Related papers: A diffuse interface model for the analysis of prop…
Atomic diffusion affects the properties of various engineering materials, which predominantly occur in the polycrystalline state. A rigorous description of polycrystalline diffusion must therefore account for crystallographic defects,…
We provide new concepts for understanding transport phenomena in flows of granular materials by using a non-Fickian macroscopic model of axial diffusion of a granular material in a finite cylindrical tumbler. The model accounts for…
A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially…
Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
Diffuse interface models are widely used to describe evolution of multi-phase systems of different nature. Dispersed "inclusions", described by the phase field distribution, are usually three dimensional objects. When describing elastic…
A non-equilibrium theory of isothermal and diffusionless evolution of incoherent interfaces within a plastically deforming solid is developed. The irreversible dynamics of the interface are driven by its normal motion, incoherency (slip and…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
We construct a simple phenomenological diffuse-interface model for composition-induced nanopatterning during ion sputtering of alloys. In simulations, this model reproduces without difficulties the high-aspect ratio structures and tilted…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…
Thermally excited capillary waves at fluid interfaces in binary liquid mixtures exhibit simultaneously both density and composition fluctuations. Based on a density functional theory for inhomogeneous binary liquid mixtures we derive an…
An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…
A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing from fluid content…
A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition…
Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the…
We derive the complete form of the van der Waals dispersion interaction between two infinitely long anisotropic semiconducting/insulating thin cylinders at all separations. The derivation is based on the general theory of dispersion…
Interfaces between demixed fluid phases of binary mixtures of hard platelets are investigated using density-functional theory. The corresponding excess free energy functional is calculated within a fundamental measure theory adapted to the…
In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…
Turbulent emulsions are ubiquitous in chemical engineering, food processing, pharmaceuticals, and other fields. However, our experimental understanding of this area remains limited due to the multi-scale nature of turbulent flow and the…