Index

From Molecular Dynamics Simulation, by J. M. Haile,
John Wiley & Sons, New York, 1997.

Abbreviations, table of, 469
Acceleration, 39
… initial values of, 203, 385, 458-459
Accuracy, see also Bias; Errors, in properties,
…… systematic
… versus precision, 180
… of theories, 20
Adelard of Bath, 8
Air, properties of, 463
Alder-Wainwright algorithm, 113-114
Angular momentum, 89-91
Apriori probability, 49, 68
Argon:
… potential parameters for, 462
… properties of, 31, 463
… second virial coefficient of, 218-219
Autocorrelation functions, 278, 319, see also
…… Time, correlation functions
… calculation algorithms for, 284-287
… code for computing, 399-410
… definition of, 278
… derivatives of, 280-281
… long-time tails of, 289-291, 303, 306
… short-time behavior of, 281-282, 323
… stress, 293-296, 305-306
… uncertainties in, 287-289, 295-296
… velocity, 233, 282-291
Average:
… ensemble, 14, 51, 341, 343
… expected, 73-76, 101
… of reciprocal kinetic energy, 236-237, 272,
…… 346
… running, 132-134, 208, 250
… sample, 72, 77, 101, 134, 143
… time, 15, 51, 60, 62-63, 70-72, 94, 131, 212,
…… 219, 225
… trajectory, 72-77, 101
… for velocity-dependent quantities, 67, 335
Avogadro's number, 462
Axilrod-Teller potential, 223

Baltimore lectures, see Thomson's Baltimore
…… lectures
B-flow, 51, 54
Bias, 74, 136. See also Accuracy; Errors,
…… in properties, systematic
… in Monte Carlo, 14
Boltzmann:
… constant, 462
… factor, 14
Boublik-Nezbeda equation, 129, 144
Boundary conditions, 12-13, 85. See also
…… Periodic boundary conditions
Box-Muller procedure, 117, 143 Brownian dynamics, 13, 18-19
Bulk modulus, 294. See also Compressibility,
…… isothermal

Calculable dynamics, 2, 123
Canonical ensemble, see Ensemble, NVT
Carnahan-Starling equation, 129, 144, 146,
…… 437
Cell translation vector, 81-84, 102, 194
Central limit theorem, 78, 98, 143-144
Check sums, 368
Chemical potential, 62, 103, 244, 352
… via test particle method, 246-253, 274,
…… 346-350
Chi-squared, 136-137, 144, 146, 214, 219
Coarse graining, 80, 132-135, 143, 219
Coefficient of rigidity, 294
Colletive correlations, 291-296
Collisions:
… effect on trajectory stability, 54-59, 91
… elastic, 54, 104
… of hard spheres, 105-110, 321-322, 422-427
… table of, 111-112, 113, 424-425
… three-body, 124-126
… time between (interval), 100, 212, 322
… time of, 108-110, 142-143, 426-427
Compiler:
… effects on results, 174-177
… to test for systematic errors, 139, 216, 222
Compressibility:
… adiabatic, 86, 237-240, 243, 269-270, 463
… factor, 127-129, 131-135, 138, 144-145.
…… See also Pressure; Virial
… isothermal, 146, 243, 269-270, 273, 294
Configuration space, 11, 43
Conservation principles, 87-91, 131, 212
Conserved quantities:
… angular momentum, 89
… energy, 87-88, 105, 131, 142-143, 163-165,
…… 220
… linear momentum, 88-89, 105, 131, 142
… particle number (mass), 87, 131
Constants, values for selected, 462
Conversion factors, 462
Corrections to properties:
… for conserved momentum, 89
… for long-range interactions, 191, 226-230,
…… 234, 248-249, 269, 271-272, 445
… for shifted-force, 193, 228
Correlation, see also Time, correlation
…… functions
… auto. See Autocorrelation functions
… coefficient, 79, 102
… serial, 78, 80, 132, 212
… time, periodic, 86-87, 289
Corresponding states, 31, 112
Coupling parameter:
… form of, 256-257
… method, 253-260
Cross-correlation function, 278, 320
Cutoff distance, 191, 248-249, 269
Delta symbol, 262-262, 273, 311-312, 314,
…… 316, 327-331
Density, 112, 199. See also Packing fraction
… local, 263, 310, 316, 327, 331
… of states, 341-343
Density-density correlations, 310-316
Deterministic dynamics, 2, 123
Diagnostics on codes, 146, 221-223
Diffusion:
… coefficient:
…… mutual, 303-305
…… self, 128, 296-298, 302-304, 321-323, 326
…… values of, 463
… equation, 296-297, 320
Dissipative forces, 47
Distribution:
… of atoms in space, 260-265
… of atoms in space and time, 310-316
… of properties, 67-70
… of velocities. seeVelocity distribution
Duration of simulations, 71, 131, 135, 145,
…… 211, 219, 221
Dynamics:
… Brownian, 13, 18-19
… calculable, 2, 123
… deterministic, 2, 91, 123
… Hamiltonian, 40-42
… hierarchy of, 46
… Langevin, 13, 18
… Newtonian, 38-40, 42
… nonlinear, 2, 59, 91, 157
… predictable, 2, 123
… stochastic, 18-19

