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Microscale energy transport processes are crucial in microelectronics, energy harvesting devices, and emerging quantum materials. To study these processes, methods that can probe transport with conveniently tunable length scales are highly…
We present a graph-based numerical method for solving hyperbolic systems of conservation laws using discontinuous finite elements. This work fills important gaps in the theory as well as practice of graph-based schemes. In particular, four…
The level set method is often used to capture interface behavior in two or three dimensions. In this paper, we present a combination of local discontinuous Galerkin (LDG) method and level set method for simulating Willmore flow. The LDG…
GB migration plays a central role in microstructural evolution. Many experiments and simulations have been conducted to clarify the relationships between GB velocity and various parameters to tailor GB networks. However, the complexity of…
Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…
In order to control the grain structure of multi-crystalline (mc) silicon during directional solidification, the development process of grain boundaries (GBs) with respect to the temperature gradient should be understood. A phase-field…
Polycrystalline thin films can be unstable with respect to island formation (agglomeration) through grooving where grain boundaries intersect the free surface and/or thin film-substrate interface. We develop a phase-field model to study the…
Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in…
Nanoindentation is a convenient method to investigate the mechanical properties of materials on small scales by utilizing low loads and small indentation depths. However, the effect of grain boundaries (GB) on the nanoindentation response…
Grain boundaries (GBs) profoundly influence the properties and performance of materials, emphasizing the importance of understanding the GB structure and phase behavior. As recent computational studies have demonstrated the existence of…
Grain boundary migration is driven by the boundary's curvature and external loads such as temperature and stress. In intercalation electrodes an additional driving force results from Li-diffusion. That is, Li-intercalation induces volume…
We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…
We present a solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. It is achieved using a cavity or message passing approach, which allows one to…
Low-angle grain boundaries (LAGBs) are often regarded as penetrable interfaces to dislocation motion, yet recent studies suggest they can also act as strong barriers. The origin of this duality remains debated, particularly regarding the…
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…
This paper proposes a Cartesian grid-based boundary integral method for efficiently and stably solving two representative moving interface problems, the Hele-Shaw flow and the Stefan problem. Elliptic and parabolic partial differential…
The grain boundary (GB) energy has a profound influence on the grain growth and properties of polycrystalline metals. Here, we show that the energy of a GB, normalized by the bulk cohesive energy, can be described purely by four geometric…
We study segregation and stratification of mixtures of grains differing in size, shape and material properties poured in two-dimensional silos using a microscopic lattice model for surface flows of grains. The model incorporates the…
The understanding of cross-field transport is crucial in order to optimize the properties of magnetic confinement in modern fusion devices. In this work, a two-dimensional, simplified model is used to study the turbulent dynamics in the…
Grain boundary (GB) migration governs microstructure evolution and can mediate plastic deformation through sliding or shear coupling. Numerous experimental and numerical studies have reported a wide range of behaviors associated with…