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We review and discuss recent advances in the simulation of bulk critical phenomena in model fluids. In particular we emphasise the extensions to finite-size scaling theory needed to cope with the lack of symmetry between coexisting fluid…

The lattice field theory approach to the statistical mechanics of a classical Coulomb gas [R. Coalson and A. Duncan, J. Chem. Phys. 97,5653(1992)] is generalized to include charged polymer chains. Saddle-point analysis is done on the…

Dynamical mean-field approximation with explicit pairing is utilized to study the properties of a two-component Fermi gas at unitarity. The problem is approximated by the lattice Hubbard Hamiltonian, and the continuum limit is realized by…

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…

We have considered a system where the interaction, v(r) = v_IS(r) + xi^2 v_MF(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v_IS(r) we have chosen the…

We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…

Using the approach formulated in the previous papers of the author, a consistent procedure is developed for calculating non-classical asymptotic power terms in the total and the direct correlation functions of a critical fluid. Analyzing…

We argue that recently proposed [Melnyk et al., Fluid Phase Equilibr., 2009, Vol. 279, 1] a criterion to split the pair interaction energy into two parts, one of which is forced to be responsible the most accurate as possible for excluded…

We introduce a non-linear differential flow equation for density matrices that provides a monotonic decrease of the free energy and reaches a fixed point at the Gibbs thermal state. We use this equation to build a variational approach for…

The change from the diffusion-limited to the reaction-limited cooperative behaviour in reaction-diffusion systems is analysed by comparing the universal long-time behaviour of the coagulation-diffusion process on a chain and on the Bethe…

This paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas…

Molecular dynamic simulations for systems with $D=2,3$ Lennard-Jones-like interactions are studied. In the model, we assume that, at long distances, the two-body attractive potential decays as $r^{-\alpha}$. Thermodynamic extensivity…

We develop a theory based on the method of collective variables to study the vapor-liquid equilibrium of asymmetric ionic fluids confined in a disordered porous matrix. The approach allows us to formulate the perturbation theory using an…

We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…

Liquid-vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been…

A semi-empirical equation of state is presented for the liquid rubidium metal. The Lennard-Jones (8.5-4) potential model, which originally has been derived for liquid cesium metal, is found to be suitable for modeling of liquid rubidium…

Recently, the intrinsic sampling method has been developed in order to obtain, from molecular simulations, the intrinsic structure of the liquid-vapor interface that is presupposed in the classical capillary wave theory. Our purpose here is…

We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density non-uniform phases characterized by localized or extended structure are…

We present a systematic study of the thermodynamics of two and three-dimensional generalized Lennard-Jones ($LJ$) systems focusing on the relationship between the range of the potential, the system density and its dimension. We found that…

Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones…