arXiv subjects

L. N. Davydov

Publications and source records attributed to L. N. Davydov.

8 recordsLinked to original sources

arXiv2026

Sixth order modification of the Cahn-Hilliard equation

We consider the sixth-order convective-viscous Cahn-Hilliard equation, different from the standard fourth-order Cahn-Hilliard equation due to the modified expression for the thermodynamic potential. In such modified thermodynamic potential the coefficient at the square gradient term is order-parameter-dependent. It also contains the square of the Laplacian. This results in a sixth-order differential equation and additional nonlinear terms in the equation. We obtained several exact static- and traveling wave solutions and studied the dependence of solutions on the parameters of the system.

cond-mat.stat-mech↗

arXiv2025

Convective Viscous Cahn-Hilliard/Allen-Cahn Equation with memory effects

The combination of the well-known Cahn-Hilliard and Allen-Cahn equations is used to describe surface processes, such as simultaneous adsorption/desorption and surface diffusion. In the present paper we have considered the convective-viscous Cahn-Hilliard/Allen-Cahn equation complemented by memory effects. Exact solutions are obtained and the combined action of the applied field, dissipation and memory are discussed.

cond-mat.stat-mech↗

arXiv2025

On the Modified Eguchi-Oki-Matsumura System

To describe the simultaneous order-disorder transformation and phase separation Eguchi, Oki and Matsumura [\doi{10.1557/proc-21-589}] introduced the system of two equations: one equation, governing the evolution of a conserved order parameter, and the second equation for the non-conserved order parameter. The key feature of their model is the free energy functional, which contains the square gradient terms of the both order parameters and a fourth power polynomial depending on both order parameters. According to the general Hohenberg-Halperin classification it is the type C model. We show that if the dynamics of the conserved order parameter is governed by the convective-viscous Cahn-Hilliard equation, this system allows exact traveling wave solution.

cond-mat.stat-mech↗

arXiv2025

Cahn-Hilliard model with Schlögl Reactions: interplay of equilibrium and non-equilibrium phase transitions. II. Memory effects

The present work is a continuation of our previous paper [Condens. Matter Phys., 2020, 23, 33602: 1-17]. It is devoted to the modelling of the interplay of equilibrium and non-equilibrium phase transitions. The modelling of equilibrium phase transition is based on the modified Cahn-Hilliard equation. The non-equilibrium phase transition is modeled by the Second Schlögl reaction system. We consider the advancing front, which combines these both transitions. Different from the first article, we consider here the memory effects, i.e., the effects of non-Fickian diffusion. The traveling wave solution is obtained, and its dependence on the model parameters is studied in detail. The relative importance of memory effects for different process regimes is estimated.

cond-mat.mtrl-sci↗

arXiv2025

Higher order potential in the modified convective-viscous Cahn-Hilliard equation

To describe highly heterogeneous systems using the Cahn-Hilliard equation, the standard form of the thermodynamic potential with a constant coefficient in the gradient term and a polynomial of the fourth degree may not be sufficient. The modification of the form of the thermodynamic potential with a polynomial of the sixth degree and the quadratic dependence of the coefficient at the gradient term is considered. Exact solutions in the form of a moving static wave and the conditions of their existence depending on the symmetry of the potential are obtained.

cond-mat.mtrl-sci↗

arXiv2025

Kinetic Model of the Emergence of Autocatalysis

We develop a formal model of the emergence of self-constructing objects (e.g. heteropolymers with autocatalytic capability) in an open system, which don't contain such objects initially. The objects are constructed from subunits (e.g. monomers). Each object is characterized by the difference of self-instructed reproduction and decomposition rate only. This difference, divided by a common dimensional constant, is called ``productivity''. Due to external influence the productivity of each object can randomly change. The system as a whole is subjected to external limitation: the total number of the objects is conserved (e.g., by the controlled influx of monomers). We consider such process as possibly simplest example of self-organization. We obtained exact solutions of our model for several presumed mechanisms of random change of the productivity. We have shown that the probability to find self-constructing objects in the system necessarily increases, even if initially it was equal to zero.

cond-mat.stat-mech↗

arXiv2020

Cahn-Hilliard model with Schlögl reactions: interplay of equilibrium and non-equilibrium phase transitions. I. Travelling wave solutions

The present work is devoted to the modelling which is based on the modified Cahn-Hilliard equation, the interplay of equilibrium and non-equilibrium phase transitions. The non-equilibrium phase transitions are modelled by the Schlögl reactions systems. We consider the advancing fronts which combine these both transitions. The traveling wave solutions are obtained; the conditions of their existence and dependence on the parameters of the models are studied in detail. The possibility of the existance of non-equilibrated phase is discussed.

cond-mat.stat-mech↗

arXiv2020

Convective Viscous Cahn-Hilliard/Allen-Cahn Equation: Exact Solutions

Recently the combination of the well-known Cahn-Hilliard and Allen-Cahn equations was used to describe surface processes, such as simultaneous adsorption/desorption and surface diffusion. In the present paper we have considered the one-dimensional version of the Cahn-Hilliard/Allen-Cahn equation complemented with convective and viscous terms. Exact solutions are obtained and the conditions of their existence as well as the influence of applied field and additional dissipation are discussed.

physics.comp-ph↗