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Ghez R. — A Primer of Diffusion Problems
Ghez R. — A Primer of Diffusion Problems

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Название: A Primer of Diffusion Problems

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1988

Количество страниц: 243

Добавлена в каталог: 16.08.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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