Einstein relations, 296-299
… for self-diffusion, 297-298, 320-321
… for viscosity, 298, 306-310, 323-325
Elastic collisions, 54, 104
Energy:
… configurational internal, 225-220, 270, 273,
… conservation of, to test algorithms, 155-157,
…… 163-166, 211-212
… fluctuations in. see Fluctuations
… kinetic, 40, 45, 60-62, 66, 94, 226, 236-237
…… 254-255, 344, 346
… of ODHO, 44-45, 155-157
… potential, 11, 189. See also Potential
…… energy, intermolecular
… total, 40, 42, 45, 192, 199-200, 211-212, 225,
…… 245-246, 254-259, 340
Ensemble:
… average, 14, 51, 341, 343
… molecular dynamics, 89, 340
… NPT, 138, 166, 244
… NVE (microcanonical), 67-70, 89, 138
…… 235-236, 340-353
… NVT (canonical), 14, 28, 64-65, 138
…… 235-236, 244, 247, 274
Entropy, 63, 67, 103, 243-246, 253-260, 275,
… 341, 352
Equations of motion, 54, 59
… Hamilton's, 41-42
… Newton's, 15, 38-39
… nonlinearities in, 2, 59, 91, 157
… for ODHO, 34-44
Equations of steat, see also particular ones;
…… Ideal, gas; Pressure
… for hard spheres, 127-129, 144-145
… for Lennard-Jones, 232, 270-271
Equilibration:
… of hard spheres, 113-114, 117-123, 131,
…… 413-415
… of soft spheres, 204-209, 211, 380-381,
…… 440-441
Equilibrium, 63
… approach to, see Equilibration
… identification of, 206-209
Equipartition, 66, 131, 207, 212, 221
Ergodic:
… hypothesis, 15-16, 51
… motion, 51, 53, 102, 108, 167-172
Errors:
… in finite difference methods:
…… control of, 157, 164, 177
…… effect of time-step on, 155-157, 163-165
…… global, 151, 178
…… local, 151, 182
…… propagation of, 153-157
…… round-off, 149, 151, 153, 163-164,
………174-179, 221
…… truncation, 149, 151, 153, 158, 163-164,
………174, 177-178, 182
… in properties:
…… friendly, 213
…… hidden, 213-214, 217
…… propagation of, 146, 269-270, 274,
………360-364
…… statistical, 74, 131-136, 146, 212-213,
………219, 269-270
…… systematic, 74, 136-140, 146, 213-216, 222
… in time-correlation functions, 287-289
… in trajectories, 166-177
…… statistical, 145
…… systematic, 143, 220
Euler's method, 150-151, 154-155, 157, 180
… as basis for simple predictor-corrector,
…… 159-160
… modified, 155, 180
Expansivity, 243, 269
… of water, 357

