相关论文: A Non-Local Formulation of the Peierls Dislocation…
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted $H^1$-semi norm to model the local part, while two different weighted $H^s$-semi norms,…
We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-D real Ginzburg-Landau equation. While for local coupling the fronts are always…
Dense granular and suspension flows under inhomogeneous shear exhibit persistent particle motion in regions where the local yield criterion is subcritical, an apparent breakdown of locality that has motivated the development of a generation…
Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use…
This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for dielectric inhomogeneity. Solving the steady-state modified PNP…
A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing known examples studied in literature. The main novelty of the work consists…
Dislocation core properties of tin (\beta-Sn) were investigated using the semi-discrete variational Peierls-Nabarro model (SVPN). The SVPN model, which connects the continuum elasticity treatment of the long-range strain field around a…
Dissipative models for the quasi-static and dynamic response due to slip in an elastic body containing a single slip plane of vanishing thickness are developed. Discrete dislocations with continuously distributed cores can glide on this…
Large-scale atomistic calculations, using empirical potentials for modeling semiconductors, have been performed on a stressed system with linear surface defects like steps. Although the elastic limits of systems with surface defects remain…
In many environmental applications involving spatially-referenced data, limitations on the number and locations of observations motivate the need for practical and efficient models for spatial interpolation, or kriging. A key component of…
Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
The friction of a nanosized sphere in commensurate contact with a flat substrate is investigated by performing molecular dynamics simulations. Particular focus is on the distribution of shear stress within the contact region. It is noticed…
Constitutive and closure models play important roles in computational mechanics and computational physics in general. Classical constitutive models for solid and fluid materials are typically local, algebraic equations or flow rules…
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-weighted H\"older/Besov-type spaces and…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. This paper studies the continuous and discrete formulations of three existing approaches for the…
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…
Relaxor ferroelectrics have been a focus of intense attention due to their anomalous dielectric characteristics, diffuse phase transitions, and strong piezoelectricity. Understanding the structure and dynamics of relaxors has been one of…