We discuss the sharp interface limit of the action functional associated with either the Glauber dynamics for Ising systems with Kac potentials or the Glauber+Kawasaki process. The corresponding limiting functionals, for which we provide explicit formulae of the mobility and transport coefficients, describe the large deviation asymptotics with respect to the mean curvature flow.
In this work, we consider a class of recursively grown fractal networks Gn(t) whose topology is controlled by two integer parameters, t and n. We first analyse the structural properties of Gn(t) (including fractal dimension, modularity, and clustering coefficient), and then we move to its transport properties. The latter are studied in terms of first-passage quantities (including the mean trapping time, the global mean first-passage time, and Kemeny’s constant), and we highlight that their asymptotic behavior is controlled by the network’s size and diameter.
We show that the presence of negative eigenvalues in the spectrum of the angular component of an electromagnetic Schr\"odinger hamiltonian $H$ generically produces a lack of the classical time-decay for the associated Schr\"odinger flow $e^{-itH}$. This is in contrast with the fact that dispersive estimates (Strichartz) still hold, in general, also in this case.
We study the effect of a large obstacle on the so-called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (two-dimensional, 2D) domain needs to cross the strip. We observe complex behavior: We find out that the residence time does not depend monotonically on the geometric properties of the obstacle, such as its width, length, and position. In some cases, due to the presence of the obstacle, the mean residence time is shorter with respect to the one measured for the obstacle-free strip.
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