Page 485 - Numerical Methods for Chemical Engineering

474 Index

Stochastic simulation Trust radius 225
Boltzmann distribution 337 Trust-region Newton optimization method 225–227
Brownian dynamics (see also Brownian dynamics)
327 Variance 327
Diffusion Limited Aggregation (DLA) 366 MATLAB var 364
Example. Monte Carlo simulation of 2-D Ising Vector
lattice 356–357 addition 5
Example. stochastic modeling of polymer chain column vector 4
length distribution 318–321 complex vectors 7
Example. stochastic modeling of polymer gelation complex conjugate 7
321–325 dot product 7
kinetic Monte Carlo 369 dot (scalar, inner) product 5, 7
Markov chain 354 length 6
Markov process 353 linear independence 26
Metropolis Monte Carlo method 353–357 metric 6
condition of detailed balance 355 norm 6, 7
optimization 361–364 null vector 5, 29
genetic algorithm 362–364 orthogonal vectors 6, 27
Particle Swarm Optimization (PSO) 367 orthonormal vectors 6, 27
simulated annealing 361–362 row vector 4
probability theory (see also Probability theory) set of complex vectors 7
317–338 set of real vectors 4
random walks 328–329 Vector space
stochastic calculus 343–347 basis set 26
Chapman-Kolmogorov equation 349 basis set expansion 27
Fokker-Planck equation (see also Fokker-Planck definition, required properties 24
equation) 347–351 Krylov subspace 287
Forward Kolmogorov equation 350 linear independence 26
Itˆo’s lemma 345 linear transformation 24
Stochastic Differential Equations (SDEs) orthogonal basis 27
342–353 orthonormal basis 27
explicit Euler SDE method 343 span 29
Itˆo-type SDE 343 subspace 29
Mil’shtein SDE method 346 von Neumann boundary condition 265
stochastic integral 343 Voronoi polyhedra 303
Stochastic Partial Differential Equations 358–360 MATLAB voronoi 303
stochastic system 317 MATLAB voronoin 303
transition probability 349
Wiener process 341–342 Weight function 304
Stokes-Einstein relation 352 Weighted residual methods 304–305
Successive Over-Relaxation (SOR) method 285 collocation method 304
Symmetric SOR (SSOR) method 286 orthogonal collocation 304
Galerkin method 304
Taylor series 62 least-squares method 304
Thiele modulus 266 residual function 304