Page 476 - Numerical Methods for Chemical Engineering

Index 465

prior probability distribution 385 Example. 1-D laminar flow of Newtonian fluid
assumption of prior independence 388 47–54
criteria for selection 386–387 Example. 1-D laminar flow of shear-thinning fluid
data translation 391 85–88
noninformative prior; defined 392; for Example. 3-D heat transfer in a stove top element
multiresponse data 415; for single-response 292–294
data 389 Example. 3-D Poisson BVP 282–285
probability as statement of belief 382 Example. chemical reaction, heat transfer, and
probability in frequentist view 381 diffusion in a spherical catalyst pellet 265–270
random measurement errors 377 Example. modeling a tubular chemical reactor with
response variables 372 dispersion 279–282
single-response regression Example. optimal control of 1-D system 250–251
approximate analytical confidence interval Example. solution of 2-D Poisson BVP by finite
395–399; for model parameters 398; for differences 260–264
predicted responses 399 Example. solving 2-D Poisson BVP with FEM
Bayesian treatment 383–386 305–309
definition 372 function-space solution methods 260
estimate of highest posterior probability 386 Poisson equation 260
estimate of maximum likelihood (MLE) 386 real-space solution methods 260
least-squares method 378–412 solution by finite differences (see also Finite
linear models 376; design matrix 377; difference method) 260–263, 264, 265–267,
MATLAB regress 400; numerical treatment 270, 279–282
of linear least-squares problem 379 solution by finite element method (see also Finite
Markov Chain Monte Carlo (MCMC) simulation element method (FEM)) 299–311
403–411; calculation of Highest Probability solution by finite volume method 297–299
Density (HPD) regions 409–411; calculation MATLAB pdepe 294
of marginal posterior densities 407–409; modeling electrostatic screening 313–314
calculation of posterior expectations 404–407 numerical issues for problems of high
MATLAB routines 399 dimension 282–286, 294
noninformative prior 389 time-dependent simulation 282
nonlinear least squares, numerical treatment von Neumann boundary condition 265, 268
388–389; Levenberg-Marquardt method 389; weak solution 306
linearized design matrix 389; MATLAB weighted residual methods (see also Weighted
nlinfit 400; MATLAB nlparci 401 residual methods) 304–305
MATLAB nlpredci 401 Brownian dynamics (see also Stochastic simulation)
sample variance 390 327
sum of squared errors 378 Einstein relation 352
statistical decision theory 404 Fluctuation Dissipation Theorem (FDT) 352
Student t-distribution 395–397 Langevin equation 340, 343
MATLAB tinv 397 Stokes-Einstein relation 352
Wishart distribution 415 velocity autocorrelation function 338
Bellman function 248 Broyden’s method 77
Bernoulli trials 327–328 Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula
Bifurcation point 224
of nonlinear algebraic system 94
Binomial coefficient 330 Cauchy point 226
Binomial distribution 329–330 Central limit theory of statistics 333
MATLAB binocdf 330 Chapman-Kolmogorov equation 349
MATLAB binofit 330 Chemical reactor modeling
MATLAB binoinv 330 Danckwert’s boundary condition 280
MATLAB binopdf 330 effectiveness factor 269
MATLAB binornd 330 Flory most probable chain length distribution 321
MATLAB binostat 330 Example. chemical reaction, heat transfer, and
Black-Scholes equation 314–315, 346–347 diffusion in a spherical catalyst pellet
Boltzmann distribution 337 265–270
Boundary conditions Example. dynamic simulation of CSTR with two
Danckwert’s type 280 reactions 181–183
Dirichlet type 260 Example. fitting enzyme kinetics to empirical data
von Neumann type 265, 268 230
Boundary Value Problems (BVPs) 258–312 Example. fitting the kinetic parameters of a
Black-Scholes equation 314–315 chemical reaction
BVPs from conservation principles 258–260 fitting kinetic parameters to rate data by
Dirichlet boundary condition 260 transformation to linear model 380