Work

Anomalous diffusion properties of stochastic transport by heavy-tailed jump processes

Year: 2026

Type: article

Abstract: In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric α -stable-like process. Motivated by recent works [17, 18] showing that complex small-scale spatial structures often lead to Brownian dispersion, we study if this principle persists when the driving noise exhibits heavy-tailed jump statistics. Our numerical results show a clear dichotomy linked with the tail behaviour of the noise. When considering standard α -stable processes, very large jumps survive the interaction with the spatial complexity and yield anomalous, super-diffusive transport. In contrast, when the α -stable noise is either truncated or exponentially tempered, suppressing extremely long jumps, the transport undergoes a transition to a classical diffusive regime.

Source: Communications in Nonlinear Science and Numerical Simulation

DOI: 10.1016/j.cnsns.2026.110070

Authors: Paolo Cifani, Franco Flandoli, Lorenzo Marino

Institution: Scuola Normale Superiore

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,710

Funders: European Commission, European Research Council