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A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
For atoms and crystals with an ideal symmetry, the optical selection rules for electronic transitions are well covered in physics textbooks. However, in studies of material systems one often encounters systems with a weakly distorted…
We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
Given a smooth convex cone in the Euclidean $(n+1)$-space ($n\geq2$), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If…
We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion bombarded surfaces. We show via theory, simulation, and experiment, that the…
We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…
In this paper, we classify the rotational surfaces with constant skew curvature in $3$-space forms. We also give a variational characterization of the profile curves of these surfaces as critical points of a curvature energy involving the…
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is…
The growth of spiral mounds containing a screw dislocation is compared to the growth of wedding cakes by two-dimensional nucleation. Using phase field simulations and homoepitaxial growth experiments on the Pt(111) surface we show that both…
We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After re-scaling by the characteristic size, the interface becomes progressively more…
In this paper, we propose a variational formulation to study the singular evolution equations that govern the dynamics of surface modulations on crystals below the roughening temperature. The basic idea of the formulation is to expand the…
This paper is the first part of an axis symmetric description of a single crystal tube growth process by micro-pulling-down method.the description concerns the following aspects:the free surfaces equations and the pressure difference across…
We propose a novel approach for optical flow estimation , targeted at large displacements with significant oc-clusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii)…
The hillslope hydrological processes are very important in watershed hydrology research. In this paper we focus on the water flow over the soil surface with vegetation in a hydrographic basin. We introduce a PDE model based on general…
We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data representing smooth, codimension-one surfaces in…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a…