Fluctuating interfaces and paths in disordered and non-equilibrium systems
Name
1132804040-MIT.pdf
Size
5.97 MB
Format
Adobe PDF
Checksum (MD5)
5015a50298132d1831b41acb317c2496
Author(s)
Chu, Sherry(Yun Sherry)
Advisor(s)
Mehran Kardar.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis, we study the statistics of fluctuating paths and interfaces in the presence of disorder. Specifically, we consider systems in the Kardar-Parisi-Zhang universality class for stochastic interface growth, from the perspectives of both fundamental statistical mechanics and applications to real world problems. We show numerically that the probability distribution associated with directed polymers in random media, a lattice model in this universality class, interpolates between Tracy-Widom and Gaussian distributions when spatial correlations are added to the random energy landscape. As a possible application, we examine the statistics of optimal paths on actual road networks as given by GPS routing, exploring connections and distinctions to directed polymers. We investigate also the effects of roughness in the growth front of a bacterial range expansion. There, we find that such roughness can account for the experimentally observed super-diffusivity, and leads to a rapid loss of genetic diversity. Finally, we explore the complete eigenvalue spectrum of products of random transfer matrices, as relevant to a finite density of non-intersecting directed polymers. We identify a correspondence in distribution to eigenvalues of Gaussian random matrices, and show that the density of states near the edge of the spectrum is altered by the presence of disorder.
Description
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2019
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 117-123).
Subjects
Physics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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