The COVID-19 pandemic triggered a global research effort to define and assess timely and effective containment policies. Understanding the role that specific venues play in the dynamics of epidemic spread is critical to guide the implementation of fine-grained non-pharmaceutical interventions (NPIs). In this paper, we present a new model of context-dependent interactions that integrates information about the surrounding territory and the social fabric.

We consider here a cell-centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity, a highly nonlinear function, by arithmetic, upstream and harmonic means. The nonlinearities in the equation can lead to changes in soil conductivity over several orders of magnitude and discretizations with respect to space variables often produce stiff systems of differential equations.

Defining accurate and flexible models for real-world networks of human beings is instrumental to understand the observed properties of phenomena taking place across those networks and to support computer simulations of dynamic processes of interest for several areas of research - including computational epidemiology, which is recently high on the agenda. In this paper we present a flexible model to generate age-stratified and geo-referenced synthetic social networks on the basis of widely available aggregated demographic data and, possibly, of estimated age-based social mixing patterns.

We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation.

We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length h of integration and that it recovers the continuous dynamic as h tends to zero.

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 show that minimizers of the Heitmann-Radin energy (Heitmann and Radin in J Stat Phys 22(3): 281-287, 1980) are unique if and only if the particle number N belongs to an infinite sequence whose first thirty-five elements are 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120 (see the paper for a closed-form description of this sequence).

We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings.

This paper deals with the variational analysis of topological singularities in two dimensions. We consider two canonical zero-temperature models: the core radius approach and the Ginzburg-Landau energy. Denoting by epsilon the length scale parameter in such models, we focus on the vertical bar log epsilon VERBAR; energy regime.