Statistical Physics
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Wildfire Spreading: a new application of the Beta distribution
(2022)This dissertation is in the mathematical physics area, more specifically, applications in the statistics field. The thesis, under the supervision of Dr. Gianni Pagnini, was carried out at the BCAM - Basque Centre for ... -
Beta Distribution in Wildfire Spreading
(2022)This paper is the result of research work carried out in collaboration with the Statistical Physics team of the Basque Center for Applied Mathematics in Bilbao, supervised by Dr. Gianni Pagnini. Main subject is PROPAGATOR, ... -
Statistical Characterization of Wildfire Dynamics: Studying the Relation Between Burned Area and Head of the Fire
(2022-06-06)We show that the probability density function (PDF) of an area enclosed by a random perimeter is driven by the PDF of the integration bounds and the mean value of the perimeter function. With reference to wildfires, if the ... -
Fractional Diffusion and Medium Heterogeneity: The Case of the Continuos Time Random Walk
Sposini, V.; Vitali, S.
; Paradisi, P.; Pagnini, G. (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 ... -
Stochastic Properties of Colliding Hard Spheres in a Non-equilibrium Thermal Bath
Bazzani, A.; Vitali, S.; Montanari, C.; Monti, M.; Rambaldi, S.; Castellani, G. (2021-07-24)
We consider the problem of describing the dynamics of a test particle moving in a thermal bath using the stochastic differential equations. We briefly recall the stochastic approach to the Brownian based on the statistical ... -
Stochastic resetting by a random amplitude
Dahlenburg, M.; Chechkin, A. V.; Schumer, R.; Metzler, R. (2021-05-18)
Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ... -
Exact distributions of the maximum and range of random diffusivity processes
(2021-02-09)We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a ... -
Surrogate based Global Sensitivity Analysis of ADM1-based Anaerobic Digestion Model
(2021)In order to calibrate the model parameters, Sensitivity Analysis routines are mandatory to rank the parameters by their relevance and fix to nominal values the least influential factors. Despite the high number of works ... -
Study of Wound Healing Dynamics by Single Pseudo-Particle Tracking in Phase Contrast Images Acquired in Time-Lapse
Scheda, R.; Vitali, S.; Giampieri, E.; Pagnini, G.; Zironi, I. (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
Pagnini, G.; Vitali, S. (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 ... -
Exact first-passage time distributions for three random diffusivity models
(2021-01-04)We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, ... -
The random diffusivity approach for diffusion in heterogeneous systems
(2020-12-16)The two hallmark features of Brownian motion are the linear growth $\langle x^2(t) \rangle = 2 D d t$ of the mean squared displacement (MSD) with diffusion coefficient $D$ in $d$ spatial dimensions, and the Gaussian ... -
Gut microbiota ecology: Biodiversity estimated from hybrid neutral-niche model increases with health status and aging
Sala, C.; Giampieri, E.; Vitali, S.; Garagnani, P.; Remondini, D.; Bazzani, A.; Franceschi, C.; Castellani, G. (2020-10-30)
In this work we propose an index to estimate the gut microbiota biodiversity using a modeling approach with the aim of describing its relationship with health and aging. The gut microbiota, a complex ecosystem that links ... -
Universal spectral features of different classes of random diffusivity processes
(2020-06-26)Stochastic models based on random diffusivities, such as the diffusing- diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically ... -
A generalized Stefan model accounting for system memory and non-locality
Garra, R.; Falcini, F.; Voller, V.R.; Pagnini, G. (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 ... -
A hypothesis about parallelism vs. seriality in dreams
Barcaro, U.; Paradisi, P.; Sebastiani, L. (2019-10-10)
The current article discusses the hypothesis about parallelism vs. Seriality in dreams. The process of dream building implies the construction of a complex network of closely interrelated sources. On the other hand, the ... -
Gaussian processes in complex media: new vistas on anomalous diffusion
Di Tullio, F.; Paradisi, P.; Spigler, R.; Pagnini, G. (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 ... -
Front Propagation in Random Media
(2019)This PhD thesis deals with the problem of the propagation of fronts under random circumstances. A statistical model to represent the motion of fronts when are evolving in a media characterized by microscopical randomness ... -
Stochastic processes for anomalous diffusion
(2019)Anomalous diffusion is a diffusion process which Mean Square Displacement (MSD) is not a linear funtion of time, what is known as normal diffusion. When the relation is faster than linear, it is called superdiffusion and ... -
Single-trajectory spectral analysis of scaled Brownian motion
(2019-06)A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the ...
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