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Berne B. — Statistical Mechanics. Part A: Equilibrium Techniques
Berne B. — Statistical Mechanics. Part A: Equilibrium Techniques



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Название: Statistical Mechanics. Part A: Equilibrium Techniques

Автор: Berne B.

Аннотация:

Statistical mechanics brings together under one roof a broad spectrum of mathematical techniques. The aim of these volumes is to provide a didactic treatment of those techniques that are most useful for the study of problems of current interest to theoretical chemists. The emphasis throughout is on the techniques themselves and not on reviewing the enormous literature in statistical mechanics. Each author was charged with the following task. Given N pages, (a) pose the problem, (b) present those aspects of the particular technique that clearly illustrate its internal workings, (c) apply the technique to the solution of several illustrative examples, and (d) write the chapter so that it will enable the reader to approach key citations to the literature intelligently.

These volumes are designed for graduate students and research workers in statistical mechanics. Nevertheless, because of the range of techniques and their general utility, they should be useful in other areas as well.


Язык: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 242

Добавлена в каталог: 09.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\gamma$-expansion      1 31—34 7
$\gamma$-ordering      58—70
$\Gamma$-ordering, lowest-order approximation      62
$\Gamma$-ordering, lowest-order approximation and the mean spherical approximation      62
$\gamma$-ordering, relation to the mean spherical approximation      59 7
$\Gamma$-ordering, second-order approximation      62—64
$\Gamma$-ordering, second-order approximation in ionic and dipolar systems      64 72—73
$\Gamma$-ordering, second-order approximation in orientation-independent systems      65— 67 73
$\Gamma$-ordering, thermodynamic properties from      67—69
$\gamma$-parameterization      48 58
Activity      95—102 106—115
Activity, coefficient      92 93 104
And integral equations      126 127
Articulation circles      115
Articulation points      5
Bijl — Jastrow wave function      183
Black circles      106 107 109 111
Blip function theory      25—29
BOND      2
Bond function      6 8
Brownon model      88
Chain sum      60
Circles, articulation      115
Circles, black      106 107 109 111
Circles, cutting      124
Circles, white      106 107
Cluster      (see Microcluster)
Cluster expansion      145 105—123
Cluster expansion for ionic systems      122 123
Cluster expansion, chemical potential      115 116
Cluster expansion, correlation functions      117 123
Cluster expansion, density      114
Cluster expansion, direct correlation function      124
Cluster expansion, grand partition function      107 112 113 117
Cluster expansion, Helmholtz free energy      115—117
Cluster expansion, Helmholtz free energy for ionic systems      118—122
Cluster expansion, Mayer resummation      118—123
Cluster functions      112 117 118
Compressibility, definition      51
Configuration integral      53 96 98
Correlation functions for BO system      96
Correlation functions for ionic systems      122 123
Correlation functions for MM system      99
Correlation functions, asymptotic behavior of      50—52 77—82
Correlation functions, cluster expansion      117 123
Correlation functions, integral equations      123—128
Correlation functions, limiting form      128
Correlation functions, pair      95 105
Correlation functions, quality tests      129—131
Cosphere      90
Cutting circles      124
Debye kappa      120
Debye — Hueckel linearized DH equation      127 128
Debye — Hueckel theory      1 16 24
Debye-Hueckel limiting law value for $A^{ex}$      121
DHLL + $B_{2}$ approximation      122
dielectric constant      88 90 118
Dipolar fluids, approximate radial distributions for      71—72
Dipolar fluids, Helmholtz free energy of $\Gamma$-ordering for      67—68
Dipolar fluids, Helmholtz free energy of Pade approximant for      55
Dipolar fluids, pair potential for      50
Dipolar fluids, saturation effects in      54
Direct correlation function      124—128
Direct correlation function in $\gamma$ ordering      58—62
Direct correlation function in the mean spherical approximation      57
Direct correlation function, asymptotic behavior of      50—51
Direct correlation function, cluster expansion      124
Direct correlation function, definition      50
Effective ionic forces      187
Entropy estimation      170ff
Ewald energy calculation      153 163
Exponential (EXP) approximation      1 37
Field points      2
Fluid, dipolar hard sphere      31
Fluid, hard sphere      26
Fluid, Lennard — Jones      31
Fluid, Polar      44
Fluid, square well      31
Fluids, dielectric properties      44
Fluids, equilibrium structure      1
