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Lim Ch., Nebus J. — Vorticity, Statistical Mechanics, and Monte Carlo Simulation
Lim Ch., Nebus J. — Vorticity, Statistical Mechanics, and Monte Carlo Simulation

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Название: Vorticity, Statistical Mechanics, and Monte Carlo Simulation

Авторы: Lim Ch., Nebus J.

Аннотация:

This book is drawn from across many active fields of mathematics and physics, and has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors of this book explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and provide the tools to answer them.

In this book, the reader will learn how to research a topic and how to understand statistical mechanics treatments of fluid dynamics. Of particular interest should be the application of Monte Carlo methods to problems like the dispersal of points on the sphere, the phase transitions of inviscid fluid flows in models that increasingly approximate the conditions of actual planetary atmospheres, and the treatment of negative-absolute temperatures and the effects these extremely high-energy states have on fluid flows. Special attention is given to spherical models as well.

This book is intended for upper-level undergraduate or beginning level graduate courses of mathematics and physics. It will also be of use to readers interested in statistical mechanics methods applied to fluid mechanics problems. Readers will gain an understanding of how to synthesize new mathematics by applying familiar tools in new ways, and developing new tools to fit particular applications.


Язык: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2006

Количество страниц: 290

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$l^1$      69 70
$l^2$      68 69 223 224 229—231 249 250 252 253 255
$S^1$      87
$S^2$      87
$\beta$-plane      234
Almost everywhere      6 71 79 224 229
Anti-prism, hexagon      208
Anti-prism, square      192 207 210
Antiparallel      134 135 139 140 142 143 158
Aperiodic      54 59
Approximation, least mean squares      139
Archimedean solid      169 201
Atomic theory      1
Average      12 13 24 39 41 55 57—59 61 123 140 143 150 151 170 219 222
Baroclinic      235 237 242 243
Barotropic      235 237 242 243 245—247 249 253 256 257 260
Barotropic bias      242
Barotropic circulation      237
Barotropic energy      131
Barotropic flow      viii 235 250 256 258—260
Barotropic fluid      235 245 248
Barotropic model      248
Barotropic rim current      242
Barotropic vortex      132
Barotropic vortex dynamics      viii 3 245
Barotropic vorticity      246 247
Barotropic vorticity equation      246 247 250 258
Barotropic vorticity model      253 255
Bath      36 41 57 58 127
Bayes, probability      25
Bayes, statistics      25
Bayes, Thomas      25 26
Beltrami, Eugenio      69
Berlin — Kac model      116 117 258 260
Berlin, TH      116
Bessel, Friedrich Wilhelm      236
Black hole      1
Boltzmann, constant      31 41 57
Boltzmann, ensemble      42
Boltzmann, Ludwig      31 126
Boltzmann, statistics      44 45
Bose — Einstein, condensate      222
Bose — Einstein, statistics      45
Bose, Satyendranath      45
Boyle, Robert      2
Brownian motion      1
Buffon, Georges Compte de      55
Buffon, needle problem      55
Burgers, Johannes Martinus      6
Canonical      30 38 39 58 87—89 117 213 237 240
Casimir, effect      88
Casimir, Hendrik Bugt      88
Casimir, invariant      88
Center, $S^2$      258
Center, mass      13
Center, polygon      98
Center, sphere      163 164
Center, vorticity      92 96 99 213 214 236
Centroid      163—165 168 169 171 173
Chandrasekhar, Subrahmanyan      1
Charles, Jacques-Alexandre-Cesar      2
Chebyshev, Pafnuty Lvovich      19 20 253
chemical potential      32 34 36 39 58 191 214 215 224 238 255
Circulation      32 36—39 57 115 116 119 121—123 127 128 143 156 219 223 224 226 227 230 231 236 237 242 248—250 255 259
Circulation, discrete      127
Code, spherical      209—211
complete      68 71
Condon — Shortley phase      78
Condon, Edward Uhler      78
conjugate      79 84 86 88
Constraint, canonical      57 58 215 245 249 256
