A general kinetic theory of liquids, by Max Born, H. S. Green

By Max Born, H. S. Green

This paper outlines a basic concept whose item is to supply a foundation from which the entire equilibrium and dynamical houses of drinks should be investigated. a suite of multiform distribution capabilities is outlined, and the generalized continuity equations chuffed through those features are derived. via introducing the equations of movement, a collection of relatives is bought from which the distribution features might be made up our minds. it truly is proven that Boltzmann's equation within the kinetic concept of gases follows as a selected case, and that, in equilibrium stipulations, the speculation supplies effects in step with statistical mechanics. An essential equation for the radial distribution functionality is got that's the normal generalization of 1 acquired through Kirkwood for 'rigid round molecules'. eventually, it really is indicated how the speculation will be utilized to unravel either equilibrium and dynamical difficulties of the liquid country.

Show description

Read Online or Download A general kinetic theory of liquids, PDF

Best thermodynamics and statistical mechanics books

Physics and probability: essays in honor of E.T.Jaynes

The pioneering paintings of Edwin T. Jaynes within the box of statistical physics, quantum optics, and chance conception has had an important and lasting impression at the examine of many actual difficulties, starting from basic theoretical questions via to sensible functions reminiscent of optical snapshot recovery.

State-Selected and State-to-State Ion-Molecule Reaction Dynamics. P. 2. Theory

The purpose of this sequence is to aid the reader receive normal information regarding a large choice of subject matters within the wide box of chemical physics. specialists current analyses of topics of curiosity to stimulate new examine and inspire the expression of person issues of view.

Additional resources for A general kinetic theory of liquids,

Sample text

This is again a special case of the L´evy distribution obtained when we set α = 1. Consider N independent and identically distributed L´evy random variables, with the common distribution denoted by L(x; α). The sum YN is again a L´evy distribution denoted by LN (x; α), obtained from L(x; α) by replacing D by N D. Let us scale YN by N 1/α and consider the random variable YN /N 1/α . Its distribution is L(x; α). Thus N 1/α provides a natural scaling for Levy distributions. We have, LN (x; α) = N −1/α LX x N 1/α ;α .

Metropolis algorithm is widely used in Monte Carlo simulation of models in statistical physics. Here I shall illustrate the technique for sampling from an arbitrary discrete distribution f (i), where the random variable takes discrete integer values i between 1 and N . We call 1, 2, · · · , N as states and denote the set of all states by Ω = {1, 2, · · · N }. 05 0 −5 −4 −3 −2 −1 0 1 2 3 4 5 x Figure 13: Sampling from a Gaussian of mean zero and variance unity employing the technique proposed by Ferna´ ndez and Criado [39].

2 (108) Repeat the above several times. After initial warm up time of say 4N iterations or so, the velocities of the pair of particles you pick up in all subsequent iterations are the desired pairs of independent Gaussian random numbers with mean zero and variance unity. Gaussian of desired mean, say µ and standard deviation, say σ can be obtained 2 by the transformation x = σv + µ. Note that N i=1 vi = N at all stages of iteration. This algorithm is found to be ten times faster than the Box-Muller algorithm.

Download PDF sample

Rated 4.62 of 5 – based on 24 votes