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Ghez R. — A Primer of Diffusion Problems
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Название: A Primer of Diffusion ProblemsАвтор: Ghez R. Аннотация: A Primer of Diffusion Problems A Primer of Diffusion Problems is a concise and lively introduction to diffusion theory in its many guises and to a variety of analytical and numerical methods for the solution of diffusion problems. It discusses the diffusion equation, the steady state, diffusion under external forces, time-dependent diffusion, and similarity, thus bridging mathematical and physical treatments of diffusion. Featured topics include a careful development of the oxidation theory of silicon, properties of the family of error functions, precipitation and phase transformations, a concise introduction to Laplace transforms, and nonlinear boundary conditions. Exercises are found throughout the text, and appendices treat rarely found advanced topics.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 1988Количество страниц: 243Добавлена в каталог: 16.08.2009Операции: Положить на полку |
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Arrhenius behavior of diffusivity 90 205 Arrhenius behavior of mobility 90 Arrhenius behavior of reaction constants 52 53 Asymptotic behavior of Laplace transforms 188—190 197 198 Asymptotic behavior of solutions 116 152 161 162—163 197 198 200 237—239 Asymptotic expansions 107 119 123 206 Beta function, definition 186 Beta function, use of 160 186—187 218 Boundary conditions, Dirichlet 18 117 129 143 154 157 185—186 Boundary conditions, far-field condition 65 93 118 143—144 Boundary conditions, for BCF model 76 Boundary conditions, for precipitation 65 150 Boundary conditions, from local thermodynamic equilibrium 61—62 Boundary conditions, in numerical methods 18—19 23 Boundary conditions, linear in time 125—126 Boundary conditions, Neumann 19 117 129 159 Boundary conditions, radiation 208 Capillarity, capillary length 59 69 Capillarity, Gibbs — Thomson effects 59 232—233 Capillarity, Laplace’s law 56 Chemical potential, constancy of 42 56 Chemical potential, dependence on concentration 59 153 Chemical potential, in Gibbs — Duhem relation 55 Chemical potential, relation to Gibbs free energy 87 Conservation laws, at fixed boundaries 10—11 111 Conservation laws, at variable boundaries see "Stefan conditions" Conservation laws, for numerical schemes 23 Conservation laws, for random walk 3 224 Conservation laws, the continuity equation 7 28 37 85 226 228 Constitutive relations, anisotropic 227 Constitutive relations, Fick’s 7 Constitutive relations, Fourier’s 31 Constitutive relations, in general 37—38 153 Constitutive relations, Newton’s 32 Constitutive relations, Ohm’s 34 Convection and drift velocity 33 36 85 Convolution theorem, proof of 184—185 Convolution theorem, use of 185—187 196 209 Decay lengths, Debye length 94 Decay lengths, diffusion distance 105 108 Decay lengths, mean surface diffusion distance 76 Decay lengths, similarity length scale 135—136 139 140 161—162 Decay lengths, skin depth 194 Delta function, definition 175—177 Delta function, use of 22 178 183 195 212 Diffusivity, anisotropic 226 Diffusivity, estimate of 7 8 90 Diffusivity, in general fields 90 91 Diffusivity, kinematic viscosity 32 Diffusivity, surface 75 Diffusivity, thermal 31 Diffusivity, variable 8 9 153 156 Einstein’s, relation 87 90 Einstein’s, summation convention 225 Error functions, definition 102 106 120 Error functions, properties 102 106 121—124 Flux, continuous form 6 27 85 228 Flux, discrete form 2 83 223 Flux, energy 31 117 193 Gamma function, definition 118 Gamma function, properties 118—119 Gamma function, use of 120 121 160 171 186 190 Gibbs see "Capillarity" "Chemical "Phase Green’s function for Dirichlet conditions 185—186 Green’s function for finite differences 25—26 Green’s function for linear oscillator 183—184 Green’s function for Neumann conditions 197 209 Green’s function in infinite domain 99—100 Growth kinetics, BCF model 76 Growth kinetics, crystal growth 76 114—115 127 Growth kinetics, oxidation 51 Growth kinetics, precipitation 66—67 150—151 Heating problem 117 193 Heaviside’s step function, definition 169 Heaviside’s step function, use of 170 172 175 178 179 199 201 Hermite polynomials, definition 236 Hermite polynomials, use of 139 179 236—238 Impurity redistribution in a half space 103—105 180—182 Impurity redistribution in a sphere 146—149 Initial conditions for error function solution 102 106 Initial conditions for gaussian solution 100 Initial conditions for numerical methods 18 Initial conditions for oxidation 51 Initial conditions for precipitation 67 151 Initial conditions, nonconstant 182 Initial conditions, relation to Boltzmann’s transformation 143—145 Interpolation 5 84 213—214 225 Invariance of diffusion equation, relation to similarity 135—136 Invariance of diffusion equation, under affine transformations 14 38 Irreversibility 14 23 38 Jump frequency, anisotropic 83 223 Jump frequency, estimate of 89 Jump frequency, in master equation 4 Jump frequency, isotropic 1 Liebnitz’s rule 11 Mean curvature 56 59—60 63—64 231 Mobility, estimate of 90 Mobility, for charged particles 33 90 Mobility, in general fields 86 Modulus, definition 17 Modulus, relation to random walk 99 Modulus, stability condition 20 Moments, calculation of 101 120 163 236 Moments, definition 235 Moments, expansions in 237 238 Newton’s Law of Cooling 208 Newton’s law of viscous friction 32 Nonlinear diffusion, Stefan problems 113 140 149 Nonlinear diffusion, through boundary conditions 212 Nonlinear diffusion, through diffusivity 8 9 43 153 156 Nucleation, critical radius of 67 69 73 Nucleation, process 62 72 Numerical methods for derivatives 16 Numerical methods for the diffusion equation 17—21 Numerical methods for Volterra integral equations 213—217 Phase rules, proof of 229 231 Phase rules, use of 58 64 111 232 Point source solution for numerical scheme 21—25 Point source solution of power-law diffusion 159 Point source solution, gaussian solution 99—100 Random walk in higher dimensions 223 Random walk, anisotropic 83 Random walk, fitting 97 Random walk, isotropic 1 Random walk, relation to central limit theorem 99 Sampling 15 213 235 Sources and sinks, as boundary conditions 48 117 195 Sources and sinks, in the diffusion equation 32 35 74 194 Starting solutions for integral equations 219 Starting solutions for the diffusion equation 146 149 Stefan conditions for crystal growth 74 127 Stefan conditions for oxidation 49 Stefan conditions for precipitation 66 Stefan conditions, at phase boundaries 11 114 150 Stefan Problem see "Nonlinear diffusion" Supersaturation, absolute 68 115 127 151 Supersaturation, due to temperature ramping 127 Supersaturation, relation to critical radius of nucleation 67 69 Supersaturation, relation to step distance 73 77 Supersaturation, relative 68 73 77 127 Symmetries see "Invariance" Symmetries, affine 14 38 Symmetries, geometrical 28—29 135 Symmetries, rotational 30 43 Temperature schedule 125 204 Thermodynamic, equilibrium 2 41 56 229 Thermodynamic, local equilibrium 12 61—62 64 111 112 113 230 231 Thermodynamic, reservoirs 57 232 Thermodynamic, variables 58 229 231 Transition frequency see "Jump frequency"
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