Fluids, hydrogen-bonded      3843
Fluids, inhomogeneous      44
Fluids, perturbation theory of      29—31 38
Fluids, polar      44
Fluids, statistical mechanics of      145
Fluids, thermodynamics      145
Forces in ionic solutions      86—91
Forces, dynamical      87 88
Forces, solvent-averaged      87 88 101
Free energy      (see Gibbs free energy Helmholtz
Free energy estimation      170ff 7
Gas-liquid interface      185
Generalized mean spherical approximation (GMSA)      128
Gibbs free energy      92 93 102—104
grand canonical ensemble      175ff
Grand partition function for BO system      96 98
Grand partition function, cluster expansion      107 112 113 117
Grand partition function, cluster expansion, thermodynamic limit      108 117
Graph      245
Graph theory      105—106
Graph theory, articulation circle      115
Graph theory, black circle      106 107 109 111
Graph theory, connectedness of graphs      117
Graph theory, cutting circle      124
Graph theory, for many components      107—110
Graph theory, protograph      121
Graph theory, q-bond node      121
Graph theory, root      114
Graph theory, white circle      106 107
Graph, connected      5
Graph, connectivity of      4
Graph, doubly connected      5
Graph, irreducible      5
Graph, labeled      3
Graph, path in      4
Graph, symmetry number of      4
Graph, value of      6 8—9
Graphical representation      (see Cluster expansions)
Graphs, ALDC      115
Graphs, ALSC      113
Graphs, connectedness of      117
Graphs, simple      106
Graphs, symmetry number of      106 122
Hamiltonian model for ionic solution      86 87
Hamiltonian model, level of description BO level      86—88 91 95 96 100 101
Hamiltonian model, level of description BOSL level      87
Hamiltonian model, level of description MM level      87—91 95 100 101 105 127
Hamiltonian model, level of description S level      86 87
Helmholtz free energy      11 102—105
Helmholtz free energy, $\Gamma$-ordering for      67—69
Helmholtz free energy, $\lambda$-expansion for      53 56
Helmholtz free energy, asymptotic behavior of      54
Helmholtz free energy, bounds on      53
Helmholtz free energy, duster expansion      115—117
Helmholtz free energy, duster expansion for ionic systems      118—122
Helmholtz free energy, limiting law result      121
Helmholtz free energy, Pade approximants for      55—56
Helmholtz free energy, Pade approximants for dipolar fluids      55
Helmholtz free energy, Pade approximants for multipolar fluids in general      56
Helmholtz free energy, Pade approximants for quadrupolar fluids      55
High-temperature approximation      30
Hydration, hydrophobic      90
Hydrogen bond      38
Hypemetted chain (HNC) approximation      125—129 131
Hypervertex      44
Importance sampling      139 140
Integral equations      123—129
Integral equations, and Mayer resummation      126 127
Integral equations, GMSA      128
Integral equations, HNC      125—129 131
Integral equations, linearized DH      127
Integral equations, MSA      91 128
Integral equations, PY      126—128
Integral equations, quality tests      129—131
Interfaces, Monte Carlo study      185
Ionic fluids, $\lambda$-expansion for      56
Ionic fluids, approximate radial distribution functions for      71—72
Ionic fluids, Helmholtz free energy of r-ordering for      67—68
Ionic fluids, internal energy of      (see Restricted primitive model)
Ionic fluids, kappa      120
Ionic fluids, mixed perturbation theory for      70—71
Ionic fluids, pair potential for      50
Ionic fluids, potential of mean force      187
Ionic fluids, saturation effects in      54
Ionic solutions      1
Ionic strength      93 94 105
Ising model      146 149
Kirkwood superposition approximation      31
Markov chain, convergence rate of      145
Markov chain, quasi-ergodic problem in      144
Markov chain, transition matrix of      144
Mayer resummation      118—123
Mayer theory of ionic solutions      16 23—25
Mayer/function      8 11 12 112
McMillan — Mayer theory      23 95—105
McMillan — Mayer theory, limitations of      100 101
McMillan — Mayer theory, LR to MM conversions      102—105
McMillan — Mayer theory, models for ionic solutions      87
McMillan — Mayer theory, thermodynamic functions      104 105
Mean spherical approximation (msa)      57 91 128
Microcluster, drop model      210
Microcluster, drop model, criticisms of      215
Microcluster, drop model, modifications of      216—224
Microcluster, equilibrium concentration      209—211
Microcluster, free energy of      209—211 216—224
Microcluster, microscopic point of view      219—224
Microcluster, surface (free) energy of      211 217—219 221- 224
Mixed perturbation theory      68 70
Mixed perturbation theory in ionic solution theory      70—71
Mixing coefficients      94
Mode expansion      34
Molecular Dynamics      87 91 100 129
Moment of correlation functions, second      130 131
