Related papers: Grain Boundary Grooving in a Bicrystal with Passiv…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
The microstructural evolution at and near pre-existing grain boundaries (GBs) and dislocations in materials under high radiation doses is still poorly understood. In this work, we use the creation relaxation algorithm (CRA) developed for…
Nanostructured materials consist of crystalline and grain boundary components. In the simplest case, both components are chemically identical. Here, we present the results of a study of a system consisting of a crystalline component built…
We prove boundary higher integrability for the (spatial) gradient of \emph{very weak} solutions of quasilinear parabolic equations of the form $$u_t - \text{div}\,\mathcal{A}(x,t, \nabla u)=0 \quad \text{on} \ \Omega \times \mathbb{R},$$…
The possible boundary conditions consistent with the integrability of the classical sine-Gordon equation are studied. A boundary value problem on the half-line $x\leq 0$ with local boundary condition at the origin is considered. The most…
We investigate a moving boundary problem for a Brownian particle on the semi-infinite line in which the boundary moves by a distance proportional to the time between successive collisions of the particle and the boundary. Phenomenologically…
This work investigates how grain boundaries (GBs) modify magnetic exchange interactions in bcc iron, with particular focus on the effect of phosphorus segregation. Using density-functional theory combined with the…
We describe an optical scattering study of grain boundary premelting in water ice. Ubiquitous long ranged attractive polarization forces act to suppress grain boundary melting whereas repulsive forces originating in screened Coulomb…
In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…
A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived…
Segregation to grain boundaries affects their cohesion, corrosion and embrittlement and plays a critical role in heterogeneous nucleation. In order to quantitatively study segregation and phase separation at grain boundaries, we derive a…
In this paper, we present a continuum model for the dynamics of low angle grain boundaries in two dimensions based on the motion of constituent dislocations of the grain boundaries. The continuum model consists of an equation for the motion…
X-ray nanodiffraction is applied to study the formation and correlation of domain boundaries in mesocrystalline superlattices of PbS nanocrystals with face-centered cubic structure. Each domain of the superlattice can be described with one…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
We present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an…
This paper aims at proving asymptotic stability of the radial stationary solution of a free boundary problem modeling the growth of nonnecrotic tumors with fluid-like tissues. In a previous paper we considered the case where the nutrient…
In this paper, we formulate a continuum theory of solidification within the context of finite-strain coupled thermoelasticity. We aim to fill a gap in the existing literature, as the existing studies on solidification typically decouple the…
Grain boundary diffusion in severely deformed Al-based AA5024 alloy is investigated. Different states are prepared by combination of equal channel angular processing and heat treatments, with the radioisotope $^{57}$Co being employed as a…
Reflection nebulae--dense cores--illuminated by surrounding stars offer a unique opportunity to directly test our quantitative model of grain alignment based on radiative torques (RATs) and to explore new effects arising from additional…
When a mixture of two kinds of grains differing in size and shape is poured in a vertical two-dimensional cell, the mixture spontaneously stratifies in alternating layers of small and large grains, whenever the large grains are more faceted…