Abstract data structures, 70
Adams-Bashforth-Moulton, 204
Address, see Memory 555
Airy functions, 421
Alias, 241
Amdahl’s law, 365
Analog, 555
filters, 250
Animations, 5, 64, 312, 314, 428, 432, 494, 495, 515, 555, 568, 586–592, 627
Antiferromagnet, 392
Architecture, 158, 169, 352–363, 368, 374, 376, 378, 555, see also Memory
dimension, 557, see also Matrices
Asymptotes, 293
predictable, 309
strange, 309
Autocorrelation function, 246–250
awt, 565
Ballistic deposition, 332–333, 338–339
BASIC beginner’s code, 7n
Basic machine language, 7, 556
Beating, 210
Bessel functions, 36–39, 202, 546
Bias, 20
diagram, 294
dimension of, 343
Binary point, 19
Binning, 295
reversal, 258
Block walls, 392
Blocking, 619
Blue Gene, see IBM Blue, 373
Boltzmann distribution, 393
Bootable cluster, 620
Bound states, 152–154, 211–221, 225, 408, 411–420, 435, 540–545
Boundary conditions, 198, 429, 437
Break command, 451
Butterfly operation, 258
data, 385
CD contents, 626
Central difference, 148
Central processing unit, see CPU, 353
Central storage, 354
Fourier analysis of, 317
of pendulum, 302
Chi squared measure, 186
CISC, 357
member, 106
structure, 106
superclass, 99
CLASSPATH, 562
Column-major order, 165, 353, 556
Command-line interpreter, 7
collective, 619
time, 365
Communicator, 605
Complex numbers, 67
lossless, 268
Computational
physics, 1
Concurrent processing, see Parallel computing, 557
default, 74
auto, 246
coefficient, 187
growth, 338
Courant stability condition, 502, 504, 512, 513
Course grain parallel, 362
Covariance, 187
CPU, 352–355, 357–360, 366, 372, 376, 385–386, 556
RISC, 357
time, 358
Crank-Nicolson method, 472–475
Cubic splines, see Splines, 179
Cumulative distribution, 143
Curie temperature, 392
Curve fitting, see Data fitting, 176
Cygwin, 568
Data
cache, see Cache 385
encapsulation, 89
fitting, 176
hiding, 101
parallel, 362
structures, 70
Daughter class, 85
Decay
spontaneous, 184
Density of states, 400
Deposition, 332
ballistic, 333
correlated ballistic, 337
central difference, 148, 151, 413n, 431
error in, 149
extrapolated difference, 149
second, 151, 180, 200, 216, 431
Differential equations, 194–229
algorithms, 200
boundary conditions, 198
dynamical form, 198
Euler’s rule, 201
initial conditions, 198
order, 196
partial, see PDEs 437
Runge–Kutta algorithm, 202
Differentiation, see Derivatives 147
Diffusion-limited aggregation, 339
Dimension, 557
array, 165
fractional, 326–329, 335–337, 342
Hausdorf-Besicovitch, 326
logical, 167
schemes, 166
Discrete Fourier transform, 237–243, 249
Distributed memory, 363
Documentation, Java, 16
Double
Drag, see Friction 226
DRAM, 354
drand, 114
Driving force, 211
Duffing oscillator, 318
DX, see OpenDX 45
Eigenvalues, 164, 170, 174, 198, 212–221, 245, 491, 540
Electrostatic potential, 439
Elliptic integral, 304
Entropy, 299
Environmental variables, 562, 595
Equations
Korteweg–de Vries, 515
Burgers’, 510
differential, 194
of motion, 226
Van der Pool, 318
Ergodic, 395
approximation, see Algorithm 30
in differentiation, 149
minimum, 42
multiplicative, 34
N-D integration, 139
random, 30
roundoff, 28, 31, 34–36, 39, 41, 42, 44, 110, 124, 129, 132, 138, 149, 200, 201, 518
types of, 30
Euler’s rule, 201–203, 413n, 416
Exceptions, 13
Exchange energy, 391
Extinction, 293
Extrapolated difference, 148
Fast Fourier transform, see FFT 256
Feigenbaum constants, 297
Ferromagnet, 392
Fetch, 360
Feynman
postulates, 411
propagator, 409
Filters
analog, 250
sinc, 253
windowed, 253
Fine grain parallel, 362
Finite
difference equation, 120
difference time domain, 499–506
differences, 120, 443, 493, 527, 532
best, 176
global, 185
goodness, 186
Newton–Raphson, 193
Fixed points in maps, 291, 307
Fixed-point numbers, 18
Floating-point numbers, 18–24, 31, 558
vs Java, 380
Forward difference, see Derivatives 147
Fourier
autocorrelation relation, 249
discrete transform, see Discrete Fourier transform 237
fast transform, see FFT 256
of half-wave, 235
integral, 236
PDE solution via, 440
of sawtooth, 234
