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Topics in multiscale modeling: numerical analysis and applications

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Title: Topics in multiscale modeling: numerical analysis and applications
Authors: Vaes, Urbain Philippe
Item Type: Thesis or dissertation
Abstract: We explore several topics in multiscale modeling, with an emphasis on numerical analysis and applications. Throughout Chapters 2 to 4, our investigation is guided by asymptotic calculations and numerical experiments based on spectral methods. In Chapter 2, we present a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, the numerical methodology that we present is based on a spectral method. We use an expansion in Hermite functions to approximate the solution of an appropriate Poisson equation, which is used in order to calculate the coefficients in the homogenized equation. Extensions of this method are presented in Chapter 3 and 4, where they are employed for the investigation of the Desai—Zwanzig mean-field model with colored noise and the generalized Langevin dynamics in a periodic potential, respectively. In Chapter 3, we study in particular the effect of colored noise on bifurcations and phase transitions induced by variations of the temperature. In Chapter 4, we investigate the dependence of the effective diffusion coefficient associated with the generalized Langevin equation on the parameters of the equation. In Chapter 5, which is independent from the rest of this thesis, we introduce a novel numerical method for phase-field models with wetting. More specifically, we consider the Cahn—Hilliard equation with a nonlinear wetting boundary condition, and we propose a class of linear, semi-implicit time-stepping schemes for its solution.
Content Version: Open Access
Issue Date: Apr-2019
Date Awarded: Aug-2019
URI: http://hdl.handle.net/10044/1/73890
DOI: https://doi.org/10.25560/73890
Copyright Statement: Creative Commons Attribution ShareAlike Licence
Supervisor: Pavliotis, Grigorios
Kalliadasis, Serafim
Sponsor/Funder: Roth PhD studentship
Department: Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Appears in Collections:Mathematics PhD theses

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