Work

Super-Resolved Anomalous Diffusion: Deciphering the Joint Distribution of Anomalous Exponent and Diffusion Coefficient

Year: 2025

Type: article

Abstract: The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement ⟨X^{2}(t)⟩=2Dt^{α}. Motivated by experiments reporting populations of the anomalous diffusion parameters α and D, we aim to disentangle their respective contributions to the observed variability when this last is due to a true population of these parameters and when it arises due to finite-duration recordings. We introduce estimators of the anomalous diffusion parameters on the basis of the time-averaged mean-squared displacement and study their statistical properties. By using a copula approach, we derive a formula for the joint density function of their estimations conditioned on their actual values. The methodology introduced is indeed universal, it is valid for any Gaussian process and can be applied to any quadratic time-averaged statistics. We also explain the experimentally reported relation D∝exp(αc_{1}+c_{2}) for which we provide the exact expression. We compare our findings to numerical simulations of the fractional Brownian motion and quantify their accuracy by using the Hellinger distance. Finally, we provide guidelines and routines for fitting experimental data.

Source: Physical Review Letters

DOI: 10.1103/y5pn-5ynd

Authors: Yann Lanoiselée, Gianni Pagnini, Agnieszka Wyłomańska

Institutions: Basque Center for Applied Mathematics, Ikerbasque, Wrocław University of Science and Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: green