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The existence of travelling waves in an atomistic model for martensitic phase transitions is the focus of study. The elastic energy is assumed to be piecewise quadratic, with two wells representing two stable phases. We develop a framework such that the existence of subsonic heteroclinic waves in a bi-infinite chain of atoms can be proved rigorously. The key is to represent the solution as a su...

We study the spreading of a disease on a population whose connectivity obeys a scaling law, a characteristic of real-life networks, by using the standard SIR model. We show that for scale-free networks with a high degree of connectivity there is no critical threshold for epidemics, but the infected population grows almost linearly with the infection probability, which is more realistic, as oppo...

We introduce a mesoscopic three-dimensional lattice Boltzmann model which attempts to mimic the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard lattice Boltzmann dynamics with self-consistent constraints based on the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamic h...