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Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
(2021-07-24)
In this contribution we show that fractional diffusion emerges from a simple Markovian Gaussian random walk when the medium displays a power-law heterogeneity. Within the framework of the continuous time random walk, the ...
Study of Wound Healing Dynamics by Single Pseudo-Particle Tracking in Phase Contrast Images Acquired in Time-Lapse
(2021-03)
Cellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities self-aligning in time. The presence of a dense ...
SHOULD I STAY OR SHOULD I GO? ZERO-SIZE JUMPS IN RANDOM WALKS FOR LÉVY FLIGHTS
(2021-02)
We study Markovian continuous-time random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal ...
A generalized Stefan model accounting for system memory and non-locality
(2020-05)
The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the ...
Gaussian processes in complex media: new vistas on anomalous diffusion
(2019-09)
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions ...
Fire-spotting generated fires. Part I: The role of atmospheric stability
(2019-02)
This is the first part of two papers concerning fire-spotting generated fires. In this part we deal with the impact of macroscale factors, such as the atmospheric stability, and in the second part we deal with mesoscale ...
Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
(2019-02-01)
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ...
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
(2019-02)
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ...
On the merits of sparse surrogates for global sensitivity analysis of multi-scale nonlinear problems: Application to turbulence and fire-spotting model in wildland fire simulators
(2019-02)
Many nonlinear phenomena, whose numerical simulation is not straightforward, depend on a set of parameters in a way which is not easy to predict beforehand. Wildland fires in presence of strong winds fall into this category, ...
Restoring property of the Michelson-Sivashinsky equation
(2019)
In this paper we propose a derivation of the Michelson-Sivashinsky
(MS) equation that is based on front propagation only, in opposition to
the classical derivation based also on the flow field. Hence, the characteristics ...