Moment of correlation functions, zeroth      130 131
Moment-cumulant relation      111 115
Monte Carlo, boundary conditions      150 186 188
Monte Carlo, energy calculations cutoff approximation      154
Monte Carlo, energy calculations discussion of      155ff
Monte Carlo, energy calculations, Ewald approximation      153
Monte Carlo, energy calculations, minimum image approximation      154
Monte Carlo, error estimation      147
Monte Carlo, free energy estimation      170ff
Monte Carlo, free energy estimation at phase transitions      173ff 181
Monte Carlo, free energy estimation by thermodynamic integration      172
Monte Carlo, free energy estimation, Cold well’s method      171
Monte Carlo, free energy estimation, grand canonical ensemble      175
Monte Carlo, free energy estimation, method      87 91 100 129
Monte Carlo, free energy estimation, multistage sampling      178
Monte Carlo, free energy estimation, umbrella sampling      178
Monte Carlo, microscopic studies      185ff
Monte Carlo, microscopic studies, gas-liquid interface      185
Monte Carlo, microscopic studies, ionic mean forces      187
Monte Carlo, quantum mechanics      182ff
Monte Carlo, quantum mechanics, solving Schroedinger’s equation      184
Monte Carlo, quantum mechanics, variational calculations      182
Monte Carlo, sampling problems      179 185 189 190
Monte Carlo, various ensembles      148
Nodal approximation      48 70 73
Nodal contraction      48 69 73
Nodal ordering      48 69 73
Nucleation, homogeneous      197 208—224
Nucleation, homogeneous, classical theory      211—215
Nucleation, homogeneous, critical supersaturation      212—214
Nucleation, homogeneous, microscopic approach      219—224
Nucleation, mathematical formalism      198—208
Nucleation, steady state rate      201—208
Nucleation, steady state rate, general theory      204—206
Nucleation, steady state rate, kinetic expression      203
Nucleation, steady state rate, Maxwell's demon      204—206
Nucleation, steady state rate, thermodynamic expression      203
Nucleation, steady state rate, Zeldovich factor      207
Nucleation, time dependence      200
Nucleation, water on ions      224—228
Omstein — Zernike equation      50 124 127 128
Optimized cluster theory      35—37
Osmotic coefficient      104 105 129 130
Pade approximant      21 31 38
Pair correlation function      1—45
Pair potential      49
Pair potential, dipolar fluids      50
Pair potential, ionic fluids      50
Pair potential, monatomic fluids      50
Partial structure factors      95
Partition function      9
Partitions      109 114
Percus—Yevick (PY) approximation      1 126— 128
Periodic boundary conditions      150
Perturbation theory of fluids      29—31 38
Point function      6 8
Points, articulation      5
Points, field      2
Points, overlapping pair of      39
Points, pair of articulation      5
Points, pair of reducible      5
Points, root      2
Polymer configuration      149
Potential for ionic solutions      86—91
Potential for ionic solutions, CAV      90
Potential for ionic solutions, COR      89
Potential for ionic solutions, GUR      90
Potential in BO system      96 99
Potential in MM system      98
Potential of average force      87 96 98 99
Potential, component      100 101 112
Potential, pairwise additivity of      100 101 107 117
Potential, primitive model      89
Potential, solvent average      87—91 99—101 117
Potential, temperature dependence of      98 100
Primitive model      89 91 128 130
Principle of unreasonable utility of asymptotic estimates      48 57
Probability density function      49
Quantum mechanics, Monte Carlo solutions      184
Quantum mechanics, variational calculations      182
Radial distribution function      49
Radial distribution function, approximations for ionic and dipolar systems      71—72
Random numbers      137 139 161
Reducible points      5
Renormalization      19 (see also Mayer resummation)
Residual      6
Restricted primitive model for ionic fluids      56
Restricted primitive model for ionic fluids, internal energy of      56
Restricted primitive model for ionic fluids, internal energy of $\lambda$-expansion for      56
Restricted primitive model for ionic fluids, internal energy of empirical equation for      56
Restricted primitive model for ionic fluids, internal energy of Pade approximant for      56
Root point      2
Saturation effects at low temperatures      54
Scattering, from ionic solutions      95
Schroedinger’s equation, Monte Carlo solution      184
screening      20
shielding      20
Single occupancy      174
Solvation coefficients      91 92 101
Solvent-averaged forces      187
Surface free energy      211
Symmetry number      4
Thermodynamic excess functions      92—94
Thermodynamic excess functions, LR to MM conversions      102—105
Thermodynamic limit      108 117
Topological reduction      1 15—45
Umbrella sampling, I      78
1 2
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