Related papers: Analysis of Boundary Conditions for Crystal Defect…
The problem of melting a crystal dendrite is modelled as a quasi-steady Stefan problem. By employing the Baiocchi transform, asymptotic results are derived in the limit that the crystal melts completely, extending previous results that hold…
The problem of finding boundary conditions for fastening of a ring membrane, which are inaccessible for direct observation from the natural frequencies of its flexural oscillations, is considered. Two theorems on the uniqueness of this…
In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in classical numerical methods, such as finite difference method…
Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention. In this paper, we investigate the relationship between two-dimensional defects and…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
The possibility of creating crystal bilayers twisted with respect to each other has led to the discovery of a wide range of novel electron correlated phenomena whose full understanding is still under debate. Here we propose and analyze a…
Using molecular dynamics calculations and the Voronoi tessellation, we study the evolution of the local structure of a soft-sphere glass versus temperature starting from the liquid phase at different quenching rates. This study is done for…
We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
We present a new method for modeling disordered solid solutions, based on the virtual crystal approximation (VCA). The VCA is a tractable way of studying configurationally disordered systems; traditionally, the potentials which represent…
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann…
Bayesian parameter estimation provides a systematic approach to compare heavy ion collision models with measurements, leading to constraints on the properties of nuclear matter with proper accounting of experimental and theoretical…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
Intergranular fracture in polycrystals is often simulated by finite elements coupled to a cohesive-zone model for the interfaces, requiring cohesive laws for grain boundaries as a function of their geometry. We discuss three challenges in…
We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement…
We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive…
The boundary element method (BEM) is an efficient numerical method for simulating harmonic wave propagation. It uses boundary integral formulations of the Helmholtz equation at the interfaces of piecewise homogeneous domains. The…
The modeling of finite-extent semiconductor nanostructures that are embedded in a host material requires the numerical treatment of the boundary in a finite simulation domain. For the study of a self-assembled InAs dot embedded in GaAs,…
Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no…
Engineering simulations using boundary-value partial differential equations often implicitly assume that the uncertainty in the location of the boundary has a negligible impact on the output of the simulation. In this work, we develop a…