Density-dependent interactions and thermodynamic consistency in integral equation theories

State-dependent diffusion: Thermodynamic consistency and its path integral formulation.

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alterna...

Integral Equation Formulation for Scatter Density Problem

Integral equation formulation for the problem of finding a circularly symmetric scatter density (SD) around the mobile is deduced, and the SD is computed assuming that the distribution of angle-of-arrival (AoA) in base station is known. The corresponding integral equation is solved by using the spline collocation method. Thus, instead of fitting a priori selected SD to estimated AoA distributio...

Central and Local Limit Theories in Markov Dependent Random Variables

Sharp limit of the viscous Cahn-Hilliard equation and thermodynamic consistency

Generating functionals, consistency, and uniqueness in the integral equation theory of liquids

We discuss and illustrate through numerical examples the relations between generating functionals, thermodynamic consistency (in particular the virial-free energy one), and uniqueness of the solution, in the integral equation theory of liquids. We propose a new approach for deriving closures automatically satisfying such characteristics. Results from a first exploration of this program are pres...