Related papers: A modified nudged elastic band algorithm with adap…
We study numerically the minimum energy path and energy barriers for dislocation nucleation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Stress relaxation processes from coherent to…
Capturing twin nucleation in full-field crystal plasticity is a long-standing problem in materials science. The challenge resides mainly in the biased regional lattice transformation associated with twin formation in defiance of its…
It has become clear in recent years that the configuration space of the nuclear Skyrme model has, in each topological class, many almost degenerate local energy minima and that the number of such minima grows with the degree (or baryon…
Path optimization methods have been widely used and highly successful for the analysis of chemical reactions. Yet, they can fail to capture intrinsically multidimensional features of potential energy surfaces (PES). We introduce the nudged…
In finite systems, such as nanoparticles and gas-phase molecules, calculations of minimum energy paths (MEPs) connecting initial and final states of transitions as well as searches for saddle points are complicated by the presence of…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
In the last few decades, several novel algorithms have been designed for finding critical points on PES and the minimum energy paths connecting them. This has led to considerably improve our understanding of reaction mechanisms and kinetics…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We study numerically the energetics and atomic mechanisms of misfit dislocation nucleation and stress relaxation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Relaxation processes from…
Adaptive algorithms like AdaGrad and AMSGrad are successful in nonconvex optimization owing to their parameter-agnostic ability -- requiring no a priori knowledge about problem-specific parameters nor tuning of learning rates. However, when…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations in arbitrary space dimension $d\ge2$. We employ…
Characterizing conformational transitions in physical systems remains a fundamental challenge, as traditional sampling methods struggle with the high-dimensional nature of molecular systems and high-energy barriers between stable states.…
We prescribe general rules to predict the existence of edge states and zero-energy flat bands in graphene nanoribbons and graphene edges of arbitrary shape. No calculations are needed. For the so-called {\it{minimal}} edges, the projection…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph $G=(V,E)$ with a positive real weight on each edge. We present two fully dynamic…
Because inorganic solid electrolytes are one of the key components for application to all-solid-state batteries, high-ionic-conductivity materials must be developed. Therefore, we propose a method of efficiently evaluating the activation…
In this paper, a novel adaptive finite element method is proposed to solve the Kohn-Sham equation based on the moving mesh (nonnested mesh) adaptive technique and the augmented subspace method. Different from the classical self-consistent…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
In this work, we propose a multi-scale protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged-Elastic Band (NEB) method driven by a cheap…