short-time transform, 268
theorem, 232
transform, 231, 236, 580, see also FFT
coastline, 334
dimension, see Dimension 326
Pollock painting, 342
Friction, 209–210, 307, 309, 317, 521, 533
Functional, 408
Galerkin decomposition, 456–459
Game of Life, 343
distribution, 144
elimination, 551
Global array languages, 361
Gnuplot, 45, 56–65, 447, 492, 520, 538, 568, 570
prompt, 57
Granularity, 363
Grid points, 132, 503, 512, 513, 519, 546, 551
Growth models, 289–297, 319–345
Hénon–Heiles potential, 318
Half-wave function, 235
Hamilton’s principle, 408
Harmonics, 232
Heap, 383
Heat bath, 424
Hexadecimal, 558
High performance computing, 352–388
Hilbert transform, 549
HPC, see High performance computing 375
Huygens’s principle, 408
Hyperbolic point, 307
I/O, see Input/output 13
Impedance, 70
import, 90
Importance sampling, 140
Inheritance, see Objects 89
Initial conditions, 198
streams, 566
Instructions
streams, 362
from splines, 181
Gaussian quadrature, 130
mapping points, 131
multi-dimensional, 138
rejection techniques for, 136
variance reduction, 140
via mean value, 137
via von Neumann rejection, 140
Integro-differential equation, 540
Intermittency, 293
Interpolation
splines, 179
Inverse, 164
Ising model, 390–407 2-D, 393, 400
Jacobi method, 445
Jacobian matrix, 162
JAMA, 168, 170–173, 187, 190, 193, 463, 545, 551, 552, 623
Java
vs Fortran, 380
developer’s kit, 564
I/O, 12
matrix storage, 353
programs on CD, 626
virtual machine, 376
javadoc, 16
Just-In-Time compiler, 377
Korteweg-de Vries equation, 515
Lag time, 246
Lagrange interpolation, 177–179
Languages
BASIC, 7
computer, 6
interpreted, 8
Laplace’s equation, 439–463, 531
Lattice computations, 390, 413n, 414, 421
Lattice points, see Grid points 390
Lax–Wendroff algorithm, 511–514
Leap frog, see Time stepping, 464
Least-squares fitting, 184–193
Length of coastline, 334
Libraries, see Subroutines 169
Limit cycles, 308
Linear
congruent method, 110
least square fitting, 186
regression, 186
superposition, 197
Link, 8
Lippmann–Schwinger equation, 547
Load, 8
balancing, 367
module, 8
Logical size, 167
Lorenz attractor, 318
Lyapunov coefficients, 298–300
Machine
numbers, 18
Master and slave, 605, see also Tasks 650
column-major order, 165
diagonalization, 164
equations, 547
tri-diagonal, 474
Mean value theorem, 137
distributed, 363
dynamic allocation, 167
heap, 383
pages, 165
Message passing, 362–363, 368–372, 593–620
Methods
dynamic, 91
override, 99
static/nonstatic, see Static/Nonstatic 76
Metropolis algorithm, 394–398, 400, 413
Microcanonical ensemble, 393, 424
Microcode, 357
Miller’s device, 37
Monte Carlo
error in, 139
simulations, 35, 109, 116, 119, 136–145, 339, 390, 394, 417, 424, 429, 609, see also Metropolis
Mother class, 85
commands, 621
Multiple-core processors, 358
Multiresolution analysis, 274
Multitasking, 356–357, 367–368
NAN, 24
Navier–Stokes equation, 509, 521–532
Netlib, 169
Newton–Raphson
algorithm, 153–157, 160–193, 221
backtracking, 156
Noise
Perlin addition, 345
reduction, 246
Nonlinear
ODE, 197
oscillations, see Oscillations 194
Nonstatic, see Static/Nonstatic 71
Normal
distribution, 144
mode expansions, 232, 440, 480
numbers, 19
Numbers binary, 17
IEEE, 19
machine, 18
normal/subnormal, 19
octal, 17
uniform, 116
Nyquist criterion, 242
Nyquist-Shannon interpolation, 254
code, 8
hierarchies, 98
properties, 71
Octal numbers, 17
second order, 227
One cycle population, 291
OOP, see Objects oriented programs 80
OpenDX, 45, 65, 347, 452, 492, 538, 568–592
Operands, 353
Operating system, 7
Optimization, 39, 158, 169, 207, 375–388, 611, 614, 627
Oscillations
anharmonic/harmonic, 194, 206, 232
driven, 210
Fourier analysis of, 232
in phase space, 306
isochronous, 206
populations, 291
other.object, 78
Over relaxation, see Relaxation 446
Overdetermined, 163
Overhead, 365, 368, 378, 609, 614
Padding of signals, 243
fault, 355
Parallel computing, 352, 360–374, 593–622
Beowulf, 593
granularity, 362
master, slave, 369
message passing, 368
performance, 364
