Miller J.J.H. (ed.) — Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods :: Электронная библиотека попечительского совета мехмата МГУ

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Miller J.J.H. (ed.) — Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods

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Название: Singular Perturbation Problems in Chemical Physics: Analytical and Computational Methods

Автор: Miller J.J.H. (ed.)

Аннотация:

Presents the work of leading Russian researchers in English for the first time. Explains the matching method for asymptotic solutions in chemical physics problems, overviews the theory and application of asymptotic approximations for problems in chemical physics governed by either ordinary or partial differential equations with boundary and interior layers, and relates numerical methods for singularly perturbed boundary value problems modeling diffusion processes. Includes sample problems and solutions. For researchers in chemical physics.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 373

Добавлена в каталог: 05.12.2009

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Предметный указатель

"Body-roller" interface, diffusion modeling, hot rolling procedures      341—346
"Brusselator" models, spike-type contrast structures      105—110
"Die-body" interaction, heat transfer diffusion, hot die-forming      321—334
"Die-body" interaction, heat transfer diffusion, plastic shear heat transfer      310—311
"Fast" variables, corner boundary layers, nonisothermal fast chemical reactions      134—139
"Fast" variables, step-type contrast structures      97—98
"Material-dye" interaction, diffusion modeling, hot rolling procedures      335—359
"Roll-body" disposition, diffusion modeling, hot rolling procedures      335—346
"Slow variables", step-type contrast structures      97—98
$K_{7}$ and $K_{i}$ determination, spectrophotometry method      44—45
$K_{7}$ and $W_{i}$ determination, chemiluminescence method      43—44
Additive representation of singularities, diffusion modeling, hot die-forming procedures      328—334
Additive representation of singularities, diffusion modeling, hot rolling procedures      348—355
Alexeevsky, M.V.      360(30) 361
Allen, D.N.      360(31) 361
Approximation errors, asymptotic solutions      5—6
Approximation errors, diffusion modeling, tables      192—206
Approximation errors, diffusion modeling, tables, classical finite difference techniques      218—231
Approximation errors, diffusion modeling, tables, concentrated sources diffusion equations      304—308
Approximation errors, diffusion modeling, tables, prescribed diffusion fluxes      261—270
Approximation errors, diffusion modeling, tables, special finite difference techniques      247—249
Approximation errors, diffusion modeling, tables, special finite difference, numerical examples      276—286
Associated systems, initial value problem      53
Asymptotic algorithms, comer boundary layers, nonisothermal fast chemical reactions      136—139
Asymptotic algorithms, critical case, boundary value problem      80—81
Asymptotic algorithms, critical case, nonlinear problem      79—80
Asymptotic algorithms, initial value problem      56—63
Asymptotic approximation, applications      35—45
Asymptotic approximation, autocatalytic reaction models, leading term construction      157—161
Asymptotic approximation, autocatalytic reaction models, physical interpretation of solution      165—166
Asymptotic approximation, autocatalytic reaction models, subsequent term construction      161—165
Asymptotic approximation, boundary layers, singularly perturbed problems      49—51
Asymptotic approximation, boundary value problem, conditionally stable case      64—73
Asymptotic approximation, corner boundary layers, elliptic equations in rectangle      119—120
Asymptotic approximation, corner boundary layers, parabolic equations      128—134
Asymptotic approximation, critical case, initial value problem, small nonlinear systems      74—79
Asymptotic approximation, defined      50—51
Asymptotic approximation, expansions of exact solution      9—10
Asymptotic approximation, explosive scale      31—34
Asymptotic approximation, initial value problem      52—63
