Page 477 - Numerical Methods for Chemical Engineering

466 Index

Chemical reactor modeling (cont.) Danckwert’s boundary condition 280
fitting rate constant and generating CI from Debye screening length 314
dynamic reactor data 402 Delaunay tessellation 303
fitting rate constant to multiresponse kinetic data MATLAB delaunay 303
418–419 MATLAB delaunayn 303
MCMC analysis of elementary reaction Design matrix 377, 389
hypothesis 411 Determinant 32
MCMC generation of CI for rate constant from as product of eigenvalues 110
multiresponse data 420–421 expansion by minors 34
MCMC rate constant fitting and CI generation general formula 33
from composite data set 422–426 MATLAB det 57
Example. heterogeneous catalysis in a packed bed numerical calculation 35, 57
reactor 199–202 properties 34–35
Example. modeling a tubular chemical reactor with Diffusion Limited Aggregation (DLA) 366
dispersion 279–282 Dirac delta function 339
Example. multiple steady states in a nonisothermal Dirichlet boundary condition 260
CSTR 204–206 Dirichlet’s theorem 436
Example. optimal steady-state design of CSTR Discrete probability distribution 325
244–245 Dispersion 279
Example. steady-state CSTR for polycondensation Divergence theorem 259, 307
89–94 Divided differences 159
Example. steady-state CSTR with two reactions Dogleg method 225–227
71–72, 85, 88–89 Dot (inner, scalar) product
Example. stochastic modeling of polymer chain complex vectors 7
length distribution 318–321 real vectors 5
Example. stochastic modeling of polymer gelation Dynamic programming (see also Optimal control)
321–325 248–251
Macosko-Miller method 322 Dynamical systems
Michaelis-Menten kinetics 58 dynamical stability 169–174
Thiele modulus 266 Jacobian matrix 172
Cholesky factorization 42 numerical simulation (see also Initial value
algorithm 43 problems) 154–208
incomplete Cholesky factorization 290 Quasi-Steady State Approximation 183
MATLAB chol 43, 57 state vector 155
MATLAB cholinc 291 steady states 170, 174, 175, 204
Complementarity condition 238 stiffness 180
Complex numbers time-dependent PDEs 282
conjugate 3, 7
dot (inner, scalar) product 7 Effectiveness factor 269
matrices 10 Eigenvalue analysis 104–149
modulus 3 characteristic polynomial 106
Euler formula 3 characteristic value 106
vectors 7 characteristic vector 106
Condition number 113 condition number 113
MATLAB cond, condest 113 determinant 110
Conditional probability 321 diagonalizable matrix 118
Conjugate Gradient (CG) method 218–223, differential equation eigenvalue problem
286–287 138
linear algebraic systems 286–287 dynamic stability 171, 172
MATLAB pcg 223, 285 eigenvalue 104, 106
performance for quadratic cost functions eigenvector 104, 106
220–223 expansion of arbitrary vector 122
Constitutive equation 259 Example. quantum states of a 1-D system
Continuous probability distribution 326 137–141
Control volume 258 Example. stability of steady states of nonlinear
Convolution (see Fourier analysis) dynamic system 172–175
Correlation (see Fourier analysis) existence and uniqueness of solutions to linear
Cost function 212 systems 110
Covariance 336 generalized eigenvalue problem 136
matrix 337 Gershgorin’s theorem 112
Crank-Nicholson method 176 Hermetian matrix 119
Credible (Confidence) Interval (CI) 397 multiplicity 110
Cumulative probability distribution 327 normal mode analysis 134