A physical interface can often be modeled as a surface that moves with a velocity determined by the local geometry. Accordingly, there is great interest in algorithms that generate such geometric interface motion. In this paper we unify and generalize two simple algorithms for constant and mean

We have studied numerically the dynamics of a driven elastic interface in a random medium, focusing on the thermal rounding of the depinning transition and on the behavior in the T = 0 pinned phase. Thermal effects are quantitatively more important than expected from simple dimensional estimates

for flexibility in behavior and efficient search and exploited for real-time avatar control. Flexibility is created by identifying plausible transitions between motion segments, and efficient search through the resulting graph structure is obtained through clustering. Three interface techniques are demonstrated

that the proposed method is stable, efficient and scales up well into three dimensional problems. KEY WORDS: interface motion; surface diffusion; level set approach; semi-implicit scheme; localized treatment; hybrid algorithm.

This talk is based on a recent work by Prof. H.-D. Alber and myself, and concerned with a phase field model for the evolution of an interface in an elastically deformable solid, which moves by diffusion of atoms along this interface. This study was started in [1] and continued in [2, 3].

. Fourth order degenerate diffusion equations arise in a `lubrication approximation' of a thin film or neck driven by surface tension. Numerical studies of the lubrication equation (LE) h t + (h n hxxx )x = 0 with various boundary conditions indicate that singularity formation in which h(x(t); t) ! 0 occurs for small enough n with `anomalous' or `second type' scaling inconsistent with usual dimensional analysis. This paper considers locally symmetric or even singularities in the (LE) and in the modified lubrication equation (MLE) h t + h n hxxxx = 0. Both equations have the property that entropy bounds forbid finite time singularities when n is sufficiently large. Power series expansions for local symmetric similarity solutions are proposed for equation (LE) with n ! 1 and (MLE) for all n 2 R. In the latter case, special boundary conditions that force singularity formation are required to produce singularities when n is large. Matching conditions at higher order terms in the expa...

We present a partially implicit hybrid method for simulating the motion of a stiff interface immersed in Stokes flow, in free space or in a rectangular domain with boundary conditions. The implicit time integration is based on the small-scale decomposition approach and does not require

Abstract. We derive hydrodynamic equations describing the evolution of a binary fluid segregated into two regions, each rich in one species, which are separated (on the macroscopic scale) by a sharp interface. Our starting point is a Vlasov-Boltzmann (VB) equation describing the evolution

, we can accurately capture complicated behaviors such as inter-face separation and coalescence. This technique solves a well known problem when treating a semi-implicit system with spectral methods, where spurious interface movements emerge when two interfaces are close to each other. Numerical

interaction. In a subsequent paper (part II), we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits