Related papers: The equilibrium measure for a nonlocal dislocation…

We consider a system of parallel straight edge dislocations and we analyse its asymptotic behaviour in the limit of many dislocations. The dislocations are represented by points in a plane, and they are arranged in vertical walls; each wall…

The minimal requirement for cosmography - a nondynamical description of the universe - is a prescription for calculating null geodesics, and timelike geodesics as a function of their proper time. In this paper, we consider the most general…

Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…

We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…

We discuss the local minimality of certain configurations for a nonlocal isoperimetric problem used to model microphase separation in diblock copolymer melts. We show that critical configurations with positive second variation are local…

We establish lower semi-continuity and strict convexity of the energy functionals for a large class of vector equilibrium problems in logarithmic potential theory. This in particular implies the existence and uniqueness of a minimizer for…

We consider the geometry of the space of Borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the Wasserstein distance to concave, nonlinear mobilities. We investigate the energy landscape of…

We define the coarse-grained entropy of a `normal' surface $\sigma$, i.e., a surface that is neither trapped nor antitrapped. Following Engelhardt and Wall, the entropy is defined in terms of the area of an auxiliary extremal surface. This…

We show that it is possible to obtain credible static anisotropic spherically symmetric matter configurations starting from known density profiles and satisfying a nonlocal equation of state. These particular types of equation of state…

Detecting and quantifying non-equilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a non-invasive approach of measuring…

We investigate the depinning transition occurring in dislocation assemblies. In particular, we consider the cases of regularly spaced pileups and low angle grain boundaries interacting with a disordered stress landscape provided by solute…

This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…

This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…

We develop a non-singular theory of three-dimensional dislocation loops in a particular version of Mindlin's anisotropic gradient elasticity with up to six length scale parameters. The theory is systematically developed as a generalization…

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that…

In this paper we look for minimizers of the energy functional for isotropic compressible elasticity taking into consideration the effect of a gravitational field induced by the body itself. We consider the displacement problem in which the…

We consider a class of nonconvex energy functionals that lies in the framework of the peridynamics model of continuum mechanics. The energy densities are functions of a nonlocal strain that describes deformation based on pairwise…

Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the…

We consider nonholonomic systems with nonlinear restrictions with respect to the velocities. The mathematical problem is formulated by means of the Voronec equations extended to the nonlinear case. The main point of the paper is the balance…

We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This problem is related by a generalized coarea formula to a…