Face-centered cubic (fcc), 113, 115-120, 130,
… 202, 418, 446
Fick's law of diffusion, 296, 299
Finite-difference methods, 148-187
… assessing performance of, 172-179
… errors in, see Errors, in finite-difference
…… methods
… Euler, 150-151, 154-155, 157, 180
… Gear, 160-165, 172-177, 183, 202, 387-389,
…… 448-452
… multistep, 152, 160
… one-step, 152, 160
… order of, 151
… predictor-corrector, 159-163, 185, 220
… Runge-Kutta, 157, 181, 186
… stability of, 153-157, 177, 180-181, 185-186,
…… 220
… Stormer, 158
… Verlet, 158-159, 164, 173-177, 181-184
Fluctuation-regression hypothesis, 297-299
Fluctuations:
… caused by truncating potential, 192
… in configurational internal energy, 208,
…… 209, 236-237, 271
… cross, 240-241
… effect of system size on, 207-208
… in energy, 192, 234-235
… in kinetic energy, 61, 206, 236-237
… in order parameter, 118-119, 131, 211
… in pressure, 209, 230-231, 238
… in properties, 60-62, 71, 131, 207, 212, 271
… in reciprocal kinetic energy, 236-237
… in temperature, 209, 271
… and transport coefficients, 296-299
Flux, 296, 333
Force:
… conservative, 12, 42, 193
… dissipative, 47
… gravitational, 27
… intermolecular, 12, 190, 193
…… dispersion, 190
…… Lennard-Jones, 190
…… overlap, 190
…… in periodic systems, 85, 194
…… shifted, 192
…… truncated, 191-192
… mean-square, 233-234, 269, 323
… for ODHO, 43-44
Force-field calculations, 1
Fourier's law of heat conduction, 296
Free energy, 63, 243-244, 304-305. See also
… Chemical potential
Fundamental equation, 103, 244, 246, 343
…… 346-347

Gamma function, 342
Gas constant, 462
Gaussian distribution, 65-66, 69-70, 272
…… 325, 361. See also Maxwell distribution
… Box-Muller procedure for, 117, 143
… central limit theorem and, 78, 98, 143
… for diffusion, 297, 320
… test for, 136-137, 214, 219
Gear algorithm, see also Finite-difference
…… methods, Gear
… compared with Verlet, 164-165, 172-177,
…… 182-183
… parameters for, 162, 444-445
… stability bound of, 220
Gibbs free energy, 244, 304-305. See also
…… Chemical potential
Gradient operator, 12, 233, 470
Green-Kubo relations, 298-301
… for longitudinal viscosity, 298
… for mutual diffusion coefficient, 304
… for self-diffusion coefficient, 298, 302-303,
…… 321, 326
… for shear viscosity, 298, 305
… for thermal conductivity, 301
Gruneisen parameter, 243