Asymptotic approximation, matching techniques      16—24
Asymptotic approximation, matching techniques, fast time scale      17 25—27
Asymptotic approximation, matching techniques, general examples      4—12
Asymptotic approximation, matching techniques, inhibited liquid-phase oxidation equations      12—15
Asymptotic approximation, matching techniques, overview      2—4
Asymptotic approximation, regular terms      51—52
Asymptotic approximation, slow time scales, first scale      17—20 27—29
Asymptotic approximation, slow time scales, second scale      20—24 30—31
Asymptotic approximation, step-type contrast structures, second-order equations      91—97
Asymptotic approximation, thin body heat conduction      168—178
Asymptotic approximation, Vishik — Lyusternik method      117—118
Asymptotic approximation, Vishik — Lyusternik method, boundary layers      116—117
Asymptotic approximation, Vishik — Lyusternik method, expansion      115
Asymptotic approximation, Vishik — Lyusternik method, local coordinates      113—115
Asymptotic approximation, Vishik — Lyusternik method, overview      113
Asymptotic method, defined      51
Asymptotic series, defined      52
Autocatalytic reaction, mathematical combustion model, asymptotic expansion      165—166
Autocatalytic reaction, mathematical combustion model, asymptotic expansion, leading terms      157—161
Autocatalytic reaction, mathematical combustion model, asymptotic expansion, overview      155—157
Autocatalytic reaction, mathematical combustion model, asymptotic expansion, subsequent terms      161—165
Autonomous identities, contrast structures      100
Bakhvalov, N.S.      242(9) 309(9) 361
Belyakov, V.A.      42(20) 46
Belyanin, M.      97(11) 178
Berge, P.      4(6) 45
Bessel function, corner boundary layers      122—124
Bobisud, L.      139(35) 179
Boundary layers, asymptotic solutions, explosive scale      32—34
Boundary layers, corner boundary layers, asymptotic expansion for parabolic problem      128—134
Boundary layers, corner boundary layers, corner boundary functions      120—124
Boundary layers, corner boundary layers, elliptic equation in rectangle      118—120
Boundary layers, corner boundary layers, first-order derivatives      124—127
Boundary layers, corner boundary layers, hyperbolic equations      134
Boundary layers, corner boundary layers, nonisothermal fast chemical reactions      134—139
Boundary layers, corner boundary layers, parabolic equations      127—128
Boundary layers, critical case, initial value problem, small nonlinear systems      75—79
Boundary layers, critical case, solution stability      111—113
Boundary layers, defined, passage to the limit theorem      54—56
Boundary layers, functions, defined      51
Boundary layers, initial value problem, asymptotic algorithm      57—63
Boundary layers, singularly perturbed differential equations      48—50
Boundary layers, spike-type contrast structures      104—110
Boundary layers, step-type contrast structures, second-order equations      92—97
Boundary layers, thin body heat conduction, asymptotic solutions      168—174
Boundary layers, thin body heat conduction, thermal diffusion coefficient      175—177
Boundary layers, thin body heat conduction, three-dimensional rod      174—175
Boundary layers, thin body heat conduction, two-dimensional approximations      172—174
Boundary layers, Vishik — Lyusternik method, asymptotic expansion      116—117
Boundary layers, Vishik — Lyusternik method, local coordinates      113—115
Boundary value problems, autocatalytic reaction models, leading term construction      158—161
Boundary value problems, autocatalytic reaction models, subsequent term construction      161—165
Boundary value problems, conditionally stable case      63—73
Boundary value problems, critical conditionally stable case      80—81
Boundary value problems, diffusion modeling, classical finite difference      211—242 255—270 300—308
Boundary value problems, diffusion modeling, computational parameters      191—206
Boundary value problems, diffusion modeling, concentrated sources diffusion equation      286—308
Boundary value problems, diffusion modeling, concentrated sources finite difference      294—300
Boundary value problems, diffusion modeling, diffusion equation, concentrated sources      286—308
