Liouville equation

Liouville equation

[′lyü‚vēl i‚kwā·zhən]
(statistical mechanics)
An equation which states that the density of points representing an ensemble of systems in phase space which are in the neighborhood of some given system does not change with time.
Mentioned in ?
References in periodicals archive ?
15) The preliminary study was based on plasma kinetics and made use of a quasi-linear approximation to the collisional Liouville equation to derive the distribution function, F (r, v), of brain activities in the neural phase space (i.
Saarloos[3] shown that the density function (mass, momentum and energy fields) obeys a Liouville equation for hydrodynamics ideal fluid.
Bikulciene, "The solitary solution of the Liouville equation produced by the Exp-function method holds not for all initial conditions", Computers and Mathematics with Applications, vol.
Tarasov in [36] based on the Liouville equation obtained the fractional analogues of the classical kinetic and transport equations.
Sturm Liouville equation has been extensively studied in both continuous and discrete cases [7, 20, 29, 33, 36].
Furthermore, the eikonal equation and the approximation of the Liouville equation based on GO have been employed for simulating the high frequency wave propagation.
For [epsilon] = 0 this is usually called the Liouville equation.
One of the retrieved results is the Liouville Equation, an equation Books24x7 has made "live.
Let us define a phase space density f(x, p; s) which evolves according to the Liouville equation
NAGAR, On the solution of the Liouville equation over a rectangle, J.
Generalized Liouville Equation and Approximate Orthogonal Decomposition Methods
This monograph is presented with the twin goals of providing a modern survey of the basic properties of the Sturm- Liouville equation and to introduce some aspects of recent research on Sturm-Liouville problems.