Hamiltonian dynamics, 40-42
Hamiltonian function, 40-42, 49-50, 225,
…… 341
Hard spheres, 104-147
… collision of, 105-108
… collision interval of, 143, 322
… collision rate of, 145, 322
… collision time of, 108-112, 142
… equation of state, 129
… equilibration of, 117-123
… initialization of, 115-117
… isothermal compressibility of, 146
… one-dimensional, 106, 147, 167,
…… 350-352
… phase diagram of, 129
… Poincare recurrence time for, 100
… postcollision velocities of, 107, 114
… potential energy function for, 104-105
… pressure, 126-130, 132, 135, 138-139,
…… 144-145
… radial distribution function of, 430-433
… second virial coefficient for, 144
… self-diffusion coefficient of, 303, 322-323,
…… 326
… simulation algorithm for, 113-114
… simulation code for, 411-437
… velocity distribution for, 434-435
… viscosity of, 306-310, 324-325
Harmonic oscillator:
… one-dimensional (ODHO), 6, 21, 43-45,
…… 45, 165
…… analytic expressions for motion of, 94
…… correlation coefficient for position of,
………102
…… ergodicity of, 53
…… Euler's method applied to, 150, 154-155,
…….180
…… Hamilton's equations for, 45
…… modified Euler's method applied to,
………155-156, 180
…… Newton's equations for, 43-44
…… phase-plane trajectory of, 43-45, 94-95,
………156
…… predictor-corrector applied to,
………159-160
…… velocity autocorrelation function of,
………282-283
… two dimensional, 47-49, 97-98
…… analytic expressions for motion of, 97
Heat capacity:
… isobaric, 243, 269, 463
… isometric, 234-236, 2450246, 272, 345-346,
…… 352, 463
… residual isometric, 237, 270, 272
Helmholtz free energy, 244
H-function:
… calculation of, 395, 434-435, 456
… definition, 67, 181
… use in equilibration, 120-123, 131, 144,
…… 168-172, 184, 205, 211, 221-222
H-theorem, 67
Hydrodynamics theory for long-time tails:
… of stress autocorrelation function, 306
… of velocity autocorrelation function,
…… 290

Ideal:
… gas, 4, 28-29, 98, 321
… . definition of, 28, 98
…… equation of state for, 4, 28, 103, 335
…… phase space of, 45-46, 102-103
…… as reference substance, 254-260
… simulation, 21
… solution, 33, 304-305
Initialization:
… for hard spheres, 113, 115-117, 413-415
… for soft spheres, 198-204, 380-381,
…… 440-441
Initial-value problem, 148
Intermolecular forces, see Force,
…… intermolecular
Intermolecular potential, see Potential
…… intermolecular
Internal energy, see Energy
Isolated system, see System, isolated

Jack and Jill, 464
Joule-Thomson coefficient, 243, 269
KAM motion, 49-51
K-flow, 51, 53-54, 59
Kinetic energy, see Energy, kinetic

Lagrange stability criterion, 185-186
Lagrangian mechanics, 42
Langevin equations of motion, 18, 37
Laplace transform, 341-342, 351, 470
Laplacian operator, 233, 470
Large numbers, law of, 464
Lattice dynamics, 1
Least squares, 270, 362-364
Leibnitz rule, 321
Length of run, see Duration of simulations
Lennard-Jones:
… one-dimensional substance:
…… ergodicity of, 170-171
…… exercises using, 181, 183-184
…… potential function of, 168
…… simulation code for, 378-398
…… used to compare algorithms, 163-165,
………173-174
… potential functions, 189-190, 218
…… for argon, 462
…… force from, 190
…… Laplacian of, 234
…… parameters in, 190, 462
…… reduced form, 199
…… round-off error in evaluating, 180
…… shifted-force, 192, 207
…… truncated, 191, 218
… substance:
…… adiabatic compressibility of, 239-240,
………269-270
…… chemical potential of, 249-253
…… configurational internal energy of,
………228-229, 269-270
…… correlation coefficients of, 79-80
…… entropy of, 257-260
…… equations of state for, 220, 232, 270-271
…… heat capacity of, 237-239, 270
…… mean-square force of, 234, 269
…… phase diagram of, 201, 271, 276
…… pressure of, 231-233, 269-271
…… radial distribution function of, 265-266,
………272-273, 455, 457
…… second virial coefficient of, 218
…… self-diffusion coefficient of, 303-304
…… shear modulus of, 294-295, 321
…… shear viscosity of, 306-307
…… simulation of, 219, 222, 272-274, 276
………438-461
…… space-time correlation function of, 313,
………315
…… thermal pressure coefficient of, 241-242,
………270
Limitations of simulation, 9, 17-23
Lissajous figures, 49
Local error, see Errors, in finite-difference
…… methods, local
Local structure, see Structure, local
Long-time tail:
… of stress autocorrelation function, 305-306
… of velocity autocorrelation function,
…… 289-291, 303
Lorenz attractor, 186-187
Lyapunov stability analysis, 157, 185

