Statistical Physics

The research of the group falls into the topic of diffusion mainly through the development of stochastic processes in the framework of Fractional Calculus with application to anomalous diffusion and wildfire propagation.


Since the advent of modern Single Particle Tracking (SPT) techniques, a large amount of data with great temporal and spatial accuracy has been produced. The emergence of anomalous diffusion has been confirmed by SPT statistics in many biological systems, with sub-diffusive behavior often associated to crowding, confinement phenomena, and strong heterogeneity of the environment. Recent experiments on molecular diffusion within the cell environment permit to distinguish the anomalous behavior caused by active mechanisms, from the one caused by crowding and confinement in the same system. The research of the group aims to develop novel approaches to generate anomalous diffusive behavior by considering the role of heterogeneity.

News frequently report devastations caused by wildfires and at any time they are labelled as the greater since ever. Climate change has an important role in increasing the frequency of record-breaking fire seasons and, in this sense, there is no need to prove the emergencies generated by wildfires and then their timely understanding and managing. Fire may be an essential element of the ecosystem, or an unnatural element to be avoided. In any case, there is no "blame game" to be played because fire is part of the Earth system, and human dimensions of fire regimes are embedded in complex ecological, economic, political, technological and social relationships. Hence, the comprehension of fire requires to consider it a step in the long-term joint-evolution of the humankind and nature, and do not restrict its study to the description of the present conditions. Finally, the importance of fire in nature and the impacts of our decisions on the related issues call for an overcoming of disciplinary and conceptual boundaries that impede our understanding of the complexities of human-fire relationships. The research of the group aims to introduce proper modelling of random phenomena in the propagation of wildfires, as those due to turbulence or fire-spotting, that are implementable in operational wildfire simulators.

SPEquivalence in distribution


Equivalence in distribution of three Centre-of-mass like models for fractional diffusion [from D’Ovidio M., Vitali S., Sposini V., Sliusarenko O., Paradisi P., Castellani G., Pagnini G., Fract. Calc. Appl. Anal. 21, 1420–1435 (2018)]


Prueba de texto para las líneas de investigación con enlace

Research on anomalous/fractional diffusion is focused on a critical analysis of the generative mechanisms and the development of the corresponding stochastic processes. For example, power-laws mark distributions that do not belong to the domain of attraction of the Gauss law but to the general domain of the stable law or, alternatively, they reveal a compound probability distribution of Gaussian densities with power-law mixing distribution. These two statistical understandings reflect indeed a dualism in the generative mechanism. During the years, an approach for heterogeneous ensembles of particles - and based on the Langevin equation - was formulated to generate fractional diffusion.

Research on random front propagation is focused on modelling wildfire propagation in particular is focused on the role and the physical parametrization of turbulence and fire-spotting. A ready-to-use software code was developed which is implementable into operational simulators.



The random diffusivity approach for diffusion in heterogeneous systems

Name: Spossini, Vittoria
Thesis advisor(s): G. Pagnini
University: Postdam University

Front Propagation in Random Media

Name: Trucchia, Andrea
Thesis advisor(s): Gianni Pagnini
University: University of the Basque Country (UPV/EHU)

Stochastic processes for anomalous diffusion

Name: Molina García, Daniel
Thesis advisor(s): Gianni Pagnini
University: University of the Basque Country (UPV/EHU)

Modeling of birth-death and diffusion processes in biological complex environments

Name: Vitali, Silvia
Thesis advisor(s): Gianni Pagnini, Gastone Castillani and Silvia Arcelli
University: University of Bologna