Masters Theses

Keywords and Phrases

Anomalous diffusion; Fractional Brownian motion; Random walk

Abstract

"Fractional Brownian Motion (FBM) is a Gaussian process whose increments are correlated over long times. FBM is an example of anomalous diffusion, and recently it has been used to model the distribution of serotonergic fibers in the brain [1, 2]. To better represent these fibers, branching FBM (bFBM), where FBM trajectories may randomly split into two, is introduced. One-dimensional bFBM is studied in both sub diffusive and super diffusive regimes, examining three potential behaviors of the correlations (memory) in a branching event: both trajectories retain the memory of previous steps, only one keeps the memory, and neither keeps the memory. Trajectories' mean-square displacements are calculated, as well as the mean-square separation and step correlations between pairs of branching trajectories and found to be in good agreement with theoretical predictions. Branching FBM's qualitative features' strong dependence on memory behavior is confirmed" -- Abstract, p. iii

Advisor(s)

Vojta, Thomas

Committee Member(s)

Yamilov, Alexey
Chernatynskiy, Aleksandr V.

Department(s)

Physics

Degree Name

M.S. in Physics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2024

Pagination

vi, 42 pages

Note about bibliography

Includes_bibliographical_references_(pages 40-41)

Rights

©2024 Reece Beattie-Hauser , All Rights Reserved

Document Type

Thesis - Open Access

File Type

text

Language

English

Thesis Number

T 12373

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Physics Commons

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