Small Scale Stochastic Dynamics For Particle Image Velocimetry Applications

dc.contributor.advisor Mucha, Peter J.
dc.contributor.author Hohenegger, Christel en_US
dc.contributor.committeeMember Evans M. Harrell
dc.contributor.committeeMember Guillormo Goldsztein
dc.contributor.committeeMember Haomin Zhou
dc.contributor.committeeMember Minami Yoda
dc.contributor.department Mathematics en_US
dc.date.accessioned 2006-06-09T18:03:43Z
dc.date.available 2006-06-09T18:03:43Z
dc.date.issued 2006-03-16 en_US
dc.description.abstract Fluid velocities and Brownian effects at nanoscales in the near-wall region of microchannels can be experimentally measured in an image plane parallel to the wall using, for example, evanescent wave illumination technique combined with particle image velocimetry [R. Sadr extit{et al.}, J. Fluid. Mech. 506, 357-367 (2004)]. The depth of field of this technique being difficult to modify, reconstruction of the out-of-plane dependence of the in-plane velocity profile remains extremely challenging. Tracer particles are not only carried by the flow, but they undergo random fluctuation imposed by the proximity of the wall. We study such a system under a particle based stochastic approach (Langevin) and a probabilistic approach (Fokker-Planck). The Langevin description leads to a coupled system of stochastic differential equations. Because the simulated data will be used to test a statistical hypothesis, we pay particular attention to the strong order of convergence of the scheme developing an appropriate Milstein scheme of strong order of convergence 1. Based on the probability density function of mean in-plane displacements, a statistical solution to the problem of the reconstruction of the out-of-plane dependence of the velocity profile is proposed. We developed a maximum likelihood algorithm which determines the most likely values for the velocity profile based on simulated perfect particle position, simulated perfect mean displacements and simulated observed mean displacements. Effects of Brownian motion on the approximation of the mean displacements are briefly discussed. A matched particle is a particle that starts and ends in the same image window after a measurement time. AS soon as the computation and observation domain are not the same, the distribution of the out-of-plane distances sampled by matched particles during the measurement time is not uniform. The combination of a forward and a backward solution of the one dimensional Fokker-Planck equation is used to determine this probability density function. The non-uniformity of the resulting distribution is believed to induce a bias in the determination of slip length and is quantified for relevant experimental parameters. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 1627976 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/10464
dc.language.iso en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Statistical methods en_US
dc.subject Fluid mechanics
dc.subject Stochastic differential equations
dc.subject Numerical simulation
dc.subject Modeling
dc.title Small Scale Stochastic Dynamics For Particle Image Velocimetry Applications en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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