Remarks on Regularization by Noise, Convex Integration and Spontaneous Stochasticity.

This note is devoted to a discussion of the potential links and differences between three topics: regularization by noise, convex integration, spontaneous stochasticity. All of them deal with the effect on large scales of a small-scale perturbation of fluid dynamic equations. The effects sometimes have something in common, like convex integration and spontaneous stochasticity, sometimes they look the opposite, as in regularization by noise.

The Mathematical modeling of Cancer growth and angiogenesis by an individual based interacting system.

We present a mathematical model for the complex system for the growth of a solid tumor. The system embeds proliferation of cells depending on the surrounding oxygen field, hypoxia caused by insufficient oxygen when the tumor reaches a certain size, consequent VEGF release and angiogenic new vasculature growth, re-oxygenation of the tumor and subsequent tumor growth restart. Specifically cancerous cells are represented by individual units, interacting as proliferating particles of a solid body, oxygen, and VEGF are fields with a source and a sink, and new angiogenic vasculature is described by a network of growing curves.

Data analysis of the unsteadily accelerating GPS and seismic records at Campi Flegrei caldera from 2000 to 2020.

Ongoing resurgence affects Campi Flegrei caldera (Italy) via bradyseism, i.e. a series of ground deformation episodes accompanied by increases in shallow seismicity.

Eddy heat exchange at the boundary under white noise turbulence.

We prove the existence of an eddy heat diffusion coefficient coming from an idealized model of turbulent fluid. A difficulty lies in the presence of a boundary, with also turbulent mixing and the eddy diffusion coefficient going to zero at the boundary. Nevertheless, enhanced diffusion takes place.