Constraint, microcanonical      127 245 254 256
Convolution      75
Coriolis, acceleration      233
Coriolis, force      233
Coriolis, Gaspard Gustave de      233
Coriolis, parameter      233 234
Correlation      62 139 140 143
Correlation, coefficient      139
Correlation, function      137 139 140
Correlation, length      140
Correlation, linear      140
Correlation, nonlinear      139
Correlation, pairwise      139
Correlation, time      61 62 127 139 140
Correlation, zero      139
Covariance      18
Coxeter, Harold Scott Mac-Donald      161 192 209
Critical slowing down      137
cube      111 113 164 169 192 197 207 210
Cuboctahedron      192 201 208
Curie, Marie Klodowska      150
Curie, Pierre      150
Curie, point      150
Cylinder      87
Degeneracy      37 52 57 253
Degenerate, case      71
Degenerate, energy      252 253
Degenerate, gas      32
Degenerate, non-      260
Degenerate, state      130 169
Density, angular      219
Density, radial      219
Detailed balance      55—57 60
DiBattista, Mark T      234 237 242
Diffusion      2
Dipole      158 159
Dirac, delta function      82 113
Dirac, Paul Adrien Maurice      32 44
Dirichlet quotient      viii 4
Discretization      79
Distribution, coarse-grain      242
Distribution, Gauss      21 22 44 62 117 242
Distribution, Gaussian      19
Distribution, marginal      17
Distribution, probability      21 25 35 38 128 243
Distribution, standard normal      21
Distribution, uniform      62
dodecahedron      201 203 208
Dual      73 87 162 169
Dynamics      3 4 36 79 80 83 85 91 99 100 103 104 111 112 188 211 233 234 249
Dynamics, aerodynamics      101
Dynamics, fluid      96 113 213 222 234
Dynamics, gas      1 31
Dynamics, Hamiltonian      90
Dynamics, molecular      79
Dynamics, ocean      234
Dynamics, particle      6 113
Dynamics, plane      91
Dynamics, vortex      3 4 7 83 133 214 257
Dynamics, vortex, double pyramid      110
Dynamics, vortex, line      99 101
Dynamics, vortex, octahedron      110
Dynamics, vortex, pair      92 94 101 103
Dynamics, vortex, polygon      96 107
Dynamics, vortex, tetrahedron      109
Dynamics, vortex, triangle      105
Dynamics, vorticity      249
EDGE      134 162—165 168 171—173
Ehrenfest, Paul      126
Eigenfunction      70—72 77 98 224 251
Eigenvalue      54 70—72 77 128 129 224 229 252 253 256
Eigenvector      54 70 71
Einstein, Albert      1 45 68
Energy      viii 3 4 7 11 29 30 32—41 44 45 51 52 56—59 62 68 72 83—86 88—90 111 113 116—122 124—127 131 134 137 141—143 145 150 158—162 168—187 189 191—206 208 210 211 213—215 217 218 223 224 227 229 236—239 243 245 247 249 251—255 257
Energy, free, vii, viii      3 4 32 41 49 117 130 162 222—224 246
Energy, gravitational potential      245
Energy, internal, vii, viii      3 32 41 223 246
Energy, kinetic, viii      3 4 12 36 57 81—83 85 115 118 127 233 245—248 250 255 257 258 260
Energy, potential      85 188 246
Energy, self      118 127
Energy, total      245
Energy-Casimir method      89
Energy-enstrophy      117 127 246 250 254—257
Energy-enstrophy-circulation      116
Ensemble      vii 29 30 34 41 58 61 139 222
Ensemble, Canonical      30
Ensemble, Grand Canonical      30
Ensemble, microcanonical      30 42
Enstrophy      viii 4 30 58 115—117 119 120 122 125 127 128 144—146 148 151 152 154 156 158 159 245—252 254 256
Enstrophy, relative      4 131 132 246 249 253 255—258 260
Enthalpy      58 133 134 137 241
entropy      vii 3 4 7 11 31 32 41 52 124 162 211 222 223 246
Equation, barotropic vorticity      247 249 258
Equation, Burgers      6
Equation, Euler      viii 3 4 6 7 80 127
Equation, Euler — Lagrange      225 250
Equation, Maxwell      69
Equation, Poisson      80
Equilibration      24 157 219
Equilibrium      3 77 101 103—107 109—113 131 145 156 161 169 186 189 192 205 206 209 211 214—216 219 222 253
Equilibrium, crystalline      3
Equilibrium, dynamic      viii 2 3 162 186 211
Equilibrium, fixed      99 102
Equilibrium, nonstatistical      41
Equilibrium, occupation vector      35
Equilibrium, polyhedron      viii 3
Equilibrium, relative      96 104 107 109 187
Equilibrium, stable      102 253
