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Browsing by Subject "Applied mathematics"
Now showing items 1-20 of 42
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A Class of Tetrahedral Finite Elements for Complex Geometry and Nonlinear Mechanics: A Variational Multiscale Approach
(2019)In this work, a stabilized finite element framework is developed to simulate small and large deformation solid mechanics problems involving complex geometries and complicated constitutive models. In particular, the focus ... -
A Geometric Approach to Biomedical Time Series Analysis
(2020)Biomedical time series are non-invasive windows through which we may observe human systems. Although a vast amount of information is hidden in the medical field's growing collection of long-term, high-resolution, and multi-modal ... -
A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications
(2016)The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the ... -
Accelerating the Computation of Density Functional Theory's Correlation Energy under Random Phase Approximations
(2019)We propose novel algorithms for the fast computation of density functional theory's exchange-correlation energy in both the particle-hole and particle-particle random phase approximations (phRPA and ppRPA). For phRPA, we ... -
Adaptive Data Representation and Analysis
(2018)This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional ... -
Adaptive Sparse Grid Approaches to Polynomial Chaos Expansions for Uncertainty Quantification
(2015)Polynomial chaos expansions provide an efficient and robust framework to analyze and quantify uncertainty in computational models. This dissertation explores the use of adaptive sparse grids to reduce the computational cost ... -
Algorithms with Applications to Anthropology
(2018)In this dissertation, we investigate several problems in shape analysis. We start by discussing the shape matching problem. Given that homeomorphisms of shapes are computed in practice by interpolating sparse correspondence, ... -
An Investigation into the Multiscale Nature of Turbulence and its Effect on Particle Transport
(2022)We study the effect of the multiscale properties of turbulence on particle transport, specifically looking at the physical mechanisms by which different turbulent flow scales impact the settling speeds of particles in turbulent ... -
Analytical and Numerical Study of Lindblad Equations
(2020)Lindblad equations, since introduced in 1976 by Lindblad, and by Gorini, Kossakowski, and Sudarshan, have received much attention in many areas of scientific research. Around the past fifty years, many properties and structures ... -
Applications of Topological Data Analysis and Sliding Window Embeddings for Learning on Novel Features of Time-Varying Dynamical Systems
(2017)This work introduces geometric and topological data analysis (TDA) tools that can be used in conjunction with sliding window transformations, also known as delay-embeddings, for discovering structure in time series and dynamical ... -
Compressive Sensing in Transmission Electron Microscopy
(2018)Electron microscopy is one of the most powerful tools available in observational science. Magnifications of 10,000,000x have been achieved with picometer precision. At this high level of magnification, individual atoms are ... -
Data Transfer between Meshes for Large Deformation Frictional Contact Problems
(2013)In the finite element simulation of problems with contact there arisesthe need to change the mesh and continue the simulation on a new mesh.This is encountered when the mesh has to be changed because the original mesh experiences ... -
Designing Quantum Channels Induced by Diagonal Gates
(2023)The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal T gate play an important role in implementing a universal set of quantum operations. We ... -
Dynamics and Steady-states of Thin Film Droplets on Homogeneous and Heterogeneous Substrates
(2019)In this dissertation, we study the dynamics and steady-states of thin liquid films on solid substrates using lubrication equations. Steady-states and bifurcation of thin films on chemically patterned substrates have been ... -
Efficient Algorithms for High-dimensional Eigenvalue Problems
(2020)The eigenvalue problem is a traditional mathematical problem and has a wide applications. Although there are many algorithms and theories, it is still challenging to solve the leading eigenvalue problem of extreme high dimension. ... -
EM Scattering from Perforated Films: Transmission and Resonance
(2012)We calculate electromagnetic transmission through periodic gratings using a mode-matching method for solving Maxwell's equations. We record the derivation of the equations involved for several variations of the problem, ... -
General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions
(2017)Hamiltonian Monte Carlo (HMC) is a state-of-the-art sampling algorithm for Bayesian computation. Popular probabilistic programming languages Stan and PyMC rely on HMC’s generality and efficiency to provide automatic Bayesian ... -
Geometric Multimedia Time Series
(2017)This thesis provides a new take on problems in multimedia times series analysis by using a shape-based perspective to quantify patterns in time, which is complementary to more traditional analysis-based time series techniques. ... -
Homeostasis-Bifurcation Singularities and Identifiability of Feedforward Networks
(2020)This dissertation addresses two aspects of dynamical systems arising from biological networks: homeostasis-bifurcation and identifiability.Homeostasis occurs when a biological quantity does not change very much as a parameter ... -
Implicit and Explicit Codes For Diffraction Tomography
(2014)Diffraction tomography is the attempt to estimate the scattering density of an object from measurements of a scattered coherent field. This work moves to overcome many of the constraints and limitations of the current state ...
