Speaker: Gianni Pagnini, BCAM & IKERBASQUE

BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009, Bilbao, Basque Country – Spain

IKERBASQUE – Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Basque Country, Spain

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube :  https://youtu.be/hJZGjnTxxpc

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  Lévy flights, Kramers–Moyal expansion, Pawula theorem, multi-order space-fractional diffusion equation 

Abstract: We study the properties of L´evy flights with index 0 < α < 2 at elapsed times smaller than those required for reaching the diffusive limit, and we focus on the bulk of the walkers’ distribution rather than on its tails. On the basis of the analogs of the Kramers–Moyal expansion and of the Pawula theorem, we show that, for any α ≤ 2/3, the bulk of the walkers’ distribution occurs at wave-numbers greater than (2/α)1/(2) ≥ 1, and it remains non-self-similar for a time-scale longer than the Markovian time-lag of at least one order of magnitude. This result highlights the fact that for Levy flights, the Markovianity time-lag is not the only time-scale of the process and indeed another and longer time-scale controls the transition to the familiar power-law regime in the final diffusive limit. The magnitude of this further time-scale is independent of the index and may compromise the reliability of applications of Levy flights to real world cases related with recurrence and transience as optimal searching, animal foraging, and site fidelity.

The talk is based on References [1, 2].

Biography: Gianni Pagnini is permanent at BCAM - Basque Center for Applied Mathematics, Bilbao, Spain, as Ikerbasque Research Associate Professor, where he leads the Statistical Physics line. His research is focused on stochastic processes and diffusion problems with applications also in biology and forest fires. His education reflects his multidisciplinary approach and scientific interests: Laurea in Physics (Bologna, 2000, Italy) on fractional diffusion equations; PhD in Environmental Sciences (Urbino, 2005, Italy) on nonlinear stochastic modelling of turbulence; and the Italian Qualification as Associate Professor in Mathematical Physics. As a young researcher, he studied analytical aspects of applications of Fractional Calculus including Mellin-Barnes integrals and H-Functions. Later, he focused on stochastic modelling of processes governed by fractional differential equation. He is now member of the Editorial Board of the journals “Fractional Calculus and Applied Analysis” and “Communications in Applied and Industrial Mathematics” (the official journal of the Italian Society for Applied and Industrial Mathematics (SIMAI)). 

Bibliography