Boundary value problems, diffusion modeling, diffusion equation, numerical solutions      206—249
Boundary value problems, diffusion modeling, finite difference schemes      300—308
Boundary value problems, diffusion modeling, finite difference schemes, concentrated sources      294—300
Boundary value problems, diffusion modeling, finite difference schemes, Neumann problem      271—275
Boundary value problems, diffusion modeling, finite difference schemes, prescribed diffusion fluxes      249—286
Boundary value problems, heat transfer applications      308—359
Boundary value problems, hot die-forming heat transfer      321—334
Boundary value problems, hot rolling heat transfer      334—359
Boundary value problems, numerical solutions for diffusion equations      206—249
Boundary value problems, overview      182—206
Boundary value problems, plastic shear heat transfer      309—321
Boundary value problems, prescribed diffusion fluxes      249—286
Boundary value problems, spike-type contrast structures, "Brusselator" models      105—110
Boundary value problems, step-type contrast structures, second-order equations      95—97
Butuzov, V.      12(11) 45 60(4) 61(4—5) 63(5) 68—69(4) 74(4) 79(8) 80(5 8) 83(8) 85(8) 97(4) 100(5) 101(17) 104(17) 105(5 18) 109—110(18) 134(29—33) 152(38) 165(45) 173(47) 178(49) 178—179
Chemical kinetics, critical case equations      81—85
Chemiluminescence (CL) method, first slow time scale      39—40
Chemiluminescence (CL) method, K7 and Wi determination      43—44
Chernavskii, D.      98(14) 178
Christenson, C.      139(35) 179
Classical finite difference equations, diffusion modeling boundary value problems      211—242 300—308
Classical finite difference equations, diffusion modeling concentrated sources, numerical examples      300—308
Classical finite difference equations, diffusion modeling concentrated sources, schemes for      294—300
Classical finite difference equations, diffusion modeling error tables      218—231
Classical finite difference equations, diffusion modeling hot die-forming procedures      328—334
Classical finite difference equations, diffusion modeling hot rolling procedures      350—355
Classical finite difference equations, diffusion modeling hot rolling procedures, numerical results      356—359
Classical finite difference equations, diffusion modeling prescribed diffusion flux solutions      255—270
Combustion model, autocatalytic reaction, asymptotic expansion      157—161
Combustion model, autocatalytic reaction, leading terms      157—161
Combustion model, autocatalytic reaction, overview      155—157
Combustion model, autocatalytic reaction, physical interpretation, asymptotic expansion      165—166
Combustion model, autocatalytic reaction, subsequent terms, asymptotic expansion      161—165
Comer boundary functions, elliptic equation in rectangle      118—120
Comer boundary functions, first-order derivatives      124—127
Comer boundary functions, hyperbolic equations      134
Comer boundary functions, nonisothermal fast chemical reactions      134—139
Comer boundary functions, parabolic equations      127—128
Comer boundary functions, parabolic equations, asymptotic solutions      128—134
Comer boundary functions, properties of      120—124
Comer boundary functions, thin body heat conduction, asymptotic solutions      168—172
Comer boundary functions, thin body heat conduction, two-dimensional approximations      172—174
Comparison theorem, autocatalytic reaction models, leading term construction      159—161
Compatibility condition, prescribed diffusion fluxes, mathematical formulation      253—255
Concentrated diffusion flux, classical and finite difference schemes      294—300
Concentrated diffusion flux, classical and finite difference schemes, mathematical formulation      286—293
Concentrated diffusion flux, classical and finite difference schemes, numerical experiments      300—308
Conditionally stable case, boundary value problem      67—73
Conditionally stable case, step—type contrast structures, second-order equations      90—97
Contrast structures, boundary and interior layers, overview      86—88
Contrast structures, boundary and interior layers, solution stability      111—113