tuning, 611
types of, 361
Partial differential equations, see PDEs 437
Path integration, 390, 411–423
elliptic, 439
explicit solution of, 493
hyperbolic, 478
implicit solution, 493
types of, 437
weak form of, 455
analytic solution, 304
bifurcation diagram, 313
Performance, see Tuning 378
Period doubling, see Bifurcation 292
Periodic boundary conditions, 429
Phantom bit, 20
Phase space, 302, 305–312, 315–317, 320, 321, 520
Phase transitions, 390
Pipelined CPU, 357
Planetary motion, 229
animation, 64
complex, 60
field, 62
parametric, 83
Poisson’s equation, 439–440, 443–445, 454
Population dynamics, 289–297, 301, 319–324
Potentials
delta shell, 544
Lennard-Jones, 426
momentum space, 544
Pov-Ray, 348
Power spectrum, 249
Precision
machine, 25
tests of, 208
Predictor-corrector methods, 205
Primitive data types, 70
Principal values, 549
printf, 12
Private objects, 100
Problem solving paradigm, 2
design, 10
for parallel, 368
structured, 10
for virtual memory, 356
visual, 579
Programs, 626
Projectile motion, 86, 225–228
Propagator, 409
Pseudorandom, see
Random numbers 110
Pyramid FFT, 279
Quadrature, 123
Quantum
bouncer, 421
scattering, 546, see also Bound states, Scattering
Race condition, 372
Radioactive decay, 119
Radix, 18
Random numbers, 109–116, 297, 329
linear congruent, 110
nonuniform, 141
for random walk, 40, 116–118, 338–339, 401–402
Rank, 605
Ray tracing, 348
Rejection techniques, 136, 396
Relaxation, 445–446, 451, 527–538
Rendering, 572
Reynolds number, 533
RLC circuits, 67
Romberg extrapolation, 136
importance, 140
Sawtooth function, 234
Scheduler, 594
Schrödinger equation, 212–221, 492, 497, 540–553,
time dependent, 492, see also Quantum 650
Script, 64, 590, 591, 596, 598, 601–603
Searching, see Trial and error 215
Section size, 360
Secular equation, 164
Self
affine connection, 329
limiting, 318
Serial computing, 362, 365, 366, 368, 560, 600, 616
Series summation, 27
Shannon Entropy, 299
Shells, 7
Sierpiski gasket, 327–329, 343
Sign bit, 22
Signal processing, 246
Significant figures/parts, 31
SIMD, 363
Sinc filter, 253
Singular integrals, 548
SISD, 363
crossing, 520
KdeV, 517
water wave, 515
Speedup, 610
Splines, 179
natural, 180
Spontaneous decay, 119, 121, 182, 184, 187, 290
SRAM, 354
Stable states, 293
Static/Nonstatic methods, 71–79, 91, 101
Statistical Mechanics, 393, 424–429
Stochastic, see Monte Carlo 119
Strange attractors, 309
see also Matrices 650
Subnormal numbers, 19
libraries, 158, 168–173, 623–625
Subscripts, see Dimension 166
Subtractive cancellation, 32–34, 37, 44, 147, 182, 187, 200, 206, 548
Successive
over-relaxation, see Relaxation 528
Symmetric multi processor, see SMP 360
Template methods, 91
Text editor, 563
Thermodynamics, 390–407, 416, 424, 428–429
this.object, 78
Three body problem, 229
Threshold in compression, 635, 637–638
Time delay, 225
Time stepping, 464, 465–468, 478, 482–484, 493–496, 510, 512–514
Top-down programming, 9
Transients, 211, 293, 294, 296, 312, 314
Trial and error, 146, 151–157, 161–163, 184, 185, 191–193, 198, 214–216, 219–222, 395, 396, 398, 402, 417, 422, 451, 455
Tuning, see Optimization 375
Two cycle, 292
Typename, see Data 71
Uncertainty principle, 266
Uniform
distribution, 109–110, 115–116, 131, 144, 297
weights, 144
Unix, 569
Value pass, 72
Van der Pool equation, 318
Variables
dynamic, 91
multitype, 105
static/nonstatic, 91
Vector processors, 359
fields, 499
Velocity Verlet algorithm, 431
Verlet algorithm, 431
Virtual machine, 376
Virtual memory, 165, 354–356, 375–378
Visual programming, 569
Visualization, 5, 45–65, 295, 568–592
of vectors, 452
von Neumann rejection, 140, 396
stability assessment, 434, 450, 468–470, 473, 475, 482, 483, 485, 502, 503
Wang–Landau Sampling (WLS), 400–409
Wave
shallow water, 515, see also Wavelets 650
basis sets, 270
Daubechies, 283
discrete transform (DWT), 274, 287
for compression, 635
multiresolution analysis, 274
Weak form of PDE, 455
Word length, 17
Worker, see Slave 605
Working set size, 376
Wrappers, 597