Synopses & Reviews
This graduate-level introduction to the theory and applications of time correlation functions and the molecular theory of fluid dynamics provides experimentalists with the theoretical tools useful for analysis of experimental results, and theoreticians a comprehensive source of illustrations of theories most relevant in practical applications. The book reviews the concepts, basic tools and basic approximations of molecular hydrodynamics, then explores self-diffusion, space-dependent diffusion, hydrodynamic fluctuations, fluctuations at finite wavelengths and finite frequencies. 110 illustrations.
Synopsis
-This book describes the study of atomic motions in classical simple fluids through time-dependent correlation functions. The emphasis is on those theoretical approaches that have been most useful in data analysis and interpretation, and in leading to the understanding of the molecular dynamic behavior of fluid systems.- -- Preface.
This excellent monograph is intended to introduce graduate-level students to the theory and applications of time correlation functions and the molecular theory of fluid dynamics, providing more content and insight than either a selected review or a general survey. At the professional level, it provides experimentalists with the theoretical tools useful for the analysis of experimental results, and it offers theoreticians a comprehensive source of illustrations of the theories most relevant in practical applications.
The book opens with a short introductory chapter followed in Chapter 2 by an extensive yet succinct review of the concepts, basic tolls and basic approximations of molecular hydrodynamics. Chapters 3 and 4 explore self-diffusion and space-dependent diffusion. The final two chapters deal at length with hydrodynamic fluctuations and fluctuations at finite wavelengths and finite frequencies.
-There has existed until now no treatment of sufficient depth and breadth to do justice to the topic.... a collaboration by two accomplished professionals.... Several threads are woven into the text to provide a natural unification.... The literature coverage ... is impressive.... The reader is led by the hand, important concepts being repeated as necessary.... the] critical attitude ... is one of] scrupulous impartiality.... An in-depth entree to the literature.- -- Jerome K. Percus, Physics Today.
Synopsis
A graduate level introduction to the theory and applications of time correlation functions and the molecular theory of fluid dynamics. "Quite well organized . . . the literature coverage is impressive." — Physics Today. 110 illustrations.
Description
Includes bibliographical references (p. 405-414) and index.
Table of Contents
Preface
Symbols and Notations
1 Hydrodynamics and Molecular Dynamics
1.1 Motivattion
1.2 Time Correlation Functions
1.3 Experimental Aspects
1.4 Theoretical Aspects
2 Time Correlation Functions: General Properties and Basic Formalism
2.1 Introduction
2.2 Space-Time Correlation Functions
2.3 Static Correlation Functions
2.4 Sum Rules and Short-Time Behavior
2.5 Long-Time Behavior and Transport Coefficients
2.6 The Memory Function Equation
2.7 Linear Response Theory
2.8 Kinetic Theory
2.9 Mode Coupling Theory
Notes
3 Self-Diffusion
3.1 Introduction
3.2 The Velocity Autocorrelation Function and Its Memory Function
3.3 Short-Time Behavior and Implications of Nonexponential Decay
3.4 Long-Time Behavior and Implications of Nonexponential Decay
3.5 Memory Function Models
3.6 Dynamical Calculations
4 Space-Dependent Diffusion
4.1 Introduction
4.2 General Properties
4.3 Two Idealized Systems
4.4 The Cumulant Expansion
4.5 The Gaussian Approximation and Non-Gaussian Corrections
4.6 The Memory Function Approach
4.7 Linear Response Theory and Higher-Order Memory Functions
4.8 Kinetic Theory Calculations
5 Hydrodynamic Fluctuations
5.1 Introduction
5.2 The Hydrodynamic Equations
5.3 The Hydrodynamic Modes
5.4 Relaxation Processes and Dispersion Effects
5.5 Two-Component Systems
Notes
6 Fluctuations at Finite Wavelengths and Finite Frequencies
6.1 Introduction
6.2 Transverse Current Fluctuations-Intuitive Approach
6.3 Density and Longitudinal Current Fluctuations-Intuitive Approach
6.4 Generalized Langevin Equation Formalism
6.5 Generalized Susceptibility Formalism-Connections with Self-Correlations
6.6 Neutron Scattering and Computer Simulation Results
6.7 Kinetic Theory and Mode-Coupling Analyses
Appendixes
A -A Light Scattering Probe of Short-Time Dynamics
B -Time and Space-Dependent Correlations in Liquid-Like Brownian Systems
References
Index