Location
Innovation Lab, Room 213
Start Date
4-2-2025 10:00 AM
End Date
4-2-2025 10:30 AM
Presentation Date
2 April 2025, 10:00am - 10:30am
Meeting Name
2025 - Miners Solving for Tomorrow Research Conference
Department(s)
Physics
Second Department
Psychological Science
Document Type
Presentation
Document Version
Citation
File Type
text
Rights
© 2025 The Authors, All rights reserved
House_slides.pdf (4324 kB)
Apr 2nd, 10:00 AM
Apr 2nd, 10:30 AM
Fractional Brownian motion with mean-density interaction
Innovation Lab, Room 213
Comments
Advisor: Thomas Vojta
Abstract:
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of particles undergoing fractional Brownian motion. Specifically, we introduce a mean-density interaction in which each particle in the ensemble is coupled to the gradient of the total, time-integrated density produced by the entire ensemble. We report the results of extensive computer simulations for the mean-square displacements and the probability densities of particles undergoing one-dimensional fractional Brownian motion with such a mean-density interaction. We find two qualitatively different regimes, depending on the anomalous diffusion exponent α characterizing the fractional Gaussian noise. The motion is governed by the interactions for α<4/3 whereas it is dominated by the fractional Gaussian noise for α>4/3. We develop a scaling theory explaining our findings.