Anomalous diffusion in complex heterogeneous systems
Mini-Symposium on
Anomalous diffusion in complex heterogeneous systems
Bari (Italy), June 3 2025
Department of Mathematics - Via E.Orabona 4 - Bari
Room XI (first floor)
P R O G R A M
15:00 - 15:45 Modelling and analysis of time series using multifractional Brownian motion (Samudrajit Thapa)
15:45 - 16:30 From diffusion of particles to diffusion of excitons and magnetic textures (Aleksei Chechkin)
16:30 - 17:15 Nothing is local: Non-Gaussianity and varying scaling exponents in long-range dependent motion (Ralf Metzler)
Participation is free and there is no need to be registered
T A L K S A N D A B S T R A C T S
Modelling and analysis of time series using multifractional Brownian motion
Prof. Samudrajit Thapa
(Max Planck Institute for the Physics of Complex Systems, Dresden, Germany)
Fractional Brownian motion (FBM), a Gaussian, self-similar process characterized by a constant Hurst exponent, is a canonical model of power-law correlated dynamics and has found utility in diverse systems including biology, hydrology and economics. However, studies of financial time series and recent single particle tracking experiments in biology show that the canonical FBM is insufficient to explain the observations. This calls for generalizations of FBM called multifractional Brownian motion (MBM) characterized by Hurst exponents that change in time along the sample paths. Inspired by these results, I will present a simple, analytically tractable model which fills the gap between mathematical formulations of MBM and empirical studies. In the proposed model, called telegraphic multifractional Brownian motion (TeMBM), the Hurst exponent is modelled by a smoothed telegraph process which results in a stationary beta distribution of exponents as observed in biological experiments. Finally, I will discuss how single-trajectory analysis of stock price data employing Bayesian inference on multifractional processes reveals crucial insights about financial markets and underscores the broad applicability of our approach.
From diffusion of particles to diffusion of excitons and magnetic textures
Prof. Aleksei Chechkin
(Max Planck Institute of Microstructure Physics, Halle, Germany)
In the first part of my talk, I consider diffusion of excitons in perovskites and transition metal dichalcogenides, which shows clear anomalous behavior in experiments. These materials are of importance for their remarkable optoelectronic applications. We developed a non-Markovian mobile-immobile model which provides an explanation for this behavior through paired theoretical and simulation approaches. In the second part I show very recent theoretical results on stochastic dynamics of domain walls and skyrmions on the racetracks, the building blocks of the new generation of computers. The racetracks with these magnetic textures represent instructive examples of the highly heterogeneous non-equilibrium systems requiring new mathematical models for the adequate description of their stochastic behavior.
Nothing is local: Non-Gaussianity and varying scaling exponents in long-range dependent motion
Prof. Ralf Metzler
Institute of Physics & Astronomy, University of Potsdam, Potsdam, Germany
Stochastic processes with long-range dependent correlations naturally emerge in many systems when degrees of freedom are integrated out, apart from the dynamic of the (tracer) particle of interest. In non-equilibrium situations, the resulting overdamped dynamics often corresponds to fractional Brownian motion (FBM). Prime examples are crowded liquids such as the cytoplasm of biological cells or biological membranes. In such disordered systems the observed displacement probability density is often non-Gaussian, and/or FBM-type processes display scaling exponents varying in time or space. This talk introduces diffusion models with stochastically and deterministically varying diffusion coefficients and scaling exponents.
Organizing committee
Prof. Roberto Garrappa (University of Bari)
Prof. Marina Popolizio (Polytechnic of Bari)