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Statistical Physics of Fluids :  Basic Concepts and Applications - V.I. Kalikmanov

Statistical Physics of Fluids

Basic Concepts and Applications


Published: January 2001
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The book focuses on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others. The book addresses researchers as well as graduate students in physics and chemistry with research interests in the statistical physics of fluids.

From the reviews of the first edition:

"The book provides a good presentation of the fundamental theory in the context of its applications to concrete examples." (Mathematical Reviews 2002j)

"This book consists of 14 chapters and analyzes the fundamental problems of statistical physics of fluids. ... This book may be useful for advanced graduate students and or researchers that are working in other fields of physics and mechanics." (Oleg A. Sinkevich, Zentralblatt MATH, Vol. 976, 2002)

Ensembles in statistical mechanicsp. 1
Notion of a phase spacep. 1
Statistical ensemble and Liouville's theoremp. 5
Microcanonical ensemblep. 6
Entropyp. 8
Canonical ensemblep. 11
Legendre transformationsp. 19
Grand canonical ensemblep. 21
Barometric formulap. 24
Method of correlation functionsp. 29
n-particle distribution functionp. 29
Calculation of thermal averagesp. 30
n-particle correlation functionp. 31
The structure factorp. 34
Equations of statep. 37
Energy equationp. 37
Pressure (virial) equationp. 38
Compressibility equationp. 39
Thermodynamic consistencyp. 41
p. 41
Virial expansionp. 44
Law of corresponding statesp. 47
Liquid-vapor interfacep. 49
Thermodynamics of the interfacep. 49
Statistical mechanical calculation of surface tensionp. 52
Fowler approximationp. 55
Perturbation approachp. 57
General remarksp. 57
Van der Waals theoryp. 57
First-order perturbation theoriesp. 62
Weeks-Chandler-Andersen theoryp. 65
Reference modelp. 66
Total free energyp. 70
Song and Mason theoryp. 70
Perturbation approach to surface tensionp. 75
Algebraic method of Ruellep. 77
Equilibrium phase transitionsp. 83
Classification of phase transitionsp. 83
Phase equilibrium and stability conditionsp. 86
Critical pointp. 89
Universality hypothesis and critical exponentsp. 90
p. 95
p. 97
Monte Carlo methodsp. 103
Basic principles of Monte Carlo. Original capabilities and typical drawbacksp. 103
Computer simulation of randomnessp. 106
Rejection methodp. 109
Simulation of "observations of random variables" for statistical ensemblesp. 112
Metropolis algorithm for canonical ensemblep. 114
p. 116
p. 117
Monte Carlo with fictitious particlesp. 119
p. 125
p. 128
Superfluous randomness to simulate microcanonical ensemblep. 129
Method of dependent trials - eliminating unnecessary randomnessp. 129
Theories of correlation functionsp. 133
General remarksp. 133
Bogolubov-Born-Green-Kirkwood-Yvon hierarchyp. 133
Ornstein-Zernike equationp. 137
Formulation and main featuresp. 137
Closuresp. 140
Percus-Yevick theory for hard spheresp. 141
Density functional theoryp. 151
Foundations of the density functional theoryp. 151
Ideal gasp. 153
General casep. 154
Intrinsic free energyp. 157
Surface tensionp. 160
Nonlocal density functional theoriesp. 163
Weighted-density approximationp. 165
Modified weighted-density approximationp. 166
Real gasesp. 169
Fisher droplet modelp. 170
Fisher parameters and critical exponentsp. 179
Surface tension of a curved interfacep. 183
Thermodynamics of a spherical interfacep. 183
Tolman lengthp. 186
Semiphenomenological theory of the Tolman lengthp. 190
Polar fluidsp. 195
Algebraic perturbation theory of a polar fluidp. 195
Dielectric constantp. 199
Extrapolation to arbitrary densitiesp. 204
Comparison of the algebraic perturbation theory with other models and computer simulationsp. 205
Mixturesp. 209
Generalization of basic conceptsp. 209
One-fluid approximationp. 212
Density functional theory for mixturesp. 213
Surface tensionp. 215
Density functional approachp. 215
One-fluid theoryp. 218
Ferrofluidsp. 223
Cell model of a ferrofluidp. 224
Magnetic subsystem in a low field. Algebraic perturbation theoryp. 228
Equation of statep. 231
Magnetic subsystem in an arbitrary field. High-temperature approximationp. 233
Properties of the reference systemp. 234
Free energy and magnetostaticsp. 234
Perturbation approach for the solventp. 237
Empirical correlations for macroscopic properties of argon, benzene and n-nonanep. 239
Angular dipole integralsp. 241
De Gennes-Pincus integralp. 243
Calculation of $$($$) and $$($$) in the algebraic perturbation theoryp. 245
Calculation of $$($$)p. 246
Calculation of $$($$)p. 248
Short-range part: 1 <R <2p. 248
Long-range part: 2 <R <$$p. 249
Mixtures of hard spheresp. 251
Pressurep. 251
Chemical potentialsp. 252
Referencesp. 253
Indexp. 257
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540417477
ISBN-10: 3540417478
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 260
Published: January 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.52