Related papers: Onsager approach to 1D solidification problem and …
We propose a systematic formulation of the migration behaviors of a vesicle in a Poiseuille flow based on Onsager's variational principle. Our model is described by a combination of the phase field theory for the vesicle and the…
The problem of the flow trough a porous media is formulated in terms of a pressure equation, based on arguments of volume conservation which state the mechanical equilibrium between the solid and the fluid phases. In the resulting governing…
The homogeneous state of a binary mixture of smooth inelastic hard disks or spheres is analyzed. The mixture is driven by a thermostat composed by two terms: a stochastic force and a drag force proportional to the particle velocity. The…
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
In the paper we apply asymptotic technique based on the method of stationary phase and obtain the approximate analytical description of thermal motions caused by a source on an isotopic defect of an arbitrary mass in a 1D harmonic crystal.…
Thin films of binary mixtures that interact through isotropic forces and directionally specific "hydrogen bonding" are considered through Monte Carlo simulations. We show, in good agreement with experiment, that the single phase of these…
The structure of polymers at solid interfaces evolves over time, but the corresponding changes in their rheological properties remain poorly understood. Here, using a home-built quartz tuning fork atomic force microscope-based…
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the…
In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is…
By the adoption of a quaternion orientational order parameter to describe solidification, the topological origins of the thermal transport properties of crystalline and non-crystalline solid states are considered herein. Global…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…
Based on the phonon Boltzmann transport equation under the relaxation time approximation, analytical expressions for the temperature profiles of both steady state and modulated heat conduction inside a thin film deposited on a substrate are…
The second gradient model of poromechanics, introduced in Part I, is here linearized in the neighborhood of a prestressed reference configuration to be applied to the one-dimensional consolidation problem originally considered by Terzaghi…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
Recent experiments and simulations have demonstrated that particle-covered interfaces can exist in stable non-spherical shapes as a result of the steric jamming of the interfacially trapped particles, which confers the interface with…
We consider a one-dimensional diffusion process with coefficients that are periodic outside of a finite 'interface region'. The question investigated in this article is the limiting long time / large scale behaviour of such a process under…
The effect of a localized drive on the steady state of an interface separating two phases in coexistence is studied. This is done using a spin conserving kinetic Ising model on a two dimensional lattice with cylindrical boundary conditions,…
Governing equations for evolution of concentration and temperature in three-component systems were derived in the framework of classical irreversible thermodynamics using Onsager variational principle and were presented for…