to Use This Book ix xiii PART I Probabilistic Systems 1. The Random Walk One- and two-dimensional walks, calculating the mean shape of a walk, determining the critical exponent, visualizing the walk 3 2. The Self-Avoiding Walk Slithering snake motion, rearrangement by pivoting 17 3. Accretion Diffusion-limited aggregation, determining the fractal dimension, ballistic deposition, visualizing DLAs 31 4. Spreading Phenomena Single cluster growth, invasion percolation 45 5. Percolation Clustering Random site percolation, cluster labeling with the Hoshen-Kopelman algorithm, continuum percolation 57 6. The Ising Model Probabilistic Ising model, the Metropolis method, magnetization behavior 75 7. Darwinian Evolution Co-evolution and punctuated equilibrium 83 PART II Cellular Automata Cellular Automata Preliminaries Defining a cellular automaton, lattices, neighborhoods, boundary conditions 91 8. The Game of Life Game of Life, diffusion, boiling and weathering cellular automata 97 9. Avalanches Self-organized criticality, sandpiles 105 10. The Q2R Ising Model Ising cellular automaton 111 11. Excitable Media Self-propagating patterns, neuron action, cyclic space cellular automata, the hodgepodge machine for oscillatory chemical reactions 117 12. Traffic One-lane traffic with car stopping, two-lane one-way road with car passing, accidents and road work, the fundamental diagram 135 13. Forest Fires Deforestation, reforestation, forest size distribution 147 14. Complexity One-dimensional cellular automata, Wolfram rules, animations 157 PART III Appendices A. Mathematica Programming Expressions, patterns, evaluation, rewrite rules, transformation rules, higher-order functions 173 B. Random Numbers Random number generators, tests for randomness, using different probability distributions 207 C. Computer Simulations and MathLink Using MathLink to call external programs from within Mathematica, techniques in MathLink programming, by Todd Gayley 221 D. Remote Computing with Mathematica Connecting to a remote computer with a local front end, computing across networks 255 E. MathLink Program Listing A listing of all MathLink programs including WaLk2DC, Seed RandomC. PhasesC, SandpileC, OneLaneC, EpidemicC, and Life GameC Index 263 291

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