We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

Among many types of defects present in crystalline materials, dislocations are the most
influential in determining the deformation process and various physical properties of the …

This work introduces a model for large-strain, geometrically nonlinear elasto-plastic
dynamics in single crystals. The key feature of our model is that the plastic dynamics are …

We consider a system of charged particles moving on the real line driven by electrostatic
interactions. Since we consider charges of both signs, collisions might occur in finite time …

Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static
setting, where the evolution of the plastic distortion is driven exclusively by the motion of …

We study a system of stochastic differential equations with singular drift which describes the
dynamics of signed particles in two dimensions interacting by the Coulomb potential. In …

We consider a large class of interacting particle systems in one dimension described by an
energy whose interaction potential is singular and nonlocal. This class covers Riesz gases …

This paper considers the equilibrium positions of n particles in one dimension. Two forces
act on the particles; a nonlocal repulsive particle-interaction force and an external force …