We explore steady-state properties of a driven lattice gas, which is a simple model of interacting many-particle systems, driven far from equilibrium by an external field. First, we study a system on a square lattice with periodic boundary conditions (PBC) along both principal lattice axes, while the drive acts along only one of these axes. For such systems, we analyze the full distribution of structure factors. Next, we investigate the effects of imposing other boundary conditions on the system. In particular, we focus on models with shifted periodic boundary conditions (SPBC) along one axis and open boundary conditions (OBC) along the other axis. The OBC allow us to have a steady flux of particles through the system while the SPBC permits us to drive the system in a range of possibilities. Using Monte Carlo simulation techniques, we discover a rich variety of phenomena, especially at low temperatures. A continuum theory for the densities, based on Langevin equations, is formulated and its predictions compared to simulation data. Many large scale properties are described successfully. / Ph. D.

Chapter 2 deals with a linear city model à la Hotelling where the two firms share linear transport costs with their customers. Mill pricing and uniform delivery pricing are special limiting cases. We characterize the conditions for the existence of a pure strategy equilibrium in the two-stage location-price game. These enable us to identify the causes for non-existence in the two limiting cases. We solve for the equilibrium of a location game between the duopolists with an exogenously given price. When the two firms are constrained to locate at the same central spot, we show the nonexistence of pure strategy equilibria, conjecture the existence of mixed strategy equilibria, and show that any such possible equilibria will always yield positive expected profits. Chapter 3 provides simulations as well as theoretical analysis of potential spatial separation of heterogeneous agents operating on a two-dimensional grid space that represents a city. Heterogeneity refers to a characteristic which is also a determinant of individual valuation of land. We study spatial separation with respect to the distinguishing characteristic and investigate the details of emerging spatial patterns. Simulations suggest that the process of interaction with little trade friction goes through stages which resemble its end-state with high trade friction. Several theoretical examples exhibit a distinguishing characteristic upon which the simulations are based. They reflect some of the causes for spatial separation. Examples for the absence of spatial separation are also given. In Chapter 4 simulations, in addition to some theory, are used to investigate certain aspects of a city formation process. The model assumes two types of economic agents, workers and employers, operating on a two-dimensional grid. The agents have simple preferences, positive for the opposite type and negative for the own type in the own location. In addition, they have positive or negative preference for agglomeration in the own location. The model helps build intuition about a potentially important factor for agglomeration formation, namely, the disparity between entrepreneurial and technical skills in localities. We also determine the minimum level of positive preference for agglomeration that leads to agglomeration formation. / Ph. D.

Atomistic computer simulations were performed using embedded atom method interatomic potentials in α-Fe with impurities and defects. The effects of intergranular carbon on fracture toughness and the mechanisms of fracture were investigated. It was found that as the average grain size changes the dominant energy release mechanism also changes. Because of this the role of the intergranular carbon changes and these mechanisms compete affecting the fracture toughness differently with changing grain size. Grain boundary accommodation mechanisms are seen to be dominant in the fracture of nanocrystalline α-Fe. To supplement this work we investigate grain boundary sliding using the Σ = 5,(310)[001] symmetrical tilt grain boundary. We observe that in this special boundary sliding is governed by grain boundary dislocation activity with Burgers vectors belonging to the DSC lattice. The sliding process was found to occur through the nucleation and glide of partial grain boundary dislocations, with a secondary grain boundary structure playing an important role in the sliding process. Interstitial impurities and vacancies were introduced in the grain boundary to study their role as nucleation sites for the grain boundary dislocations. While vacancies and H interstitials act as preferred nucleation sites, C interstitials do not. / Ph. D.

In an attempt to reach a better understanding of the properties and critical behavior of non-equilibrium systems, we investigate the steady state properties of three simple models, variations of the prototype, the driven Ising lattice gas. Our first system studied is the bilayer model, a stack of two driven Ising lattice gases allowed to interact. We study this model using a very simple analytic approximation, the high temperature expansion. Building on existing simulation data and field theory results, our goal is to test how faithfully the series expansion can reproduce the Monte Carlo phase diagram. We find that the agreement between our calculations and the already reported simulations results is remarkably good. Next, we investigate the critical behavior of a two-dimensional Ising lattice gas driven into a non-equilibrium steady state, subject to a local modification of the dynamics, namely, having anisotropic attempt frequencies for exchanges along different spatial directions. We employ both Monte Carlo simulation techniques and a high temperature expansion approximation and find the phase diagram of the system, perform a finite-size scaling study in order to determine the universality class of the model and compare our simulation results with the phase diagram obtained using the high temperature expansion. We conclude that the bias in the jump rates does not affect the universal critical properties of the system: the modified model is in the same universality class as the driven Ising lattice gas. Our last objective concerns a different inroad into the study of non-equilibrium steady states. Instead of investigating a non-equilibrium steady state via indirect observables, such as correlation functions and order parameters, we seek to compute the steady state probability distribution directly. This is feasible only for systems with a small number of degrees of freedom. We chose to study a one-dimensional version of the so-called two-temperature kinetic Ising model. We solve the master equation exactly for a 1x6 system, and compare the full configurational probability distribution with its equilibrium counterpart. / Ph. D.

