Fractional Langevin equation with a reflecting barrier
Department
Physics
Major
Physics
Research Advisor
Vojta, Thomas
Advisor's Department
Physics
Funding Source
NSF under Grant No. DMR-1506152 and DMR-1828489
Abstract
The Fractional Langevin equation describes the motion of a particle under the influence of a random force with long-time correlations. This stochastic differential equation is a common model for anomalous diffusion. We investigate the fractional Langevin equation in the presence of a reflecting wall using Monte Carlo simulations. The mean-square displacement shows the expected anomalous diffusion behavior, < xA2 > - tA(2-alpha) , as in the unconfined case. However, the probability density close to the wall shows highly non-Gaussian behavior. For reference, we compare our results to reflected fractional Brownian motion for which the probability density shows a power law singularity at the barrier.
Biography
Sarah's entire life has been dedicated to the development of a navigation app for flat earthers and pastafarianism.
Research Category
Sciences
Presentation Type
Poster Presentation
Document Type
Poster
Location
Upper Atrium
Presentation Date
16 Apr 2019, 9:00 am - 3:00 pm
Fractional Langevin equation with a reflecting barrier
Upper Atrium
The Fractional Langevin equation describes the motion of a particle under the influence of a random force with long-time correlations. This stochastic differential equation is a common model for anomalous diffusion. We investigate the fractional Langevin equation in the presence of a reflecting wall using Monte Carlo simulations. The mean-square displacement shows the expected anomalous diffusion behavior, < xA2 > - tA(2-alpha) , as in the unconfined case. However, the probability density close to the wall shows highly non-Gaussian behavior. For reference, we compare our results to reflected fractional Brownian motion for which the probability density shows a power law singularity at the barrier.
