In a power system, operators maintain voltage stability through adequate reactive reserves. Maintaining and accessing an efficient allocation of reactive reserves is prohibitively complex because of reactive line losses, the variety of reactive resources, and either limited or variable reactive outputs from renewable sources. By clustering the system into smaller...
In this thesis we analyze a model for Kerr optical materials consisting of Maxwell's equations along with the dispersive Duffing model. We consider Duffing models with cubic and quintic polynomial nonlinearities. We assume a traveling wave solution to this nonlinear electromagnetic system and analyze it using the theory of dynamical...
Statistical mechanics studies the probability that a system is in a certain state given one or more constraints which are usually fixed conserved quantities. It is a particularly useful and powerful approach for problems with a large number of degrees of freedom where a complete knowledge of the system is...
Generating abundant, renewable energy from Earth’s oceans is an attractive option for meeting increasing energy demand. Marine renewable energy also comes with the variability of renewable sources, which impact the reliability and power quality of the electrical grid. On a transmission-level, this dissertation looks at ensuring reliability of the power...
In this dissertation, we introduce a family of fully discrete finite difference time-domain (FDTD) methods for Maxwell’s equations in linear and nonlinear materials. Onecategory of methods is constructed using multiscale techniques involving operator splittings. We present the sequential splitting scheme, the Strang Marchuk splitting scheme,the weighted sequential splitting scheme including...
Random fields are frequently used in computational simulations of real-life processes. In particular, in this work they are used in modeling of flow and transport in porous media. Porous media as they arise in geological formations are intrinsically deterministic but there is significant uncertainty involved in determination of their properties...
Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
Coastal multi-hazards, i.e., earthquakes followed by tsunamis, induce severe damage to coastal infrastructure. The multi-hazards can cause soil liquefaction, which is one of the major concerns for evaluating sediments transport potential and structure failure mechanisms. The objectives for this work is threefold. First, to build and validate a soil numerical...
There exists a variety of methods to solve the radiation transport equation in stochastic materials, including the Levermore-Pomraning method and the atomic mix method, each of which is designed to replicate the results given by benchmarks with materials rearranged in a randomized fashion. While the atomic mix method is very...
Adjoint-derived weight windowing is a hybrid deterministic/Monte Carlo method to simulate radiation transport. In adjoint-derived weight windowing, a deterministic adjoint solution is used to create weight windows for a Monte Carlo simulation. The intent of this work is to identify factors that reduce the Figure of Merit (FOM) of Monte...
Load flow studies are one of the most essential engineering applications for grid operators because they provide a clear picture of the operating conditions of the power system. Traditionally, the load flow problem is assumed to be deterministic; that is, the system variables contain no randomness. Unfortunately, this assumption is...
In this work we will analyze branching Brownian motion on a finite interval with oneabsorbing and one reflecting boundary, having constant drift rate toward the absorbingboundary. Similar processes have been considered by Kesten ([12]), and more recently byHarris, Hesse, and Kyprianou ([11]). The current offering is motivated largely by the...
In this work we consider the dependence of solutions to a partial differential equations system on its data. The problem of interest is a coupled model of nonlinear flow and transport in porous media, with applications, e.g. to environmental modeling. The model of flow we consider is known as the...
A perfectly matched layer (PML) is widely used to model many different types of wave propagation in different media. It has been found that a PML is often very effective and also easy to set, but still many questions remain.
We introduce a new formulation from regularizing the classical Un-Split...
In this dissertation we develop mathematical treatment for two important applications: (i) evolution of methane in coalbeds with the associated phenomena of adsorption, and (ii) formation of methane hydrates in seabed. We use simplified models for (i) and (ii) since we are more interested in qualitative properties of the solutions...
Modeling and analyzing the combined effects of disease and population dynamics
is important in understanding the effects of mechanisms such as pathogen transmission
and direct competition between host species on the distribution and abundance of different
species in an ecological community. Mathematical analysis of such models in a
spatially explicit...
In this thesis, we consider Maxwell's Equations and their numerical discretization using finite difference and finite element methods. We first describe Maxwell's equations in linear dielectrics and then present finite difference and finite element methods for this case. We then describe Maxwell's equations in linear metamaterials using the Lorentz and...
An automated method, requiring the fabrication of a small set of test structures, efficiently extracts the coefficients of Z-parameter based macromodels. The extraction approach has been validated for both heavily and lightly doped substrates and can be applied to a variety of technologies. After the parameters of a macromodel have...
In biological models, advection is inherently a non-local process. Coupled with diffusion, it typically models chemotaxis, which is the response of bacteria to the presence of some chemo attractant. For example, E. coli cells use their flagella to probe their surroundings to determine where they should move. The advection-diffusion equation...
Living in the Pacific Northwest, we are acutely aware of the dangers posed by wildfires. Largely due to the worsening effects of climate change, this danger is only increasing. Along with causing property and economic damage to those communities affected by wildfires, exposure to the smoke generated by wildfires can...
