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A random polymer model is a one-dimensional Jacobi matrix randomly composed of two finite building blocks. If the two associated transfer matrices commute, the corresponding energy is called critical. Such critical energies appear in…

We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…

The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…

A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the…

The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…

The focus is on discrete defects that can be modeled by continuum mechanics, but where the discreteness of the carriers of plastic deformation plays a significant role. The formulations are restricted to small deformation kinematics and the…

A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow…

Distributed optimization for resource allocation problems is investigated and a sub-optimal continuous-time algorithm is proposed. Our algorithm has lower order dynamics than others to reduce burdens of computation and communication, and is…

In this paper we study the relaxation process of Peierls-Nabarro dislocation model, which is a gradient flow with singular nonlocal energy and double well potential describing how the materials relax to its equilibrium with the presence of…

We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…

This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight,…

A phase field model is presented to investigate dislocation formation (coherency loss) and workhardening in two-phase binary alloys. In our model the elastic energy density is a periodic function of the shear and tetragonal strains, which…

We show that the numerical results contained in a recent paper are affected by a non optimal implementation of the methods which have been used to obtain these results. A careful analysis done using the Rayleigh-Ritz method provides a…

Under an applied external load the global load-sharing fiber bundle model, with individual fiber strength thresholds sampled randomly from a probability distribution, will relax to an equilibrium state, or to complete bundle breakdown. The…

In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is determined by the renormalised energy. The interaction of one…

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the…

A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…

In this article, we study scaling laws for singularly perturbed two-well energies with prescribed Dirichlet boundary data in settings where the wells and/or the boundary data are incompatible. Our main focus is the geometrically linear…

We constructed a model that evolved from a non-equilibrium state to an equilibrium state. The model only needs two basic coefficients, including self-similar coefficients and non-equilibrium coefficients. The coefficients of the model can…

Twin growth in hexagonal close-packed zirconium is investigated at the atomic scale by modeling the various disconnections that can exist on twin boundaries. Thanks to a coupling with elasticity theory, core energies are extracted from…