Big Jump Principle in Physical Models and Data Sets: From Levy Walk to Porous Media
Final Report Abstract
The project consisted of two parts both related to the big jump principle. First, the big jump principle itself was established in different physical systems based on the advancement of extreme value theory. In particular, the big jump principle was found in the ballistic Lévy walk, the heavy-tailed random walk, and transport in disordered systems for the biased continuous time random walk and the quenched trap model. All these examples show that the big jump principle is an important part of nature. While this first part might be interesting for experts in the field, the second part of the projects promises wide interest in the future. The second part of the project aimed to exploit the big jump principle for extreme event management. We presented a simple but effective method to speed up transport in disordered systems. Such complex systems are ubiquitous in nature, and the transport of tracers or particles within them typically experiences high resistance and strong slow-downs. For example, chemical contaminants in hydrogeological media will be trapped in poorly conducting regions so that the system remains contaminated for a long time. Despite the complexity of disordered systems, we were able to describe a concept and delineate a methodology to overcome this dramatic slow-down of the motion. With rigorous theory and extensive numerical analysis, we demonstrated that the elimination of a single element per tracer path speeds up the transport to a surprisingly great extent. This single element is the so-called maximum trapping time, which is the main research object in the field of extreme value theory. In recent decades, there has been and there still is an enormous interdisciplinary effort to describe the physical properties of transport in disordered systems. Yet, there is no general methodology to speed up the transport. Thus, our results present a fundamental theoretical discovery that has the potential to influence current and future research, and to have a long-lasting and profound impact in the field of transport in disordered systems. Furthermore, our technique can be utilized in diverse fields and equips experimentalists with a cost-efficient tool to actively improve transport in disordered systems.
Publications
- Extreme value theory for constrained physical systems, Phys.Rev. E 102, 042141 (2020)
M. Höll, W. Wang and E. Barkai
(See online at https://doi.org/10.1103/physreve.102.042141) - Large deviations of the ballistic Lévy walk model, Phys. Rev E 102, 052115 (2020)
W. Wang, M. Höll and E. Barkai
(See online at https://doi.org/10.1103/physreve.102.052115) - Big jump principle for heavy-tailed random walks with correlated increments, Eur. Phys. J. B 94, 1 (2021). Special issue: Extreme Value statistics and Search in Biology: Theory and Simulations
M. Höll and E. Barkai
(See online at https://doi.org/10.1140/epjb/s10051-021-00215-7) - Controls that expedite scaleinvariant transport in disordered systems, arXiv
M. Höll, A. Nissan, B. Berkowitz, and E. Barkai
(See online at https://doi.org/10.48550/arXiv.2208.10262)