Markov chain, 13
Mass:
… of atom in simulation, 112, 198-199, 221
… center of, 329-331
Maxwell-Boltzmann distribution, 65
Maxwell distribution, 65-67, 72, 106, 113,
…… 117, 120-123, 131, 144, 146, 167-172,
…… 206-207, 211, 221
Mean free path, 98-99, 322
Mean square:
… displacement:
…… long-time limit of, 297-298, 301, 321, 324
…… short-time behavior of, 301-302
…… and time correlation functions, 299-301
…… used to distiguish solid from fluid,
………209-210
… error, 74-75, 102
… fluctuation, 234-239, 271-272
… force, 233-234, 269, 323
Melting, 117-119, 128
Metastabilities, 52, 62-63, 102, 119, 121, 130,
…… 221, 266, 306
Methane, 29-31
Metropolis Monte Carlo, 14. See also
…… Monte Carlo
Microcanonical ensemble, see Ensemble,
…… NVE
Minimum image criterion, 114-115, 193-196,
…… 220, 308-309, 390-391, 423, 450-451
Mixing motion, 51, 53-54
Mixtures of fluids, 32-34, 146, 223, 303-305
Model, 5-7, 28-34
… molecular, 11-12, 188
… realism of, 19
… system-environment, 12-13 Modeling, 27-34
… dynamic, 16, 188-189
Molecular dynamics:
… compared with Monte Carlo, 17-18, 139
… limitations of, 9, 17-23
… nonequilibrium, 17, 47
… overview of, 15-17
… simulation code:
…… for hard spheres, 411-437
Molecular dynamics simulation code
…… (Continued)
…… for one-dimensional soft spheres,
………378-398
…… reliability of, 131, 138-140, 211-214, 216
…… for soft spheres, 438-461
… trajectories, 53
Molecular mechanics, 1
Momentum:
… angular, 89-91
… integration over, 341-342
… linear, 88-89, 105, 304
… scaling to zero, 113, 117, 203, 220, 419, 447
… space, 43, 344
… through two-body collision, 105
Monopoly, 26-27
Monte Carlo, 13-15, 34-36, 51
… compared with molecular dynamics,
…… 17-18, 139
… force-biased, 14-15
… Metropolis, 14
Multibody collisions, 123-126

Nabla, 233
Names in Fortran, 365-367
N-dependence, see Size effects
Neighbor list, 196-197, 220, 449, 455
Newton's law:
… first, 39
… second, 15, 38, 40, 127, 161, 203, 307, 333
… third, 39-40, 161, 308
… of viscosity, 296
Nicolas et al. equation of state, 220, 232
Noether's theorem, 87
Nonequilibrium molecular dynamics, 17, 47
Nonmeasurable properties, 63, 243-265
Normal distribution, see Gaussian
…… distribution
Notation, 466-470

ODHO, see Harmonic oscillator
Ohm's law, 296
One-dimensional system:
… analytic results for properties of, 166, 352
… of hard spheres, 105-107, 167, 350-352
… Lennard-Jones, 163-165, 168, 170-174, 177,
…… 181, 183-184
…… simulation code for, 378-398
… minimum image criterion for, 194-196
… oscillator in, 95-97. See also Harmonic
…… oscillator
… repulsive soft sphere, 167-170
Optimized code, 175-177
Order:
… of finite-difference algorithm, 151, 181
… parameter, 117-120, 131, 143-144, 205, 209,
…… 211, 221, 222, 436, 455
Oscillators, see Harmonic oscillator;
…… One-dimensional system

