Related papers: Nonlocal-to-local limit in linearized viscoelastic…
Nonlocal magic quantifies the irreducible nonstabilizerness of a bipartite quantum state after optimizing over local basis changes. We study nonlocal magic for pure fermionic Gaussian states, and derive a simple closed-form entanglement…
In this work we study the homogenization for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening and general non-associative monotone plastic flows. The constitutive equations in the models we study are…
Nonlocal quasistatic fracture evolution for interacting cracks is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationarity and fixed point methods. It is proved that the fracture…
Motivated by Pan-Yang [PY] and Ma-Cheng [MC], we study a general linear nonlocal curvature flow for convex closed plane curves and discuss the short time existence and asymptotic convergence behavior of the flow. Due to the linear structure…
In this paper we study the $L^2$-gradient flow of the penalized elastic energy on networks of $q$-curves in $\R^{n}$ for $q \geq 3$. Each curve is fixed at one end-point and at the other is joint to the other curves at a movable…
In this paper, we study the solvability of a Cauchy- Dirichlet problem for nonlinear parabolic equation with non standard growths and nonlocal terms. We show the existence of weak solutions of the considered problem under more general…
We consider the nonlocal formulation of continuum mechanics described by peridynamics. We provide a link between peridynamic evolution and brittle fracture evolution for a broad class of peridynamic potentials associated with unstable…
A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in…
In this paper, we quantify the asymptotic limit of collective behavior kinetic equations arising in mathematical biology modeled by Vlasov-type equations with nonlocal interaction forces and alignment. More precisely, we investigate the…
Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the spirit of this novel concept,…
We study the curl-div-system with variable coefficients and a nonlocal homogenisation problem associated with it. Using, in part refining, techniques from nonlocal $H$-convergence for closed Hilbert complexes, we define the appropriate…
Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…
We introduce a nonlocal extension of the Kim-Kim-Suzuki (KKS) phase-field corrosion model aimed at bridging local and nonlocal corrosion modeling approaches, such as phase-field and peridynamic frameworks. In this formulation, classical…
We consider a variational problem modeling transition between flat and wrinkled region in a thin elastic sheet, and identify the $\Gamma$-limit as the sheet thickness goes to 0, thus extending the previous work of the first author [Bella,…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
In this paper we consider optimal control problems in the nonlocal function space framework of Bellido-2023, where there are two different parameters: a horizon parameter $\delta > 0$; and a fractional parameter $s \in (0, 1)$. The…
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…
We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…