Related papers: A Three-Dimensional Continuum Simulation Method fo…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
Development of algorithms and growth of computational resources in the past decades have enabled simulations of sediment transport processes with unprecedented fidelities. The Computational Fluid Dynamics--Discrete Element Method (CFD--DEM)…
The dislocation core is an important region as it controls many important properties of materials. Elasticity breaks down in the core and the stress, force, and energy diverge at the dislocation line. We consider three commonest methods…
This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elasto-plastic effects on…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were…
Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…
We present a new framework to quantify the effect of hydrogen on dislocations using large scale three-dimensional (3D) discrete dislocation dynamics (DDD) simulations. In this model, the first order elastic interaction energy associated…
A three-dimensional continuum dislocation theory for single crystals containing curved dislocations is proposed. A set of governing equations and boundary conditions is derived for the true placement, plastic slips, and loop functions in…
We introduce a simulation strategy to consistently couple continuum biomembrane dynamics to the motion of discrete biological macromolecules residing within or on the membrane. The methodology is used to study the diffusion of integral…
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…
We present a higher-order boundary condition for atomistic simulations of dislocations that address the slow convergence of standard supercell methods. The method is based on a multipole expansion of the equilibrium displacement, combining…
In this paper, we study a constrained minimization problem that arise from materials science to determine the dislocation (line defect) structure of grain boundaries. The problems aims to minimize the energy of the grain boundary with…
Granular media surround us, comprising everything from the ground we walk on to the foods we eat. Owing to their ubiquity our ability to understand and predict the mechanical evolution of grains is not only of key scientific importance, but…
We develop a fully coupled theoretical description of dislocation dynamics on deformable crystalline surfaces, using continuum modeling and the amplitude-phase-field crystal (APFC) framework extended to curved geometries. We derive a…
A computational approach has been developed for the analysis of the properties of 3D dislocation substructures generated by the vector density continuum dislocation dynamics (CDD), within the framework of crystal plasticity. In the CDD…
The dynamical mechanisms underlying the grain evolution and growth are of fundamental importance in controlling the structural properties of large-scale polycrystalline materials, but the effects of lattice ordering and distinct atomic…
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…