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Now showing items 1-10 of 12

#### Mathematical Topics in Fluid-Particle Interaction

(2014)

Models for particles interacting with compressible fluids are useful to several areas of science. This dissertation considers some of the mathematical issues of the Navier-Stokes-Smoluchowski and Euler-Smoluchowski models ...

#### Exploiting Data-Dependent Structure for Improving Sensor Acquisition and Integration

(2014)

This thesis deals with two approaches to building efficient representations of data. The first is a study of compressive sensing and improved data acquisition. We outline the development of the theory, and proceed into ...

#### A Fokker-Planck Study Motivated by a Problem in Fluid-Particle Interactions

(2014)

This dissertation is a study of problems that relate to a Fokker-Planck (Klein-Kramers)
equation with hypoelliptic structure. The equation describes the statistics of motion
of an ensemble of particles in a viscous fluid ...

#### Asymptotic problems for stochastic processes and corresponding partial differential equations

(2014)

We consider asymptotic problems for diffusion processes that rely on large deviations.
In Chapter 2, we study the long time behavior (at times of order exp(λ/&Alt 238; &Alt253;) of solutions to quasi-linear
parabolic ...

#### TRADING ADVANTAGES OF STRUCTURED PRODUCTS AND OPTION IMPLIED LIQUIDITY

(2011)

The two-price market theory is based on a new performance measure - acceptability indices, and provides a new way to describe incomplete markets. Unlike the classical option pricing theory, in which the risk-neutral measure ...

#### Network Algorithms for Complex Systems with Applications to Non-linear Oscillators and Genome Assembly

(2013)

Network and complex system models are useful for studying a wide range of phenomena, from disease spread to traffic flow. Because of the broad applicability of the framework it is important to develop effective simulations ...

#### The Hunt Variance Gamma Process with Applications to Option Pricing

(2013)

In this dissertation we develop a spatially inhomogeneous Markov process as a model for financial asset prices. This model is called the Hunt variance gamma process. We define it via its infinitesimal generator and prove ...

#### Using a Discriminator to Improve Compressive Sensing Efficiency

(2012)

Our work defines, implements, and evaluates a modification to a spectrum-based compression scheme for data streams coming from jet aircraft health-monitoring sensors. The modification consists of the addition of a ...

#### Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

(2016)

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest ...

#### Existence and weak-strong uniqueness for the Navier-Stokes-Smoluchowski system over moving domains

(2016)

This dissertation concerns the well-posedness of the Navier-Stokes-Smoluchowski system. The system models a mixture of fluid and particles in the so-called bubbling regime. The compressible Navier-Stokes equations governing ...