Related papers: Analysis of Boundary Conditions for Crystal Defect…
Detection of crystal structures from particle positions of crystalline assemblies formed in computer simulations is an unsolved problem. The standard protocol, formulated in the reciprocal space, for structure determination from…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such…
Accurate modeling of boundary conditions is crucial in computational physics. The ever increasing use of neural networks as surrogates for physics-related problems calls for an improved understanding of boundary condition treatment, and its…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We…
Most AI-for-Materials research to date has focused on ideal crystals, whereas real-world materials inevitably contain defects that play a critical role in modern functional technologies. The defects break geometric symmetry and increase…
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must…
We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of…
Crucial to gaining control over crystallisation in multicomponent materials or accurately modelling rheological behaviour of magma flows is to understand the mechanisms by which crystal nuclei form. The microscopic nature of such nuclei,…
Numerical methods for the simulation of cavitation processes have been developed for more than 50 years. The rich variety of physical phenomena triggered by the collapse of a bubble has several applications in medicine and environmental…
In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses.…
Employing a recently developed method that is numerically accurate within a model space simulating the real-time dynamics of few-body systems interacting with macroscopic environmental quantum fields, we analyze the full dynamics of an…
Crystal truncation rods calculated in the kinematical approximation are shown to quantitatively agree with the sum of the diffracted waves obtained in the two-beam dynamical calculations for different reflections along the rod. The choice…
This paper studies satisfying temporal logic specifications on stochastic dynamical systems, where the predicates evolve randomly over time. Such randomness may arise from uncertain environment models or external stochastic processes…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…