Critical events, entropy, and the grain boundary character distribution

K Barmak, E Eggeling, M Emelianenko, Y Epshteyn… - Physical Review B …, 2011 - APS
Mesoscale experiment and simulation permit harvesting information about both geometric
features and texture in polycrystals. The grain boundary character distribution (GBCD) is an …

Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag

Y Epshteyn, C Liu, M Mizuno - SIAM Journal on Mathematical Analysis, 2021 - SIAM
Most technologically useful materials are polycrystalline microstructures composed of
myriad small monocrystalline grains separated by grain boundaries. The energetics and …

Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag

Y Epshteyn, C Liu, M Mizuno - arXiv preprint arXiv:1910.08022, 2019 - arxiv.org
Many technologically useful materials are polycrystals composed of a myriad of small
monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play …

A stochastic model of grain boundary dynamics: A Fokker–Planck perspective

Y Epshteyn, C Liu, M Mizuno - Mathematical Models and Methods in …, 2022 - World Scientific
Many technologically useful materials are polycrystals composed of small monocrystalline
grains that are separated by grain boundaries of crystallites with different lattice orientations …

[PDF][PDF] An entropy based theory of the grain boundary character distribution

K Barmak, E Eggeling, M Emelianenko… - Discrete Contin. Dyn …, 2011 - math.gmu.edu
Cellular networks are ubiquitous in nature. They exhibit behavior on many different length
and time scales and are generally metastable. Most technologically useful materials are …

Towards a gradient flow for microstructure

P Bardsley, K Barmak, E Eggeling, Y Epshteyn… - Rendiconti Lincei, 2017 - ems.press
A central problem of microstructure is to develop technologies capable of producing an
arrangement, or ordering, of a polycrystalline material, in terms of mesoscopic parameters …

Nonlinear inhomogeneous Fokker–Planck models: Energetic-variational structures and long-time behavior

Y Epshteyn, C Liu, C Liu, M Mizuno - Analysis and Applications, 2022 - World Scientific
Inspired by the modeling of grain growth in polycrystalline materials, we consider a
nonlinear Fokker–Plank model, with inhomogeneous diffusion and with variable mobility …

Grain growth and the effect of different time scales

K Barmak, A Dunca, Y Epshteyn, C Liu… - Research in Mathematics …, 2022 - Springer
Many technologically useful materials are polycrystals composed of a myriad of small
monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a …

Longtime Asymptotic Behavior of Nonlinear Fokker-Planck Type Equations with Periodic Boundary Conditions

Y Epshteyn, C Liu, M Mizuno - arXiv preprint arXiv:2404.05157, 2024 - arxiv.org
In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type
equations in a bounded domain with periodic boundary conditions. The system is motivated …

Predictive theory for the grain boundary character distribution

K Barmak, E Eggeling, M Emelianenko… - Materials Science …, 2012 - Trans Tech Publ
Mesoscale experiment and simulation permit harvesting information about both geometric
featuresand texture in material microstructures. The grain boundary character distribution …