Packing fraction, 112, 116-117
Pairwise additivity, 11, 34, 189, 336
Paleontologists, 2
Periodic boundary conditions, 81-86. See
…… also Boundary conditions
… effect on properties, 86, 137, 215, 289
… forces when using, 194-196
… for hard spheres, 111-112, 114
… for soft spheres. 210. 386-387, 453
… transformations for, 85
Periodic correlation time, 86, 289
Phase diagram:
… hard sphere, 129
… Lennard-Jones, 201
Phase space:
… trajectories:
…… B-flow, 49, 51
…… ergodic, 49, 51, 53
…… Hamiltonian, 47, 53
…… hierarchy of, 46
…… of ideal gas, 45, 98
…… integrable, 47-49
…… KAM, 49-51
…… K-flow, 49, 51, 53
…… mixing, 49, 51, 53
…… nonergodic, 49-51, 106, 167-172
…… nonHamiltonian, 47
…… nonintegrable, 49-53
…… nonmixing, 52
…… nonrecurrent, 46
…… of ODHO, 44-45, 155-156
…… periodic, 47, 49, 57
…… quasi-ergodic, 51
…… quasiperiodic, 47-49, 52, 56-57
…… recurrent, 46-47, 100
…… reliability of computed, 166-177
…… stable, 50, 94-95
…… unstable, 49-52, 57-59
… volume, 63, 67, 102-103, 243-244, 340,
…… 350, 352
Pi, value of, 34
Planck's constant, 462
Poincare recurrence theorem, 47, 100
Pond, depth of, 34-36
Positions:
… initial:
…… for hard spheres, 113, 115
…… for soft spheres, 202
… vector to locate, 39, 203
Potential energy, intermolecular, 11-12
… hard sphere, 104-105
… Lennard-Jones, 168, 180, 189-190, 218
… pairwise additive, 11, 34, 189, 336
… parameters in, 190
… in periodic systems, 84-85
… repulsive soft-sphere, 167, 274
… shifted-force, 192-193
… square-well, 147
… three-body, 223
… truncated, 190-192
Pottle, 464
Precision, see Errors, in properties, statistical
Predictable dynamics, 2, 123
Predicotr-corrector methods, see
…… Finite-difference methods; Gear
…… algorithm
Pressure, see also Compressibility, factor;
…… Virial
… derivation for, 332, 339
… fluctuations in, 209, 230-231, 238-239
… for hard spheres, 126-129, 138-139,
…… 144-145, 352
… for ideal gas, 4, 28, 103, 335
… as momentum flux, 333
… residual, 231-233
… serial correlations of, 80, 132
… for soft spheres, 229-233, 269-271, 273
… tensor, 292
Primary cell, See Periodic boundary
…… conditions
Production, 114, 210-211, 380-381, 413-415,
…… 440-441
Properties, see also particular ones
… of air, 463
… of argon, 31, 218-219, 463
… configurational, 11, 14
… corrections to, see Corrections to properties
… determination of, 59-64
… effect of run-length on, 135-136, 211, 219
… effect of system size on, 137-138, 215, 220
… fluctuation in, see Fluctuations
… macroscopic, 15, 60-62, 224
… nonmeasurable, 63, 243-265
… of one-dimensional hard spheres, 35
… of one-dimensional soft sphers, 166
… reduced forms for, 199
… residual, 231-233, 236-237, 247-260
… stability of, 207-209, 221
… structural:
…… dynamic, 310-316
…… static, 260-265
… thermodynamic:
…… entropic, 243-260
…… response functions, 234-243
…… simple, 225-234
… transport, 296-310
… of water, 31, 357, 463

Radial distribution function, 224, 315-316
… determination from simulation, 261-263,
…… 430-433, 455, 457
… to distinguish solid from fluid, 210,
…… 263-265
… effect of density on, 263-265
… for hard spheres at contact, 144-145
… for Lennard-Jones substance, 265-266
… relation to simple thermodynamics, 226,
…… 272-273
… uncertainties in, 273
… uniform-fluid approximation to, 227, 230
Random number generator, 376-377
Realism of models, 19-20
Recurrence theorem, see Poincare
…… recurrence theorem
Reductionism, 8-11, 19
Ree equation of state, 232, 270-271
Relaxation time, 18, 62, 79, 132, 212, 289,
…… 323, 325
Reliability of simulations, 131, 138-140,
…… 211-214, 216
Repulsive soft spheres, see Soft spheres
…… repulsive
Round-off error, see Errors, in
…… finite-difference methods
Runge-Kutta algorithms, 157, 181, 186
Running average, see Average, running