Practical engineering design problems are generally multi-disciplinary with limited budget and high risk in terms of life loss, economic resources, etc. In the early phase of such problems, selection of true efficient designs is desired while minimizing overall design cost by avoiding expensive search processes. However, the task is difficult...
Topology optimization (TO) is a mathematical method to find the optimal size, shape and connectivity of a domain under specified conditions, and has had many applications in engineering design. However, challenges remain in realizing TO as an effective design tool for many design situations. Uncertainty is ubiquitous in nature and...
Simulations of combustion and reacting flows often encounter stiffness in the equations governing chemical kinetics. Explicit solvers for these ordinary differential equations offer low computational expense, but typically cannot efficiently handle stiff systems. In contrast, implicit methods demand greater expense but offer unconditional stability—as a result, most reactive-flow solvers rely...
A common problem in energy allocation problems is managing the trade-off between selling surplus energy to maximize short term revenue, versus holding surplus energy to hedge against future shortfalls. For energy allocation problems, this surplus represents resource flexibility and is quantified as the surplus energy after meeting the demand. The...
In order to more effectively design large, complex systems, risk must be accounted for throughout the design process. A systematic way to account for risk is by using system model simulation. During the conceptual design phase, functional models can be drawn to help the engineer design their system's functional architecture....
The current state of research on gossip techniques for wireless broadcasting is very limited because past research efforts have mostly focused on using gossip techniques for multicast communication. On the other hand, those research efforts that have focused on using gossip techniques for wireless broadcast communications ignore energy efficiency and...
Synchrophasor technology has gained great momentum with the widely adopted concept of smart grids in power systems at transmission and generation level. This has led to an improved state estimation of a power system with the advent of Phasor Measurement Units (PMU). PMUs contribute in providing real-time information about the...
Rising energy demands and the continual push to find more energy efficient technologies have been the impetus for the investigation of waste heat recovery techniques. Diesel engine exhaust heat utilization has the potential to significantly reduce the consumption of fossil fuels and reduce the release of greenhouse gases, because diesel...
We construct an implicit derivative matching (IDM) technique for restoring the accuracy of the Yee scheme for Maxwell's equations in dispersive media with material interfaces in one dimension. We consider media exhibiting orientational polarization, which are represented using a Debye dispersive model, examples of which are water and living tissue....
We hypothesize that the extraordinary maneuverability and efficiency of bats in flight are in part due to the compliant nature of their wing structures. We utilize the parameters of bat bones measured by biologists to create a biologically inspired model of a flapping system consisting of a rotating hub actuator...
In this thesis, we investigate the problem of simulating Maxwell's equations in dispersive dielectric media. We begin by explaining the relevance of Maxwell's equations to
21st century problems. We also discuss the previous work on the numerical simulations of
Maxwell's equations. Introductions to Maxwell's equations and the Yee finite difference...
Single-scattering tomography describes a model of photon transfer through a object in which photons are assumed to scatter at most once. The Broken Ray transform arises from this model, and was first investigated by Lucia Florescu, Vadim A. Markel, and John C. Schotland, [2], in 2010, followed by an inversion,...
The continued development of organic semiconductor materials relies on an understanding of the relationship between optoelectronic properties, molecular structure, and molecular interaction. Several detailed studies of electronic properties in functionalized polyacene materials are presented. A computational model which allows the extraction of charge generation and transport properties from experimental data...
This thesis presents a novel approach for propagation of uncertainty in river systems. Errors in data observations and predictions (e.g., stream inflows), in model parameters, and resulting from the discretization of continuous systems, all point to the need to accurately quantify the amount of uncertainty carried through the modeling process....
Advances in electronic systems have lead to the demand for high resolution, high bandwidth Analog-to-Digital Converters (ADCs). Oversampled ADCs are well- known for high accuracy applications since they benefit from noise shaping and they usually do not need highly accurate components. However, as a consequence of oversampling, they have limited...
This dissertation concerns several problems in the fields of light interaction with nanostructured media, metamaterials, and plasmonics. We present a technique capable of extending operational bandwidth of hyperbolic metamaterials based on interleaved highly-doped InGaAs and undoped AlInAs multilayer stacks. The experimental results confirm theoretical predictions, exhibiting broadband negative refraction response...
Modern day digital systems employ frequency
synthesizers to provide a common clock to the system.
They are undergoing large scale integration due to which, mitigation
of the effect of noise on power supply has become a major design consideration
in clocking circuits. Rapid scaling of CMOS technology mandates the
design...
Deep-sea chemosynthetic ecosystems remain a frontier in marine science. Essential to their role in the ocean ecosystem are endosymbiotic bacteria which support larger megafauna, including the widespread symbiont-bearing Vesicomyid clams. The diversity and characteristics of these symbionts in these clams is only just beginning to be understood with technological advances...