Page 478 - Numerical Methods for Chemical Engineering

Index 467

numerical calculation quantum states of a 1-D system 137–141
demonstrated use of MATLAB routines 123–126 solution of 2-D Poisson BVP by finite differences
inverse inflation for smallest, closest eigenvalues 260–264
129 solving 2-D Poisson BVP with FEM 305–309
MATLAB eig 123, 149 stability of steady states of nonlinear dynamic
MATLAB eigs 124, 149 system 172–175
power method for largest eigenvalues 128 steady-state CSTR for polycondensation 89–94
QR method 131 steady-state CSTR with two reactions 71–72, 85,
orthogonal matrix 119 88–89
positive-definite matrices 122 stochastic modeling of polymer chain length
Principle Component Analysis (PCA) distribution 318–321
412–414 stochastic modeling of polymer gelation 321–325
properties of general matrices 117–120 Expectation 322
properties of normal matrices 121–123 conditional 323
quantum mechanics 138
real, symmetric matrix 119 Fast Fourier Transform (FFT) (see Fourier analysis)
relation to matrix determinant 110 Field 258
relation to matrix norm 113 Field theory 358–360
relation to matrix trace 110 Landau free energy model 358
roots of a polynomial 148 mean-field approximation 359
Schur decomposition 119 Time-Dependent Ginzburg-Landau Model A
similar matrices 118 (TDGL-A) dynamics 359
Singular Value Decomposition (SVD) (see also Flory most probable chain length distribution 321
Singular Value Decomposition) 141–148 Fluid mechanics
spectral decomposition 122 Example. 1-D laminar flow of Newtonian fluid
spectral radius 113 47–54
unitary matrix 119 Example. 1-D laminar flow of shear-thinning fluid
Einstein relation 352 85–88
Elliptic PDEs 278 Fick’s law 259
Euler angles 150 Finite difference method
Euler formula 3, 438 accuracy of approximations 262–263
Euler integration method approximation of first derivative 48, 262–263
backward (implicit) method 176 approximation of Jacobian matrix 77
forward (explicit) method 177 approximation of second derivative 48, 262–263
Example problems. Central Difference Scheme (CDS) 271–272
1-D laminar flow of Newtonian fluid 47–54 complex geometries 294–297
1-D laminar flow of shear-thinning fluid 85–88 Example. 1-D laminar flow of Newtonian fluid
3-D heat transfer in a stove top element 292–294 47–54
3-D Poisson BVP 282–285 Example. 1-D laminar flow of shear-thinning fluid
chemical reaction, heat transfer, and diffusion in a 85–88
spherical catalyst pellet 265–270 Example. 3-D heat transfer in a stove top element
comparing protein expression levels of two 292–294
bacterial strains Example. 3-D Poisson BVP 282–285
as linear regression problem 380–381 Example. chemical reaction, heat transfer, and
MCMC analysis of hypothesis 406–407 diffusion in a spherical catalyst pellet 265–270
MCMC calculation of marginal posterior density Example. modeling a tubular chemical reactor with
408–409 dispersion 279–282
dynamic simulation of CSTR with two reactions non Cartesian, non uniform grid 267
172–175 numerical (artifical) diffusion 274
dynamics on the 2-D circle 199 numerical issues for problems of high dimension
finding closest points on two ellipses 235 282–286, 294
fitting enzyme kinetics to empirical data 230 treatment of convection terms 270–275
heterogeneous catalysis in a packed bed reactor treatment of von Neumann BC 268
199–202 Upwind Difference Scheme (UDS) 273–275
modeling a separation system 45–46 Finite element method (FEM) 299–311
modeling a tubular chemical reactor with dispersion automatic mesh generation (see also Automatic
279–282 mesh generation) 300–303
Monte Carlo simulation of 2-D Ising lattice convection terms in FEM 309
356–357 Example. solving 2-D Poisson BVP with FEM
multiple steady states in a nonisothermal CSTR 305–309
204–206 Galerkin method 304–305
optimal control of 1-D system 250–251 MATLAB pdetool 301–303, 309–311
optimal steady-state design of CSTR 244–245 mesh refinement 300