Related papers: Basis functions on the grain boundary space: Theor…
We measure stability of two-dimensional granular mixtures in a rotating drum and relate grain configurations to stability. For our system, the smaller but smoother grains cluster near the center of the drum, while the larger, rougher grains…
Grain-boundary grooving is a general phenomenon occurring in all polycrystalline materials at the intersection between the grain-boundary and the interface or free surface. It has been studied theoretically for some time. Grain-boundary…
Some boundedness properties of function spaces (considered as topological groups) are studied.
Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary…
In this paper, we develop a mean-field model for simulating the microstructure evolution of crystalline materials during static recrystallization. The model considers a population of individual cells (i.e. grains and subgrains) growing in a…
The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…
We describe a molecular dynamics framework for the direct calculation of the short-ranged structural forces underlying grain-boundary premelting and grain-coalescence in solidification. The method is applied in a comparative study of (i) a…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
Interaction of vacancies with grain boundaries (GBs) is involved in many processes occurring in materials, including radiation damage healing, diffusional creep, and solid-state sintering. We analyze a model describing a set of processes…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
A continuum model of the two dimensional low angle grain boundary motion and the dislocation structure evolution on the grain boundaries has been developed in Ref. [48]. The model is based on the motion and reaction of the constituent…
We present a method for obtaining qualitatively accurate grain boundary plane distributions (GBPD) for textured microstructures using a stereological calculation applied to two-dimensional electron backscatter diffraction (EBSD) orientation…
Twist grain boundaries are widely observed in lamellar phases of block copolymers. A mesoscopic model of the copolymer is used to obtain stationary configurations that include a twist grain boundary, and to analyze their stability against…
Polarization arising from aligned dust grains presents a unique opportunity to study magnetic fields in the diffuse interstellar medium and molecular clouds. Polarization from circumstellar regions, accretion disks and comet atmospheres can…
In this work we derive conditions that predict the existence of two-phase periodic-pattern grain boundary structures that are stable against coarsening. While previous research has established that elastic effects can lead to phase pattern…
We show that grains can be efficiently aligned by interacting with a subsonic gaseous flow. The alignment arises from grains having irregularities that scatter atoms with different efficiency in the right and left directions. The grains…
We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such…
Grain growth in polycrystals is often simulated using orientation-field models, which employ a field to represent the local orientation of the crystal lattice. These models can be challenging to represent a realistic misorientation…