Contrast structures, partial differential equations, Fisher's equation      154—155
Contrast structures, partial differential equations, phase transition models      152—154
Contrast structures, partial differential equations, spike-type solutions      148—152
Contrast structures, partial differential equations, step-type solutions, critical case      146—148
Contrast structures, partial differential equations, step-type solutions, noncritical case      139—146
Contrast structures, spike type structures      101—110
Contrast structures, spike type structures, "brusselator" model      105—110
Contrast structures, spike type structures, "step with spike" type      110
Contrast structures, spike type structures, boundary conditions      104—105
Contrast structures, spike type structures, second-order equations      101—104
Contrast structures, step-type structures      88—101
Contrast structures, step-type structures, autonomous identities      100
Contrast structures, step-type structures, fast and slow variables      97—98
Contrast structures, step-type structures, multiple roots for equations      100—101
Contrast structures, step-type structures, parabolic systems      98—100
Contrast structures, step-type structures, phase plane cell      97
Contrast structures, step-type structures, second-order equation      88—97
Critical case problems, boundary value problem      80—81
Critical case problems, chemical kinetics equations      81—85
Critical case problems, corner boundary layers, nonisothermal fast chemical reactions      136—139
Critical case problems, initial value problem, small nonlinearity systems      74—79
Critical case problems, nonlinear problem      79—80
Critical case problems, step-type contrast structures      97
Critical case problems, step-type contrast structures, partial differential equations      146—148
Degenerate systems, initial value problem      52—53
Denisov, E.T.      2(2) 12(14—15) 45—46
Differential equations, asymptotic solutions, approximation errors      5—6
Differential equations, diffusion modeling, boundary value problems, Neumann construction, special finite difference      271—275
Differential equations, diffusion modeling, boundary value problems, one-dimensional problems      243—249
Differential equations, diffusion modeling, boundary value problems, special construction principles      233—242
Differential equations, diffusion modeling, boundary value problems, special finite difference, numerical examples      275—286
Diffusion flux, boundary value problems, normalized computations      196—206
Diffusion flux, concentrated sources, equations      286—308
Diffusion flux, concentrated sources, equations, classical and special finite difference schemes      294—300
Diffusion flux, concentrated sources, equations, mathematical formulation      286—293
Diffusion flux, concentrated sources, equations, numerical experiments, classical and special finite difference schemes      300—308
Diffusion flux, prescribed diffusion flux solutions      249—286
Diffusion flux, prescribed diffusion flux solutions, classical finite difference schemes      255—270
Diffusion flux, prescribed diffusion flux solutions, mathematical formulation      250—255
Diffusion flux, prescribed diffusion flux solutions, Neymann problem, special finite difference schemes      271—275
Diffusion flux, prescribed diffusion flux solutions, special finite difference schemes      275—286
Dimensional variables, boundary value problem, conditionally stable case      73—74
Dimensional variables, boundary value problem, critical conditionally stable case      80—81
Dimensional variables, diffusion modeling, hot rolling procedures      338—346
Dimensional variables, time scales, fast time scale      37—38
Dirichlet boundary condition, asymptotic solution, Vishik — Lyusternik method      113
Dirichlet boundary condition, concentrated sources, diffusion equations for      289—293
Dirichlet boundary condition, concentrated sources, diffusion equations for, numerical computations      301—308
Dirichlet boundary condition, concentrated sources, diffusion equations for, special and classical finite difference schemes      297—300
Dirichlet boundary condition, diffusion modeling, classical finite difference techniques      211—231
Dirichlet boundary condition, diffusion modeling, plastic shear heat transfer      314—315
Dirichlet boundary condition, diffusion modeling, prescribed values, numerical solutions      209—211
Dirichlet boundary condition, diffusion modeling, special construction principles      232—242 271—274 277—286
Dirichlet boundary condition, partial differential equations, noncritical step-type solutions      140—146
Dirichlet boundary condition, prescribed diffusion fluxes, mathematical formulation      251—255
Dobowitckii, A.Ya.      3(4) 45
Dobowitckii, V.A.      3(4) 45
Domain boundary, prescribed diffusion fluxes, finite difference equations      250—286
Doolan, E.P.      309(13) 360(13) 361
Dubinsky, V.Z.      38(16) 46
Effective rate constant, K7 and Wi determination      43—44
Eigenvalues, critical case, initial value problem, small nonlinear systems      75—79
Eigenvalues, critical case, nonlinear problem      79—80
Electron spin resonance (ESR), first slow time scale      39—40
Electron spin resonance (ESR), second slow time scale      42—43
Elliptic equations, asymptotic solutions, Vishik — Lyusternik method      117—118
Elliptic equations, corner boundary layers, rectangle      118—120
Elliptic equations, diffusion modeling, boundary conditions      203—206
Elliptic equations, diffusion modeling, overview      183—191
Emanuel, N.M.      12(14) 41(18) 134(34) 46 179
Emel'yanov, K.V.      360(32—33) 361
Esipova, V.      74(6) 178
Existence theorem, asymptotic solutions, approximation formulas      10—12
