Related papers: Two-dimensional grain boundary networks: stochasti…
We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1-D Schr\"odinger map with values on the…
A mesoscopic model of a diblock copolymer is used to study the motion of a grain boundary separating two regions of perfectly ordered lamellar structures under an oscillatory but uniform shear flow. The case considered is a grain boundary…
A novel continuum theory of incoherent interfaces with triple junctions is applied to study three-dimensional coupled grain boundary (GB) motion in polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and…
We consider a family of axisymmetric curves evolving by its mean curvature with driving force in the half space. We impose a boundary condition that the curves are perpendicular to the boundary for $t>0$, however, the initial curve…
The dynamics of dislocations confined to grain boundaries in a striped system are studied using electroconvection in the nematic liquid crystal N4. In electroconvection, a striped pattern of convection rolls forms for sufficiently high…
Inspired by holographic Wilsonian renormalization, we consider coarse graining a quantum system divided between short distance and long distance degrees of freedom, coupled via the Hamiltonian. Observations using purely long distance…
Grain growth is a well-known and complex phenomenon occurring during annealing of all polycrystalline materials. Its numerical modeling is a complex task when anisotropy sources such as grain orientation and grain boundary inclination have…
Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain…
We develop a continuum model for the dynamics of grain boundaries in three dimensions that incorporates the motion and reaction of the constituent dislocations. The continuum model is based on a simple representation of densities of curved…
We present experimental data corresponding to a two dimensional dense granular flow, namely, the gravity-driven discharge of grains from a small opening in a silo. We study the microscopic velocity field with the help of particle tracking…
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…
Interface migration in microstructures is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a continuum model for arbitrarily-curved grain boundaries or heterophase interfaces…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the…
Abnormal grain growth in the presence of second phase particles is investigated with the help of a two-dimensional Monte Carlo simulation. An aggregate of equiaxed grains is considered with constant grain boundary energy and mobility. The…
A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation principle. Gradient estimates and large time asymptotic…
We study, using simulations, the steady-state flow of dry sand driven by gravity in two-dimensions. An investigation of the microscopic grain dynamics reveals that grains remain separated but with a power-law distribution of distances and…
Many physical situations are characterized by interfaces with a non trivial shape so that relevant geometric features, such as interfacial area, curvature or unit normal vector, can be used as main indicators of the topology of the…
The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a…
Grain growth in polycrystals is traditionally considered a capillarity-driven process, where grain boundaries (GBs) migrate toward their centers of curvature (i.e., mean curvature flow) with a velocity proportional to the local curvature…