We explore the nature of driven stochastic lattice systems with non-periodic boundary conditions. The systems consist of particle and holes which move by exchanges of nearest neighbor particle-hole pairs. These exchanges are controlled by the energetics associated with an internal Hamiltonian, an external drive and a stochastic coupling to a heat reservoir. The effect of the drive is to bias particle-hole exchanges along the field in such a way that a particle current can be established. Hard-core volume constraints limit the occupation of only one particle (hole) per lattice site. For certain regimes of the overall particle density and temperature, a system displays a homogeneous disordered phase. We investigate cooperative behavior in this phase by using two-point spatial correlation functions and structure factors. By varying the particle density and the temperature, the system orders into a phase separated state, consisting of particle-rich and particle-poor regions. The temperature and density for the co-existence state depend on the boundary conditions. By using Monte Carlo simulations, we establish co-existence curves for systems with shifted periodic boundary conditions. / Ph. D.

This dissertation studies the micromechanical behavior of high-performance carbon fiber-reinforced polymer (CFRP) composites through high-fidelity numerical simulations. We investigated multiple transverse cracking of cross-ply CFRP laminates on the microstructure level through simulating large numerical models. Such an investigation demands an efficient numerical framework along with significant computational power. Hence, an efficient numerical framework was developed for simulating 2-D representations of CFRP composites' microstructure. The framework utilizes a nonlinear interface-enriched generalized finite element method (IGFEM) scheme which significantly decreases the computational cost. The framework was also designed to be fast and memory-efficient to enable simulating large numerical models. By utilizing the developed framework, the impacts of a few parameters on the evolution of transverse crack density in cross-ply CFRP laminates were studied. The considered parameters were characteristics of fiber/matrix cohesive interfaces, matrix stiffness, $0^{circ}$~plies longitudinal stiffness. We also developed a micromechanical framework for efficient and accurate simulation of damage propagation and failure in aligned discontinuous carbon fiber-reinforced composites under loading along the fibers' direction. The framework was validated based on the experimental results of a recently developed 3-D printed aligned discontinuous carbon fiber-reinforced composite as the composite of interest. The framework was then utilized to investigate the impacts of a few parameters of the constitutive equations on the strength and failure pattern of the composites of interest. This dissertation also contributes towards improving the computational efficiency of CFRP composites' simulations. We exhaustively investigated the cause of a convergence difficulty in finite element analyses caused by cohesive zone models (CZMs) which are commonly used to simulate fiber/matrix interfaces in CFRP composites. The CZMs' convergence difficulty significantly increases the computational burden. For the first time, we explained the root of the convergence difficulty and proposed a simple technique to overcome the convergence issue. The proposed technique outperformed the existing methods in terms of accuracy and computational cost. We also proposed a deep learning framework for predicting full-field distributions of mechanical responses in 2-D representations of CFRP composites based on the geometry of the microstructures. The deep learning framework can be used as a surrogate to the expensive and time-consuming finite element simulations. The proposed framework was able to accurately predict the stress distribution at an early stage of damage initiation and the failure pattern in representations of CFRP composites microstructure under transverse tension. / Doctor of Philosophy / Carbon fiber-reinforced polymers (CFRPs) are materials that are lightweight with excellent mechanical performance. Hence, these materials have a wide range of applications in various industries such as aerospace, automotive, and civil engineering. The extensive use of CFRPs has made them an active area of research and there have been great efforts to better understand and improve the mechanical properties of these materials over the past few decades. Therefore, CFRP materials and their manufacturing process are constantly changing and new types of CFRPs are kept being developed. As a result, the mechanical behavior of CFRPs needs to be exhaustively investigated to provide guidelines for their optimal engineering design and indicate the future direction of manufacturing improvements. This dissertation studied the mechanical behavior of CFRPs through high-fidelity simulations. Two types of CFRP were investigated: laminates and 3-D printed CFRPs. Laminates are the most popular type of CFRPs which are commonly used to construct the body of aircraft. 3-D printed CFRPs are new types of material that are gaining traction due to their ability to construct structures with complex geometries at high speed and without direct human supervision. The numerical simulations of CFRPs under mechanical loading are time-consuming and require significant computational power even when run on a supercomputer. Hence, this dissertation also contributes to improving the computational efficiency of numerical simulations. To decrease the computational cost, we proposed a technique that can significantly speed up the numerical simulations of CFRPs. Moreover, we utilized artificial intelligence to develop a new framework that can be substituted for the expensive and time-consuming conventional numerical simulations to quickly predict specific mechanical responses of CFRPs.