Explosive scale, asymptotic solutions      31—34
Farrell, P.A.      309(16) 361
Fast time scales, asymptotic solution      16—17 37—38
Fife, P.      98(13) 146(36) 152(39) 178—179
Finite difference techniques, concentrated source diffusion equations, classical and special schemes      294—300
Finite difference techniques, concentrated source diffusion equations, numerical experiments      300—308
Finite difference techniques, diffusion modeling, boundary value problems, classical experiments      211—231
Finite difference techniques, diffusion modeling, computational techniques      191—206
Finite difference techniques, diffusion modeling, mathematical formulation      207—211
Finite difference techniques, diffusion modeling, numerical solutions      206—249
Finite difference techniques, diffusion modeling, overview      188—191
Finite difference techniques, diffusion modeling, special construction principles      231—242
Finite difference techniques, heat transfer diffusion modeling, hot die-forming procedures      328—334
Finite difference techniques, heat transfer diffusion modeling, hot rolling procedures      346—355
Finite difference techniques, heat transfer diffusion modeling, plastic shear heat transfer      315—321
Finite difference techniques, prescribed diffusion fluxes      249—286
Finite difference techniques, prescribed diffusion fluxes, classical schemes      255—270
Finite difference techniques, prescribed diffusion fluxes, mathematical formulation      250—255
Finite difference techniques, prescribed diffusion fluxes, Neumann problem equations      271—275
Finite difference techniques, prescribed diffusion fluxes, special finite techniques      275—286
First-order derivatives, corner boundary layers      124—127
First-order derivatives, diffusion modeling, boundary value problems, overview      189—191
First-order derivatives, diffusion modeling, boundary value problems, special finite difference techniques      243—249
First-order derivatives, partial differential equations, step-type contrast, critical case      147—148
First-order derivatives, partial differential equations, step-type contrast, noncritical case      144—146
Fisher's equation, boundary conditions      154—155
Fourier series expansion, autocatalytic reaction models      163—165
Fourier series expansion, diffusion modeling, prescribed values      209—211
Fourier series expansion, thin body heat conduction, asymptotic solutions      169—174
Fourier series expansion, thin body heat conduction, thermal diffusion coefficient      176—177
Fourier series expansion, thin body heat conduction, three-dimensional rod      174—175
Frank-Kamenetskii, D.      158(42) 179
Free radicals, liquid-phase chain oxidation      12—15
Fujii, H.      113(25) 179
Gagarina, A.B.      41(18) 46
Galaxy theory, step-type contrast structures      97
Gel'fand, I.      158(41) 179
Gol'denberg, M.Ya.      2(1) 45
Goltberg, V.M.      42(19) 46
Gorskii, V.G.      12(13) 45
Green's function, corner boundary layers, boundary conditions      122—124
Green's function, corner boundary layers, nonisothermal fast chemical reactions      138—139
Green's function, corner boundary layers, parabolic equations      133—134
Grid function, concentrated source diffusion equations      294—300
Grid function, diffusion modeling, boundary value problems, classical finite difference techniques      217—231
Grid function, diffusion modeling, boundary value problems, hot die-forming heat exchange      332—334
Grid function, diffusion modeling, boundary value problems, hot rolling procedures      353—355
Grid function, diffusion modeling, boundary value problems, Neumann construction, special finite difference      274—275
Grid function, diffusion modeling, boundary value problems, overview      183—191
Grid function, diffusion modeling, boundary value problems, plastic shear heat transfer      316—321
Grid function, diffusion modeling, boundary value problems, prescribed diffusion fluxes      261—270
Grid function, diffusion modeling, boundary value problems, special construction principles      231—242
Grid function, diffusion modeling, boundary value problems, special finite difference, numerical examples      276—286
Grid function, diffusion modeling, boundary value problems, special finite difference, techniques      242—249
Grinlee, Y.      146(36) 179
Hale, J.      113(24) 179
Heat transfer, concentrated diffusion flux equations      286—293
Heat transfer, diffusion modeling, applications      308—359
Heat transfer, diffusion modeling, applications, hot die-forming      321—334
Heat transfer, diffusion modeling, applications, hot rolling      334—359
Heat transfer, diffusion modeling, applications, overview      182—191
Heat transfer, diffusion modeling, applications, plastic shear perturbation      309—321
Heat transfer, diffusion modeling, applications, prescribed values, numerical solutions      206—249
Heat transfer, thin bodies, asymptotic approximation construction      168—172
Heat transfer, thin bodies, boundary layer functions      172—174
Heat transfer, thin bodies, overview      166—167
Heat transfer, thin bodies, small thermal diffusion coefficient      175—177
Heat transfer, thin bodies, thermoelasticity      177—178
Heat transfer, thin bodies, three-dimensional rod      174—175
Hegarty, A.F.      360(34—36) 361—362
Hemker, P.W.      309(16—17) 360(17 37—38) 361—362
Homogeneous equations, corner boundary layers      121—122
Homogeneous equations, spike-type contrast solutions      150—152
Homogeneous equations, spike-type contrast structures      103—104
Hot die-forming, diffusion modeling      321—334
Hot die-forming, finite difference techniques      328—331
Hot die-forming, heat exchange problem formulation      321—328

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