Now showing items 21-40 of 70

• Gaussian Polynomial Filters and Generalized Shift-Invariant Frames ﻿

(December 2)
We present and study a family of filters on $L^2(\mathbb{R}^d)$ consisting of Gaussian polynomials. That is, multipliers in the frequency domain that are products of polynomials and Gaussians. These filters are constructed ...
• Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions ﻿

(2013-08)
We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. ...
• High-Order Numerical Methods for Time-Dependent Problems with Applications ﻿

(2015-08)
In this dissertation, several high-order numerical methods for solving time dependent problems are studied. In the first part, a maximum principle preserving (MPP) finite-volume (FV) weighted essentially non-oscillatory ...

(2017)
• Image Analysis Using Directional Multiscale Representations and Applications for Characterization of Neuronal Morphology ﻿

(2015-12)
Recent advances in high-resolution fluorescence microscopy have enabled the system- atic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery ...
• Large Deviations Approach for Stochastic Genetic Evolution ﻿

(2013-08)
Theoretical ecologists have long strived to explain how the persistence of populations depends on biotic and abiotic factors and have proposed various models to predict the long time behavior of biological populations. We ...
• Large Time Step and Overlapping Grids for Conservation Laws ﻿

(2014-05)
One focus of this dissertation is to construct a large time step Finite Volume Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for ...
• Mass spectrometry data mining for cancer detection ﻿

(2013-12)
Early detection of cancer is crucial for successful intervention strategies. Mass spectrometry-based high throughput proteomics is recognized as a major breakthrough in cancer detection. Many machine learning methods have ...
• Mechanical Constraint and Cell Shape Interaction Modeling of Bacterial Growth in Microfluidic Traps ﻿

(August 201)
Modeling mechanical interactions of bacteria is integral to capturing their dynamics in close-knit populations, because mechanical signals can be a primary means of inter-cellular communication in these environments. ...
• Mixed Finite Element Methods with Piece-Wise Constant Fluxes ﻿

(2015-05)
In this dissertation, we consider a new mixed finite element discretization, its error estimation, monotonicity and the approaches to implement local refinement. We also do some numerical experiments to verify error estimates ...
• Mixed-Finite-Element Method on Hexahedral Meshes ﻿

(2014-08)
In this dissertation, we have three goals. The first goal is to investigate the accuracy behavior due to lumping procedure. The second goal is to investigate the effects of different boundary partitions of macro-cells. The ...
• Modeling, analysis and numerical simulation of reactive solute transport problems in moving domains ﻿

(2014-05)
In this thesis, we study mathematical models and numerical schemes for reactive transport of a soluble substance in deformable media. The medium is a cylindrical channel with compliant adsorbing walls. The solutes are ...
• New Insights on Quasistatic and Acoustic Cloaking ﻿

(2014-05)
In the first four chapters 1-4, we study, in the quasistatic regime, the behavior of the dissipated power inside the boundary layers of a two dimensional metamaterial slab of negative permittivity . We consider a compactly ...
• NUMERICAL SIMULATION AND MODELING OF CELL MOTION IN MICROCHANNELS ﻿

(2013-12)
The motion of cells in flow has been studied in vivo, in viro, and in silico. Different models have been developed. In this dissertation we have compared the cell mostion with Navier-Stokes model and the Stokes model in ...
• Numerical Simulation of 4th Order Total Variation Flow Problem by using C^0 IPDG Method ﻿

(May 2018)
This dissertation is devoted to the the numerical solution of the regularized fourth order total variation flow problem in material science representing surface relaxation below the roughening temperature. Based on ...
• Numerical Simulation of Cell Motion in Microchannels ﻿

(2013-05)
An immersed boundary method combined with an elastic spring model is applied to simulate the red blood cell (RBC) motion and deformation in bounded Poiseuille flows. As a benchmarking test, the dynamical behavior of a RBC ...
• Numerical Simulation of Red Blood Cells in Capillaries ﻿

(2014-12)
A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology with an immersed boundary method. We combine the above methodology with a distributed Lagrange ...
• NUMERICAL SIMULATION OF TWO-PHASE FLOW USING THE LEVEL SET APPROACH ﻿

(2014-12)
In this dissertation, we present numerical schemes in simulating immiscible two-phase flow problems. The goal of this work is to find unified solutions for numerical modeling of any kind of immiscible two-phase flow with ...
• On Holomorphic Sectional Curvature and Fibrations ﻿

(2016-12)
In this dissertation, we prove the existence of a metric of definite holomorphic sectional curvature on certain compact fibrations. The basic idea for these curvature computations is to use the already available information ...
• On the Positive Holomorphic Sectional Curvature of Projectivized Vector Bundles over Compact Complex Manifolds ﻿

(2016-05)
In complex geometry, there are few known examples of, and few known results about, manifolds with metrics of positive curvature. For instance, the geometry of fiber bundles and total spaces of fibrations over positively-curved ...