Dynamical effects of noise on nonlinear systems

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dc.contributor.advisorVolpe, Giovanni
dc.contributor.authorDuman, Özer
dc.date.accessioned2016-07-01T11:10:28Z
dc.date.available2016-07-01T11:10:28Z
dc.date.issued2014
dc.departmentDepartment of Physicsen_US
dc.descriptionCataloged from PDF version of article.en_US
dc.description.abstractRandomness and nonlinear dynamics consitute the most essential part of many events in nature. Therefore, a better and comprehensive understanding of them is a crucial step in describing natural phenomena as well as the prospect of predicting their future outcome. Besides the interest from a fundamental point of view, it is also useful in a wide variety of applications requiring delicate and careful use of energy. Especially recent advances in micro- and nano-scale technology requires harnessing the underlying noise itself as it is relatively hard to exert forces without damaging the system at that scale. The main aim of this work is to study the effects of noise on nonlinear dynamics. We show that the interplay between noise, nonlinearity and nonequilibrium conditions leads to a finite drift with the potential to change the dynamics of the system completely in a predictable and tunable fashion. We report that the noise-induced drift disrupts the phase space of a 2-D nonlinear system by shifting the fixed point by a finite amount which may result in dramatic alterations over the temporal behavior of the system. We track such alterations to several multi-dimensional model systems from ecology, soft matter and statistical physics. In a 2-D ecological model describing two species competing for the same resource, it is found that the system switches between coexistence and extinction states depending on the shift due to the noise-induced drift whereas for an aggregate of Brownian particles, it is shown that noise-induced drift selectively shifts the probability distribution in certain geometries which can be used in the realization of a microparticle sorter in the mould of Feynman ratchets. In the case of the aggregate consisting of microswimmers, tunable anomalous diffusion depending on the confinement length is reported.en_US
dc.description.degreeM.S.en_US
dc.description.statementofresponsibilityDuman, Özeren_US
dc.format.extentxii, 74 leaves, graphics, illustrations, 30 cmen_US
dc.identifier.itemidB148310
dc.identifier.urihttp://hdl.handle.net/11693/30010
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectStochastic differential equationsen_US
dc.subjectStochastic differential delay equationsen_US
dc.subjectNonlinear dynamicsen_US
dc.subjectDiffusion processesen_US
dc.subjectBrownian motionen_US
dc.subjectMicroswimmersen_US
dc.subject.lccQA274.23 .D86 2014en_US
dc.subject.lcshStochastic differential equations.en_US
dc.titleDynamical effects of noise on nonlinear systemsen_US
dc.typeThesisen_US
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