Browsing by Author "Kuchment, Peter"
Now showing items 1-20 of 37
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Chen, Xianjin (2009-05-15)We study computational theory and methods for finding multiple unstable solutions (corresponding to saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. We ...
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Liu, Zhonghai (2010-07-14)We study thoroughly Casimir energy and Casimir force in a rectangular cavity and piston with various boundary conditions, for both scalar field and electromagnetic (EM) field. Using the cylinder kernel approach, we find ...
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Terzioglu, Fatma (2018-02-16)In this dissertation, we focus on analytic and numerical inversion of an integral transform (cone or Compton transform) that maps a function to its integrals over conical surfaces with a weight equal to some power of the ...
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Yahl, Thomas J. (2023-08-09)To an enumerative problem, one may associate a Galois group which encodes symmetries of the solutions to the problem. Galois groups of enumerative problems were first defined and studied by Jordan who considered them in ...
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Corbin, James Edward (2019-10-22)We consider a compact C ∞-stratified 2D variety M in R^3 and its ε-neighborhood Mvε , which we call a “fattened open book structure.” Assuming absence of zero-dimensional strata, i.e. “corners,” we show that the (discrete) ...
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Liu, Zhonghai (Texas A&M University, 2006-10-30)We compute the Casimir energy of a massless scalar field obeying the Robin boundary condition on one plate and the Dirichlet boundary condition on another plate for two parallel plates with a separation of alpha. The ...
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Behne, Patrick Alan (2022-05-25)This work explores the application of data-driven, projection-based, reduced-order models (ROMs) to parametric steady-state, neutral particle, no-fission, source-driven radiation transport. In the offline phase, ROM basis ...
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Liu, Wen (2016-06-14)In this dissertation, we analyze the spectrum of the Laplace operator on graphs. In particular, we are interested in generic eigenpairs. We consider a wide range of vertex conditions on vertices of a quantum graph. ...
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Zhao, Wei (2017-12-01)We identify graphene layer on a disordered substrate as a system where Anderson localization of phonons can be observed. Generally, observation of localization for scattering waves is not simple, because the Rayleigh ...
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Baines, Weston Theodore Cotter (2022-05-18)Several tasks in the fields of medicine and homeland security require the ability to detect weak signals under stymieing conditions. For instance, in medical imaging single photon emission computed tomography can be used ...
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Dutta, Sourav (2017-07-28)We study multiphase, multicomponent flow of incompressible fluids through porous media. Such flows are of vital interest in various applied science and engineering disciplines like geomechanics, groundwater flow and ...
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Georgieva-Hristova, Yulia Nekova (2011-10-21)The results presented in this dissertation concern two different types of tomographic imaging. The first part of the dissertation is devoted to the time reversal method for approximate reconstruction of images in ...
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Nguyen, Linh V. (2010-10-12)Thermoacoustic tomography (TAT) is a newly emerging modality in biomedical imaging. It combines the good contrast of electromagnetic and good resolution of ultrasound imaging. The mathematical model of TAT is the observability ...
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Dorfman, Konstantin Evgenievich (2009-05-15)The mesoscopic effects in the quantum trapped gases of the Bose atoms constitute the main subject of the present thesis. These effects are the most difficult for the theoretical analysis in the quantum statistical physics ...
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Jin, Xing (2009-05-15)This research is primarily focused on developing potential applications for microwaveinduced thermoacoustic tomography and correcting for image degradations caused by acoustic heterogeneities. Microwave-induced thermoacoustic ...
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Allmaras, Moritz (2012-02-14)In this dissertation, two recent problems from tomographic imaging are studied, and results from numerical simulations with synthetic data are presented. The first part deals with ultrasound modulated optical tomography, ...
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Dorfman, Konstantin E. (2010-07-14)In this dissertation, I have studied theoretical problems in statistical physics and electrodynamics of Bose particles, namely, mesoscopic effects in statistics of Bose- Einstein condensate (BEC) of atoms and electromagnetic ...
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Sendova, Tsvetanka Bozhidarova (2009-05-15)The dissertation focuses on the analysis, through combined analytical and numerical techniques, of the partial differential equations arising from a new approach to modeling brittle fracture, based on extension of continuum ...
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Ibdah, Hussain A. (2021-07-08)In this work, we study how Lipschitz continuity propagates by a certain class of nonlinear, nonlocal parabolic equations. This work draws inspiration from ideas developed in recent years by Kiselev, Nazarov, Volberg and ...
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Liu, Ankang (2023-05-18)Spin waves are the collective wave excitations in the magnetically ordered system, which have the frequencies typically ranged from GHz up to even THz. In recent years, the study of spin waves, which is referred to as ...