arXiv subjects

Giuseppe Forte

Publications and source records attributed to Giuseppe Forte.

4 recordsLinked to original sources

arXiv2017

Iterative control strategies for non-linear systems

In this paper, we focus on the control of the mean field equilibrium of non linear networks of the Langevin type in the limit of small noise. Using iterative linear approximations, we derive a formula that prescribes a control strategy in order to displace the equilibrium state of a given system, and remarkably find that the control function has a "universal" form under certain physical conditions. This result can be employed to define universal protocols useful, for example, in the optimal work extraction from a given reservoir. Generalizations and limits of application of the method are discussed.

cond-mat.stat-mech↗

arXiv2014

Transport and fluctuation-dissipation relations in asymptotic and pre-asymptotic diffusion across channels with variable section

We study the asymptotic and pre-asymptotic diffusive properties of Brownian particles in channels whose section varies periodically in space. The effective diffusion coefficient $D_{\mathrm{eff}}$ is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries, considering even cases of steep variations of the channel boundaries. Moreover, we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known Fick-Jacobs approximation. Building an effective one dimensional equation for the longitudinal diffusion, we obtain an approximation for the effective diffusion coefficient. Such a result goes beyond a perturbation approach, and it is in good agreement with the actual values obtained by the numerical simulations. We discuss also the pre-asymptotic diffusion which is observed up to a crossover time whose value, in the presence of strong spatial variation of the channel cross section, can be very large. In addition, we show how the Einstein's relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and pre-asymptotic regimes.

cond-mat.stat-mech↗

arXiv2014

Non-anomalous diffusion is not always Gaussian

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: i) the high-order moments, $\langle [x(t)]^q \rangle$ for $q>2$ and the probability density of the process exhibit multiscaling; ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; iii) positive order moments satisfying standard scaling do not imply an exact scaling property of the probability density.

cond-mat.stat-mech↗

arXiv2013

Anomalous diffusion and response in branched systems: a simple analysis

We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling arguments is able to predict the correct anomalous regime for different topologies. In addition, we show that even in the presence of anomalous diffusion, Einstein's relation still holds, implying a proportionality between the mean square displacement of the unperturbed systems and the drift induced by an external forcing.

cond-mat.stat-mech↗