Related papers: Influence of microscopic parameters on phase behav…
We investigate how microscopic features of interparticle potentials influence macroscopic critical point parameters. Our analytical calculations are based on the cell model for continuous many-particle systems. We explore two types of pair…
The object of this study is a cell model with Curie-Weiss interaction potential. We have already proved the possibility of a mathematically rigorous transition from a continuous system of interacting particles to such a model and made an…
The present manuscript gives a theoretical description of the first-order phase transition in a cell fluid model with a modified Morse potential and additional repulsive interaction. In the framework of the grand canonical ensemble, the…
We study a cell fluid model of a many-particle system with Curie-Weiss-type interaction potential. It is considered as an open system in a fixed volume partitioned into a large number of congruent cubic cells. The interaction potential…
Entropy of the cell fluid model with Curie-Weiss interaction is obtained in analytical form as a function of temperature and chemical potential. A parametric equation is derived representing the entropy as a function of density. Features of…
We propose a method of describing a phase transition in a cell fluid model with pair interaction potential that includes repulsive and attractive parts. An exact representation of the grand partition function of this model is obtained in…
A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$…
We investigate the macroscopic effects of the ingredients that drive the origin of species through sympatric speciation. In our model, sympatric speciation is obtained as we tune up the strength of competition between individuals with…
A microscopic model of the lipid membrane is constructed that provides analytically tractable description of the physical mechanism of the first order liquid-gel phase transition. We demonstrate that liquid-gel phase transition is…
We study the phase behaviour of a fluid composed of particles which interact via a pair potential that is repulsive for large inter-particle distances, is attractive at intermediate distances and is strongly repulsive at short distances…
We investigate the large time behavior of an agent based model describing tumor growth. The microscopic model combines short-range repulsion and cell division. As the number of cells increases exponentially in time, the microscopic model is…
An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie-Weiss-type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…
Thermodynamic response functions, including the isothermal compressibility, the thermal pressure coefficient, and the thermal expansion coefficient, isochoric and isobaric heat capacities are explicitly derived for a many-particle system…
Properties of nanoparticles have been studied within the framework of Ising model and the method of random-field interactions: the average magnetic moment and position of critical points of the magnetic and the concentration phase…
The paper is devoted to the development of a microscopic description of the critical behavior of a cell fluid model with allowance for the contributions from collective variables with nonzero values of the wave vector. The mathematical…
We introduce and test via molecular simulation a simple model for predicting the manner in which interparticle interactions and thermodynamic conditions impact the single-particle free-volume distributions of equilibrium fluids. The model…
We analyze the Glauber dynamics for a bi-populated Curie-Weiss model. We obtain the limiting behavior of the empirical averages in the limit of infinitely many particles. We then characterize the phase space of the model in absence of…
An analog of the continuum Widom-Rowlinson model is introduced and studied. Its two-component version is a gas of point particles of types 0 and 1 placed in $\mathds{R}^d$, in which like particles do not interact and unlike particles…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…