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Mehran Kardar. Chu, Sherry(Yun Sherry) Massachusetts Institute of Technology. Department of Physics. Massachusetts Institute of Technology. Department of Physics 2020-01-08T19:32:16Z 2020-01-08T19:32:16Z 2019 2019 https://hdl.handle.net/1721.1/123352 1132804040 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). 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. by Sherry Chu. Ph.D. Ph.D. Massachusetts Institute of Technology, Department of Physics 123 pages eng Massachusetts Institute of Technology MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 Physics. Fluctuating interfaces and paths in disordered and non-equilibrium systems Thesis application/pdf 2020-01-08T19:32:15Z Publication Doctoral Phys unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="d4b01b79-4cc6-4b0c-a73e-7c041d49655f"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Fluctuating interfaces and paths in disordered and non-equilibrium systems</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2019</PublicationDate> <Authors> <Author> <DisplayName>Chu, Sherry(Yun Sherry)</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Physics.</Keyword> <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.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>