Equilibrium, state      52
Equilibrium, statistical      vii viii 2 3 7 38 41 42 48 54 55 57 59 60 126—128 134 144 159 162 188 189 211 213—216 218 222 223 242 245 246 249
Equilibrium, thermal      viii 3 4 57
Ergodic      59 249
Error, mean square      71 72
Euler, Leonhard      4
Event      9 10 18 19 21 25 26 55
Extremal      3 251
f-plane      234
Face      110 113 162—165 168 169 173 201
Fermi — Dirac statistics      44 45
Fermi, Enrico      44
ferromagnetism      52 116 126 137 150
Fibonacci, generator      63 64
Fibonacci, Leonardo Pisano      63
Fibonacci, sequence      63
First integral      115 214
Fisher, Michael Ellis      126
Fitzgerald, George      217
Flow, fluid      2
Flow, geophysical      245
Flow, relative      255
Flow, vortex      2
Fluctuation      2 42—44 62 78 126 137 145 158 159 189
Fluid, barotropic      245
Fluid, inviscid      3 4 6 81 113 116 127 159 222 233
Fluid, turbulence      3
Fluid, viscous      4
Formula, Stirling      43
Fourier transform, fast      76
Fourier, coefficient      76
Fourier, component      252
Fourier, decomposition      8
Fourier, expansion      240
Fourier, Jean Baptiste Joseph, Baron de      67
Fourier, mode      128
Fourier, series      71 72 74 75
Fourier, transform      73—77 256
Froude, William      235
Fuller, Richard Buckminster      161
Function, Bessel      236
Function, characteristic      20 118 120 224 225 254
Function, cumulative distribution      11 12
Function, discrete mass      21
Function, Green      80—83 118 122 129 225 236
Function, indicator      20 254
Function, moment generating      21 22
Function, partition      260
Function, probability      32
Function, probability density      12—14 18 22 239
Function, probability distribution      27
Function, probability mass      11 13 17
Function, radial distribution      161 166—168 170 173—185 189—206 208
Function, reduced distribution      215
Functional      viii 4 35 67 68 71—73 223—225 227 229 238 246 250 251
Fundamental solution      69 77 82 118
Galois, Evariste      89
Gauss, Johann Carl Friedrich      14 19 87 119
Gaussian      242
Gaussian, condition      131
Gaussian, integral      128
Gaussian, model      117 246 254 255
Gaussian, partition      255
Generator, add-with-carry      63
Generator, combined      65
Generator, Fibonacci      63
Generator, inverse congruential      64
Generator, linear congruence      62
Generator, multiple recursive      63
Generator, random number      62
Generator, subtract-with-carry      63
Geodesic      163—165 168—171 173
Geodesic, word      166—169 171
Gibbs, factor      48 144 217 223
Gibbs, Josiah Willard      34 42
Gibbs, partition function      241
Gibbs, picture      34 40 44
Gibbs, statistics      127
Graph      134 162
Graph, bipartite      134
Gravity      1
Green, George      5
Hamilton, Sir William Rowan      7 188
Hamiltonian      7 68 79 83—90 92 93 103 105 111 113 116—118 125 128 141 187 215 216 225 241 246 254 256
Hamiltonian, N-body      79 83 85
Hastings, rule      56
Hastings, W Keith      56
Hermite, Charles      69
Hermitian      69
Heton      113 234 241 242
Hilbert, David      68 214
Hogg, Nelson George      234
icosahedron      113 162 169—171 173 182 199 201 208
Inequality, Chebyshev      20 21
Inner product      67—69 87 258
Integral, Lebesgue — Stieltjes      14
Invariance time      79
Invariance translation      16 215
Involution      89 91 92 111—113
Irreducible      54 59
Ising, Ernst      52
Ising, interaction      259
Ising, model      52 116 117 126 128 248 254 256 259 260
Isotropy      172
Jacobi, Carl Gustav Jacob      14 87
Jacobian      87 89 247
Kac, Mark      116
Kamiltonian      89
Kelvin, William Thomson, Lord      96
Kernel      69 116 229
Kerr, Roy      1
Kraichnan, R.H.      vii 246
Kutta, Martin Wilhelm      79
Lagrange, Joseph-Louis      32
Lagrange, multiplier      32 34 35 40 42 213 237 250
Laplace — Beltrami, equation      225
Laplace — Beltrami, inverse      77
Laplace — Beltrami, operator      69 77 81 82 119 129 224 229
Laplace, integral      128 256
Laplace, operator      70
Laplace, Pierre-Simon de      69
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