Related papers: Grain boundary dynamics in stripe phases of non po…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
In an external electric field, a system of conductive grains embedded in a dielectric matrix becomes unstable and relaxes towards a conductive state. We describe and discuss the elementary acts of this relaxation. When the grains packing…
We investigate the formation of stripe patterns that appear on the surface of a dry granular system as the container is deformed very slowly. In an experimental study using nearly mono-disperse glass beads, we found that many faults develop…
In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems,…
The grain boundary network of nanocrystalline Cu foils was modified by the systematic application of cyclic loadings and elevated temperatures having a range of magnitudes. Most broadly, the changes to the boundary network were directly…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
We investigate the energetic ground states of a model two-phase system with 1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous formation of two kinds of periodic domain structure. A striped domain structure is…
Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…
Topological defects in graphene, dislocations and grain boundaries, are still not well understood despites the considerable number of experimental observations. We introduce a general approach for constructing dislocations in graphene…
We study the Grain Boundary (GB) migration based on the underlying disconnection structure and mechanism. Disconnections are line defects that lie solely within a GB and are characterized by both a Burgers vector and a step height, as set…
Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…
Based on the formula for the number density of vacancies in a solid under the stress or tension, the model of grain boundary diffusion in crystalline solids is developed. We obtain the activation energy of grain boundary diffusion…
We analyze a two-dimensional phase field model designed to describe the dynamics of crystalline grains. The phenomenological free energy is a functional of two order parameters. The first one reflects the orientational order while the…
Phase separation can drive spatial organization of multicomponent mixtures. For instance in developing animal embryos, effective phase separation descriptions have been used to account for the spatial organization of different tissue types.…
The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon…