相关论文: Boundary Dynamics of Sweeping Interface

Diffusion in heterogeneous media partitioned by semi-permeable interfaces has a wide range of applications in the physical and life sciences, including gas permeation in soils, diffusion magnetic resonance imaging (dMRI), drug delivery,…

Imbibition phenomena have been widely used experimentally and theoretically to study the kinetic roughening of interfaces. We critically discuss the existing experiments and some associated theoretical approaches on the scaling properties…

Interfaces in tissues are ubiquitous, both between tissue and environment as well as between populations of different cell types. The propagation of an interface can be driven mechanically. % e.g. by a difference in the respective…

When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…

The movement of a purely elastic interface driven on a disordered energy potential is characterized by a depinning transition: when the pulling force S is larger than some critical value S_1 the system is in a flowing regime and moves at a…

Boundary conditions for the solid-liquid interface of the solidifying pure melt have been derived. In the derivation the model of Gibbs interface is used. The boundary conditions include both the state quantities of bulk phases are taken at…

This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…

We have studied anomalous diffusion of a particle in a random medium in which the passage of the particle may modify the state of the visited sites. The simplicity of the dynamics allows analytic solution. Interesting propagation and…

We study the genetic interfaces between two species of an expanding colony that consists of individual microorganisms that reproduce and undergo diffusion, both at the frontier and in the interior. Within the bulk of the colony, the genetic…

We consider a sharp interface formulation for the multi-phase Mullins-Sekerka flow. The flow is characterized by a network of curves evolving such that the total surface energy of the curves is reduced, while the areas of the enclosed…

The fiber bundle model is essentially an array of elements that break when sufficient load is applied on them. With a local loading mechanism, this can serve as a model for a one-dimensional interface separating the broken and unbroken…

We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…

We study the Mullins' problem that was proposed by Mullins in 1957 and is one of the models of the thermal grooving by surface diffusion. Mathematically, this is the problem of evolving curves in the half space that is governed by the…

We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…

Recent advances in emergent geometry have identified a new class of models that represent spacetime as the graph obtained as the ground state of interacting Ising spins. These models have many desirable features, including stable…

The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…

Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…

On the basis of a previous theoretical approach to the plastic flow of highly refined materials, a physical explanation for diffusion bonding is essayed, which yields closed--form equations relating the bonding progress with time,…

We consider the Helmholtz problem in the context of the evolution of uniform initial distribution of a physical attribute in general porous media subject to a partially absorbing boundary condition. Its spectral property as a reflection of…