Sampling:
… coasre graining, 80, 132-134, 143, 219
… distribution, 73
… simple random, 76-78, 101
… statistics, 71-73
… stratified random, 80, 213, 219
… stratified systematic, 80, 212-213, 216, 219
… systematic, 78-81
… theory of, 70-81
… two-stage, see Coarse graining
… unbiased, 75, 102
Scaling velocities, see Velocity, initial
…… assignment of
Schwarz inequality, 319
Serial correlations, 78, 80, 132, 212
Shear modulus, 294-295, 321
Shifted-force potential, 192-193, 207, 228, 274
Simulation, see also Molecular dynamics
… compared to modeling, 4-7
… compared to reductionism, 8-11
… ideal, 21
… length of, 72, 131, 135, 145, 211, 219, 221
… limitations of, 9, 17-23
Simulation (Continued)
… as theory or experiment, 7-8, 10
… validity of, 20-23
Size effects, 137-138, 207-208, 215, 220
Soft spheres, see also Lennard-Jones
… … substance
… intermolecular potentials for, 189-193
… one-dimensional, 166-177
…… ergodicity of, 167-172
…… simulation code for, 378-398
…… used to assess finite-difference
………algorithms, 172-177
…… repulsive, 167-170, 274
… simulation of:
…… calculation of forces for, 193-197
…… code for, 438-461
…… equilibration of, 204-210
…… identification of phase of, 209-210
…… initialization of, 198-203
…… production run of, 210-211
Solid, 128-130, 209-210, 263-266, 294
Solutions, see Mixtures of fluids
Sonic velocity, see Velocity of sound
Space-time correlation function, 310-311,
…… 325
… distinct, 314-316, 326
… self, 311-314, 325-326
Specular reflection, 54, 107
Speed:
… of simulation, 18, 246, 266-267, 316
… of sound, see Velocity of sound
Spheres, see also Hard spheres; Soft spheres
… n-dimensional, 102-103
Square-well potential, 147
Stability:
… of finite-difference algorithms, 153-157,
…… 177, 180-181, 185-186, 220
… matrix, 154
… of properties, 207-209, 221
… of trajectories, 49-59
Standard deviation, see also Variance
… of sample average from trajectory
…… average, 77, 134
… of value from average, 77
State conditions, 3-4, 112-113, 199-201
Static correlation function, 281-283
Stationarity, 278, 281-282, 319
Statistical error, see Errors, in properties
Statistical sampling, see Sampling
Step function, 470
Stirling's approximation, 463
Stochastic dynamics, 294
Stones, skipping, 294
Stormer algorithm, 158. See also Verlet
…… algorithm
Stress:
… autocorrelation function, 293-296, 305-306
… tensor, 291-293, 324
Structure, local:
… dynamic, 310-316, 325-326
… static, 260-265
Symbols, list of, 466-470
System, isolated, 3-4, 39-40, 42, 60, 63, 65,
…… 71, 87-90, 102, 199, 205-206, 235, 340, 350
… equilibrium in, 63, 67, 206-209
Systematic error, see Errors, in properties

