Related papers: Elimination of surface diffusion in the non-diagon…
Multiphase flows are commonly found in chemical engineering processes such as distillation columns, bubble columns, fluidized beds and heat exchangers. The physical boundaries of domains in numerical simulations of multiphase flows are…
We show global well-posedness and exponential stability of equilibria for a general class of nonlinear dissipative bulk-interface systems. They correspond to thermodynamically consistent gradient structure models of bulk-interface…
We study the surface phase diagram of the three-dimensional kinetic Ising model below the equilibrium critical point subjected to a periodically oscillating magnetic field. Changing the surface interaction strength as well as the period of…
A mean-field density-functional model for three-phase equilibria in fluids (or other soft condensed matter) with two spatially varying densities is analyzed analytically and numerically. The interfacial tension between any two out of three…
We study a diffusion model of phase field type, consisting of a system of two partial differential equations encoding the balances of microforces and microenergy; the two unknowns are the order parameter and the chemical potential. By a…
The paper considers a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids. The model allows for a non-linear dependence of fluid density on the phase-field order parameter. Driven by…
This paper provides a mathematical approach to study metasurfaces in non flat geometries. Analytical conditions between the curvature of the surface and the set of refracted directions are introduced to guarantee the existence of phase…
The classical phase-field modeling approaches for multiphase problems represent each phase using a regularized characteristic function, which necessarily introduces a simplex constraint for the phase-field variables. Additionally, the…
We present a phase field model for isothermal transformations of two component alloys that includes Onsager kinetic cross coupling between the non-conserved phase field and the conserved concentration field. We also provide the reduction of…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
A numerical framework is developed to model contrail formation in the near-field exhaust of aircraft engines, resolving non-equilibrium phase transitions in compressible, multi-component, non-ideal fluid flows. The approach combines…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
The conversion of phase variations in an optical wavefield into intensity information is of fundamental importance for optical imaging technology including microscopy of biological cells. While conventional approaches to phase-imaging…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
In recent prior work, the author derived interfacial mass and heat flux conditions for phase-change processes. The mass flux condition is identical to the Schrage equation, but the additional heat flux expression enables one to couple the…
This paper tackles the approximation of surface diffusion flow using a Cahn--Hilliard-type model. We introduce and analyze a new second order variational phase field model which associates the classical Cahn--Hilliard energy with two…
A phase-field approach describing the dynamics of a strained solid in contact with its melt is developed. By rigorous asymptotic analysis we show that the sharp-interface limit of this model recovers the continuum model equations for the…
In earlier work \cite{bedeaux/vdW/I, bedeaux/vdW/II, bedeaux/vdW/III} a systematic extension of the van der Waals square gradient model to non-equilibrium one-component systems was given. In this work the focus was on heat and mass transfer…
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 nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…