The interaction of a high power, high frequency (HF) pump/electromagnetic (EM) wave transmitted from a ground-based station with the ionosphere, experiments which have been termed "ionospheric heating", produces secondary radiation known as stimulated electromagnetic emissions (SEEs). SEEs have been developed into powerful diagnostics yielding information such as electron temperature, ion species and hydrodynamic evolution of the modified ionospheric plasma. Classic SEEs which exist outside ±1 kHz of the pump wave frequency (ω0) have recently been classified into wideband SEEs (PW-WSEEs) and distinguished from narrowband SEEs (PW-NSEEs) which exist within ±1 kHz of ω0, where the "PW" prefix has been used to indicate that the frequency regimes in the aforementioned classification are relative to the pump wave (PW) frequency. The occurrence of SEEs near 2ω0 is known as second harmonic generation (SHG). SHG is longstanding and well-established in the field of Laser Plasma Interactions (LPI) where SHG has been harnessed to yield diagnostics such as the velocity of the critical region of the plasma, inference of the region in the plasma where the interaction that results in SHG occurs, plasma turbulence and density scale lengths. Past studies of ionospheric heating SHG were limited by the effective radiated power (ERP) available at ionospheric heating facilities and the frequency resolution of receivers/spectrum analyzers of the time. Experimental observations from these past studies reported either SEEs produced as a result of SHG in isolation or compared these SEEs with PW- WSEEs. Moreover, these experiments did not evaluate effects such as transmit ERP, tilt of the transmit antenna beam from the geomagnetic field (B0) and the offset of ω0 from harmonics of the electron gyrofrequency (ωce) on SEEs within a narrowband of twice the pump wave frequency produced as a result of SHG. Also, these studies did not attempt to draw from the knowledge-base on SHG from LPI. The novelty of the experimental observations in this dissertation is the juxtaposition of PW-NSEEs and second harmonic narrowband SEEs (SH-NSEEs), which are SEEs within kHz of 2ω0, measured at the same time. The heating experiments were all performed at HAARP using an O-mode polarized EM pump wave. Additionally, these measurements evaluate the effects on SHG of the transmit ERP, tilt of the transmit station antenna beam from the geomagnetic field (B0) and the offset of ω0 from nωce, n = 2, 3. The experimental observations show, for the first time, a clear association between PW-NSEEs and SH-NSEEs. This association is subsequently used, in conjunction with theories from LPI to propose the non-linear wave-mixing mechanisms responsible for the SH-NSEEs. As a prelude to harnessing the wealth of diagnostics that can be obtained from SHG, initial diagnostics of the velocity of the critical region and the interaction region where SHG occurs are determined using theories from LPI. With the association between PW-NSEEs and SH-NSEEs established, Particle- In-Cell (PIC) simulations are used to investigate the characteristics of a PW- NSEE herein referred to as the "SBS line", produced as a result of stimulated Brillouin scatter (SBS) instability in which the pump EM wave decays into a backscattered EM wave and an ion acoustic wave. The PIC simulations reveal that for high pump powers, the SBS line, which is intense at the onset of the heating experiment, is suppressed within 3 seconds due to the development of cavities in the ionospheric plasma (density) in which the pump wave depletes its energy in heating up electrons. Although, no PIC simulation results of SHG have been presented in this work, the association between PW-NSEEs and SH-NSEEs shown in this work is used to propose that similar mechanisms are responsible for the suppression the SBS line and its associated SH-NSEE for high pump powers. Results from ionospheric heating experiments presented in this dissertation show a rapid suppression of both the SBS line and its associated SH-NSEE for high pump powers. The attribution of the suppression of SH-NSEEs to the development of artificial field-aligned irregularities (AFAIs) in a past study fails to explain the rapid suppression in the experimental observations contained herein since the suppression occurs on a much faster timescale than the development of AFAIs. Thus, the PIC model results have led to a more feasible interpretation of the observed rapid suppression. To re-iterate, the contributions of this dissertation are as follows: 1. First observations of an SH-NSEE named "SH decay line" within 2ω0±30 Hz. The SH decay line occurs at the same transmit power as the SBS line within ω0±30 Hz and both of these SEEs are suppressed for ω0 ≈ 3ωce. Offset of the SH decay line from 2ω0 is twice the offset of the SBS line from ω0. 2. First experimental evaluation of the impact of B0 assessed by stepping the transmit beam offset from B0 and stepping ω0 near 2ωce shows contemporaneous SH-NSEEs and PW-NSEEs both ordered by the O+ ion cyclotron frequency. 3. First experimental observations of suppression of SBS line and SH decay line for high pump powers, which unlike a past study cannot be attributed to AFAIs. 