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Anomalous Transport: Applications, Mathematical Perspectives, and Big Data

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Diffusion addresses the broadening of distribution functions in the course of time. When the variance grows linearly, we speak of diffusion; otherwise, the transport is anomalous. Anomalous transport is observed in a vast variety of systems like transport in porous media and other complex geometries,
in ...

Diffusion addresses the broadening of distribution functions in the course of time. When the variance grows linearly, we speak of diffusion; otherwise, the transport is anomalous. Anomalous transport is observed in a vast variety of systems like transport in porous media and other complex geometries,
in solid-state disordered systems, crowded environments of cell interiors, the collective behavior of living organisms, and heat transport in low-dimensional systems.

There is a wealth of theoretical research devoted to mechanisms that can induce anomalous transport. However, the past decade has vividly changed the field. Video Microscopy and particle tracking are providing a rapidly increasing wealth of highly-resolved experimental observations. Moreover, numerical simulations of ensembles of trajectories are now feasible also for disordered systems where one must average over many realizations of the geometry. The resulting data sets should best be addressed from a big data perspective to extract characteristic transport properties. Firstly, this poses challenges for the automatic data processing and parameter inference. Secondly, it calls for new mathematical perspectives that underpin the data analysis from a unified point of view. In particular, data sets are big enough now to address the anomalous decay of correlations in the dynamics and to search for universality in the transport.

The aim of this Research Topic is to unify different visions, approaches and methodologies around the field of anomalous diffusion. We welcome contributions that review the current state of affairs in different fields of applications and mathematical models, opinion papers pointing towards urging open challenges, and original research articles. Altogether, they will provide a thorough overview of the status of the field, and insight into the main directions of current research.


Keywords: anomalous transport, billiards and dynamical systems, stochastic dynamics, applications


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