相关论文: Uniqueness and existence of spirals moving by forc…

Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes or fullerenes. Such a geometrical…

We establish the existence of solutions to common noise McKean-Vlasov martingale problems for coefficients with low regularity. Our approach is able to handle the key challenge posed by drift coefficients that are discontinuous with respect…

In this paper, we prove that 2 dimensional transversal small perturbations of d-dimensional Euclidean planes under the skew mean curvature flow lead to global solutions which converge to the unperturbed planes in suitable norms. And we…

Supported nanoscale lead crystallites with a step emerging from a non-centered screw dislocation on the circular top facet were prepared by rapid cooling from just above the melting temperature. STM observations of the top facet show a…

A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…

In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they…

Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…

Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the…

Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…

We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…

We explore the phenomenon of spiral defect chaos in two types of generalized Swift-Hohenberg model equations that include the effects of long-range drift velocity or mean flow. We use spatially-extended domains and integrate the equations…

Dislocations are topological defects known to be crucial in the onset of plasticity and in many properties of crystals. Classical Elasticity still fails to fully explain their dynamics under extreme conditions of high strain gradients and…

In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist…

In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are…

We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…

We study in this work the 2D dynamics of an experimental system of disk-shaped rotors, fluidized by turbulent upflow. Contrary to previous knowledge, our experiments show the same particle chiral geometry can produce flows with different…

The sliding motion of objects is typically governed by their friction with the underlying surface. Compared to translational friction, however, rotational friction has received much less attention. Here, we experimentally and theoretically…

The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their…

Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures,…