N. Fusco | Searcharxiv

arXiv2025

The isoperimetric inequality for the capillary energy outside convex sets

We study the isoperimetric problem for capillary hypersurfaces with a general contact angle $\theta \in (0, \pi)$, outside arbitrary convex sets. We prove that the capillary energy of any surface supported on any such convex set is larger than that of a spherical cap with the same volume and the same contact angle on a flat support, and we characterize the equality cases. This provides a complete solution to the isoperimetric problem for capillary surfaces outside convex sets at arbitrary contact angles, generalizing the well-known Choe-Ghomi-Ritor\'e inequality, which corresponds to the case $\theta=\frac\pi2$.

math.AP↗

arXiv2002

Relaxation and overlap probability function in the spherical and mean spherical model

The problem of the equivalence of the spherical and mean spherical models, which has been thoroughly studied and understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to below the critical temperature. It is found that there exists a crossover time $t^* \sim V^{2/d}$ such that for $t < t^*$ the two models are equivalent, while for $t > t^*$ macroscopic discrepancies arise. The relation between the off equilibrium response function and the structure of the equilibrium state, which usually holds for phase ordering systems, is found to hold for the spherical model but not for the mean spherical one. The latter model offers an explicit example of a system which is not stochastically stable.

cond-mat.stat-mech↗