# 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.