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Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in literature. An estimation…
The Ornstein-Zernike integral equation method has been employed for a single-component hard sphere fluid in terms of the Percus-Yevick (PY) and Martynov-Sarkisov (MS) approximations. Virial equation of state has been computed in both…
The mean-field theory for lossy nonlinear composites, described by complex and field-dependent dielectric functions, is presented. By using the spectral representation of linear composites with identical microstructure, we develop…
The mechanical properties of many supramolecular materials are often determined by non-covalent interactions that arise from an interplay between chemical composition and molecular microstructural organization. The reversible nature of…
Transport equations for heavy inertial particles in turbulent boundary layers may be derived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure…
A tight mass-temperature relation, M(r)/r ~ T_X, is expected in most cosmological models if clusters of galaxies are homologous and the intracluster gas is in global equilibrium with the dark matter. We here calibrate this relation using 8…
Random first order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random…
We develop the scaled particle theory to describe the thermodynamic properties and orientation ordering of a binary mixture of hard spheres (HS) and hard spherocylinders (HSC) confined in a disordered porous medium. Using this theory the…
Integral equation theory of molecular liquids based on statistical mechanics is quite promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. Beginning with a molecular interaction…
The most recent development of the quark-meson coupling (QMC) model, in which the effect of the mean scalar field in-medium on the hyperfine interaction is also included self-consistently, is used to compute the properties of finite…
We present a lattice model for polymer solutions, explicitly incorporating interactions with a bath of solvent and cosolvent molecules. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the…
We propose a continuum theory to model the Mullins effect, which is ubiquitously observed in polymer composites. In the theory, the softening of the materials during the stretching process is accounted for by considering the delamination of…
We consider the imitative monomer-dimer model on the complete graph introduced in [1]. It was understood that this model is described by the monomer density and has a phase transition along certain critical line. By reverting the model to a…
A simple theory for glassy polymeric mechanical response which accounts for large scale chain relaxation is presented. It captures the crossover from perfect-plastic response to strong strain hardening as the degree of polymerization $N$…
Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded…
In the semi-classical limit, the quantum mechanics of a stationary beam of counter-streaming relativistic electrons and ions is described by a nonlinear system of finite-temperature Thomas-Fermi equations. In the high temperature / low…
This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic…
This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to {\phi}-divergences and a corresponding…
The Poisson-Boltzmann mean-field description of ionic solutions has been successfully used in predicting charge distributions and interactions between charged macromolecules. While the electrostatic model of charged fluids, on which the…
In recent years moment-closure approximations (MA) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in…