Temperature:
… conversion of, 354-356
… corrections for drift in, 245-246
… distribution of instantaneous, 70
… fluctuations in, 209, 219
… for hard spheres, 112-113
… in microcanonical ensemble, 342-344
… related to kinetic energy, 61-62, 66, 89,
…… 207, 226, 343-344
… related to velocity autocorrelation
…… function, 283
… scale velocities for, see Velocity, initial
…… assignment of
… serial correlation time for, 80
… thermodynamic limit of, 215-216
… units for soft spheres, 199
Test-particle method, 246-253, 346-350
Thermal:
… conductivity, 301, 306
… de Brogli wavelength, 349
… pressure coefficient, 240-243, 246, 270,
…… 275, 463
Thermodynamic:
… equilibrium, 63, 67, 206-209
… integration, 244-246, 256, 259
… limit, 65, 70, 137-138, 214-215, 253, 270
… properties, see Properties, thermodynamic
… state, see State condition
Thomson's Baltimore lectures, quaotations
…… from, v, x, 2, 4, 40, 45, 47, 104, 149,
…… 199, 224, 233, 294, 471
Three-body:
… collisions, 124-126
… potential, 223
Thurber, James, 8
Time:
… averages, see Average, time
… correlation functions, 79-80, 86, 277-296,
…… 310
…… auto, 278, 319. See also Autocorrelation
………functions
…… code for computing, 399-410
…… collective, 291-296
…… cross, 278, 320
…… definition of, 278
…… derivatives of, 280-281
…… for ODHO, 102, 282-283, 320
…… short-time behavior of, 281-282
…… single-particle, 282-291
…… static, 281-282
…… stationary property of, 278, 281-282,
………319
…… stress, 293-296, 305-306
…… velocity, 233, 282-291
… reversal invariance, 145, 182-183
… units of, 113, 199, 219
Time-step, 202
… effect on errors, 152-153, 164, 175
… effect on stability, 154-157, 180-181, 183,
…… 220
… as indicator of order of finite-difference
…… method, 151, 181, 184
… units of, 163, 219
… value of, for Gear algorithms, 163, 183,
…… 202, 220
Torus, 47, 49-50, 98
Trains:
… passing, 292
… at station, 310
Trajectories, phase-space, see Phase-space
…… trajectories
Trajectory stability, see Stability, of
…… trajectories
Transport properties, 296-310
Truncated potential, 190-192
… corrections for, 227, 229-230, 234, 248-249,
…… 269, 271-272
Truncation error, see Errors, in
…… finite-difference methods
Turkey shoot, 180
Two-dimensional harmonic oscillator, see
…… Harmonic oscillator
Two-way plots, 354-359

Unit cell, for fcc lattice, 115-116, 418,
…… 446
Units:
… conversion factors for, 462
… for hard spheres, 112-113
… for soft spheres, 198-199
Uncertainties, see Errors
Unpredictable dynamics, see Dynamics,
…… predictable
Unstable trajectories, see Stability, of
…… trajectories

Validity of a simulation, 20-23
Van Hove correlation functions, 310-311
Variance, 72-77, 101
Vaudeville, 8
Velocity:
… autocorrelation function, 282-291
…… calculation of, 284-287
…… long-time tail of, 289-291, 303
…… of ODHO, 282-283, 320
…… relation to mean square force, 233, 323
…… relation to temperature, 283
…… short-time behavior of, 281-282, 323
…… uncertainties in, 287-289
… distribution, 64-66, 106, 113, 117, 120-123,
…… 131, 167-172, 206-207, 211, 394-397,
…… 434, 456
… initial assignment of:
…… to adjust for zero momentum, 113, 117,
………203, 220, 384-385, 419, 447
…… for hard spheres, 113, 117, 419
…… to scale for energy, 200, 220, 459
…… to scale for temperature, 200, 384-385,
………396-397, 459
…… for soft spheres, 202
… peculiar, 62
… postcollision, 105-107, 114, 423
… precollision, 105-107
… reversal, 178, 183, 184
… of sound, 86-87, 98, 243, 289, 463
Verlet algorithm, 158-159, 181-184
… compared with Gear, 164-165, 172-177,
…… 182-183
Virial, 127, 132, 292, 338, 429, 451
… coefficient, second, 144, 218-219
… theorem, 126-127, 292, 332-333
Viscosity:
… bulk, 294, 298, 306, 309
… longitudinal, 298
… shear, 290, 294, 298, 305-310, 323-325, 463
Volume:
… phase-space, 63, 67, 102-103, 243-244, 340,
…… 350, 352
… units of, in English system, 464

Water, 29, 31, 217, 357, 463
Wobegon, Lake, 293-294
Work, 40, 94, 246-247