In Alicandro et al. (J Mech Phys Solids 92:87-104, 2016) a simple discrete scheme for the motion of screw dislocations toward low energy configurations has been proposed. There, a formal limit of such a scheme, as the lattice spacing and the time step tend to zero, has been described. The limiting dynamics agrees with the maximal dissipation criterion introduced in Cermelli and Gurtin (Arch Ration Mech Anal 148, 1999) and predicts motion along the glide directions of the crystal.

We consider low-energy configurations for the Heitmann-Radin sticky discs functional, in the limit of diverging number of discs. More precisely, we renormalize the Heitmann-Radin potential by subtracting the minimal energy per particle, i.e. the so-called kissing number.

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations.

Trends of soil organic carbon (SOC) are significant indicators for land and soil degradation. Decrease in SOC compromises the efforts to achieve by 2030, a land degradation neutral world, as required by Target 15.3 of the Seventeen Sustainable Development Goals (SDGs) adopted by United Nations in September 2015.

In this paper, we use the Z-control approach to get further insight on the role of awareness in the management of epidemics that, just like Covid-19, display a high rate of overexposure because of the large number of asymptomatic people. We focus on a SEIR model including a overexposure mechanism and consider awareness as a time-dependent variable whose dynamics is not assigned a priori.

This paper aims at building a variational approach to the dynamics of discrete topological singularities in two dimensions, based on I"-convergence. We consider discrete systems, described by scalar functions defined on a square lattice and governed by periodic interaction potentials. Our main motivation comes from XY spin systems, described by the phase parameter, and screw dislocations, described by the displacement function. For these systems, we introduce a discrete notion of vorticity.

The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradient flow structure of the equation and establish differential and algebraic relationships between the energy, the dissipation, and the squared H -1 distance to a kink.

The crack density within a fault's damage zone is thought to vary as seismic rupture is approached, as well as in the postseismic period. Moreover, external stress loads, seasonal or tidal, may also change the crack density in rocks, and all such processes can leave detectable signatures on seismic attenuation. Here we show that attenuation time histories from the San Andreas Fault at Parkfield are affected by seasonal loading cycles, as well as by 1.5-3-year periodic variations of creep rates, consistent with Turner et al.

The aim of this paper is to deepen the application of value at risk in the cyber domain, with particular attention to its potential role in security investment valuation. Cyber risk is a fundamental component of the overall risk faced by any organization. In order to plan the size of security investments and to estimate the consequent risk reduction, managers strongly need to quantify it. Accordingly, they can decide about the possibility of sharing residual risk with a third party, such as an insurance company.

The Internet evolution is one of the greatest innovations of the twentieth century and has changed lives of individuals and business organizations. On the other hand, potential attacks on the information systems and eventual crash may cause heavy losses on data, services and business operation. Executives and security professionals are accepting that it is not a matter of if but a matter of when their organization will be hit by a cyber-attack. As a consequence, cyber risk is a fast-growing area of concern.