Related papers: Velocity selection problem in the presence of the …
We discuss a simple model of the melting kinetics along the solid-solid interface in eutectic and peritectic systems. The process is controlled by the diffusion inside the liquid phase and the existence of a triple junction is crucial for…
We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial…
We prove a local existence result for a PDE system that describes curvature motion of networks with a dynamic boundary condition known as triple junction drag. This model arises in the study of grain boundary evolution in polycrystalline…
Triple junctions, line defects formed by the intersection of different grain boundaries, exist within all polycrystalline materials. While it has long been recognized that triple junctions could play an important role in microstructural…
Grain boundary networks and their evolution are strongly influenced by triple junctions. The defect nature of these line defects significantly affects the properties of the network, but they have not been fully characterized to date. Here,…
Grain Boundaries (GB) whose energy is larger than twice the energy of the solid/liquid interface exhibit the premelting phenomenon, for which an atomically thin liquid layer develops at temperatures slightly below the bulk melting…
Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where…
We discuss melting of alloys along grain boundaries as a free boundary problem for two moving solid-liquid interfaces. One of them is the melting front and the other is the solidification front. The presence of the triple junction plays an…
We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution.
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…
Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivities of grain boundaries play a crucial role in…
Rate of grain growth, which aides in achieving desired properties in polycrystalline materials, is conventionally estimated by measuring the size of grains and tracking its change in micrographs reflecting the temporal evolution. Techniques…
Coupled grain boundary (GB) motion has been studied in a two-dimensional tricrystal where a cylindrical grain is embedded at the center of the planar GB of a large bicrystal. Kinetic relations for GB dynamics, grain orientations, and…
We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether…
We study mechanical problems with multiple solutions and introduce a thermodynamic framework to formulate two different selection criteria in terms of macroscopic energy productions and fluxes. Studying simple examples for lattice motion we…
This study investigates the melting process of a three-phase Stefan problem in a semi-infinite material, imposing a convective boundary condition at the fixed face. By employing a similarity-type transformation, the problem is reduced to a…
We study some optimal control problems on networks with junctions, approximate the junctions by a switching rule of delay-relay type and study the passage to the limit when $\varepsilon$, the parameter of the approximation, goes to zero.…
We investigate a model which couples diffusional melting and nanoscale structural forces via a combined nano-mesoscale description. Specifically, we obtain analytic and numerical solutions for melting processes at grain boundaries…
Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case…