Related papers: New methods derived from energy minimization probl…
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as…
The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very…
Simulations of nano- to micro-meter scale fluidic systems under thermal gradients require consistent mesoscopic methods accounting for both hydrodynamic interactions and proper transport of energy. One such method is dissipative particle…
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…
Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…
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…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
The fundamental interactions between an edge dislocation and a random solid solution are studied by analyzing dislocation line roughness profiles obtained from molecular dynamics simulations of Fe0.70Ni0.11 Cr0.19 over a range of stresses…
We discuss a dynamical systems perspective on discrete optimization. Departing from the fact that many combinatorial optimization problems can be reformulated as finding low energy spin configurations in corresponding Ising models, we…
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical…
The speed-stress relation for gliding edge dislocations was experimentally measured for the first time. The experimental system used, a two-dimensional plasma crystal, allowed observation of individual dislocations at the "atomistic" level…
We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of…
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain…
In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the…
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…
Ordinary differential equations (ODEs) are widely used to model biological, (bio-)chemical and technical processes. The parameters of these ODEs are often estimated from experimental data using ODE-constrained optimisation. This article…
This paper investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate 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…
Driven by the growing interest in numerical simulations of dislocation-interface interactions in general crystalline materials with elastic anisotropy, we develop algorithms for the integration of interface tractions needed to couple…
Continuum models of dislocation plasticity require constitutive closure assumptions, e.g., by relating details of the dislocation microstructure to energy densities. Currently, there is no systematic way for deriving or extracting such…