4. First PIC simulation investigation of suppression of SBS line observed during high pump power ionospheric heating, revealing depletion of pump energy in heating electrons in cavities created in the plasma (density) as the mechanism responsible for the suppression. Broadening of SBS line observed in ionospheric heating with high power is also observed in PIC simulation results. This work has laid the foundations to develop SHG into powerful ionospheric diagnostics. / Doctor of Philosophy / When a high power, high frequency radio wave is injected from a ground-based transmit station into the ionosphere, a region of Earth's atmosphere containing charged particles in addition some neutral atoms and molecules, the frequency spectrum measured at a location removed from the transmit station shows emissions at other frequencies in addition to an emission at the transmit frequency. The emissions at these other frequencies are known as stimulated electromagnetic emissions (SEEs). The frequency offsets of SEEs contain information such as the average kinetic energy associated with random motion of electrons, a parameter known as electron temperature and the ion species present in the region of the ionosphere the radio wave is injected into. The occurrence of SEEs near twice the pump wave frequency is known as second harmonic generation. This dissertation presents experimental observations that compare SEEs which exist within ±1 kHz of the transmit frequency with SEEs which exist within a similar frequency range of twice the transmit frequency unlike past studies. This dissertation also investigates effects of varying the transmit frequency, power and the direction of the transmit station antenna beam relative to the local direction of the magnetic field of the Earth. These new studies reveal, for the first time, a similarity in characteristics of the SEEs near the transmit frequency and two times the transmit frequency. This similarity is used in conjunction with theories from studies of Laser Plasma Interaction (LPI), which have corollaries with high power radio wave-ionosphere interaction, to propose the processes that underlie the occurrence of SEEs near twice the transmit frequency. Methods from LPI have also been used for the first time to obtain measurements of some parameters of the ionosphere. High power radio wave-ionosphere interaction experiments are very expensive and moreover, direct measurement of ionospheric parameters/processes require radar facilities which may not be available or sounding rockets or satellites which increase the cost of experiments. Computer simulations offer a facile and an inexpensive means to investigate SEEs and processes internal to the ionosphere. Computer simulations have been used for the first time in this dissertation to investigate the mechanisms responsible for the characteristics of SEEs near the transmit frequency for low and high transmit powers. Since an association has been established in this dissertation between SEEs near the transmit frequency and SEEs near twice the transmit frequency, the mechanisms responsible for the characteristics for the SEEs near the transmit frequency for high transmit power, have been proposed to be the same mechanisms responsible for the characteristics of SEEs near twice the transmit frequency for a similar transmit power regime. The experimental results, computer simulation results and the corollaries drawn between high power radio wave-ionosphere interaction and LPI detailed in this dissertation have opened new doors to develop SEEs near twice the transmit frequency into a powerful tool to study the ionosphere.

Coarse-grained (CG) molecular dynamics (MD) simulations have seen a wide range of applications from biomolecules, polymers to graphene and metals. In CG MD simulations, atomistic groups are represented by beads, which reduces the degrees of freedom in the systems and allows larger timesteps. Thus, large time and length scales could be achieved in CG MD simulations with inexpensive computational cost. The representative example of large time- and length-scale phenomena is the conformation transitions of single polymer chains as well as polymer chains in their architectures, self-assembly of biomaterials, etc. Polymers exist in many aspects of our life, for example, plastic packages, automobile parts, and even medical devices. However, the large chemical and structural diversity of polymers poses a challenge to the existing CG MD models due to their limited accuracy and transferabilities. In this regard, this dissertation has developed CG models of polymers on the basis of accurate and transferable hydrocarbon models, which are important components of the polymer backbone. CG hydrocarbon models were created with 2:1 and 3:1 mapping schemes and their force-field (FF) parameters were optimized by using particle swarm optimization (PSO). The newly developed CG hydrocarbon models could reproduce their experimental properties including density, enthalpy of vaporization, surface tension and self-diffusion coefficients very well. The cross interaction parameters between CG hydrocarbon and water models were also optimized by the PSO to repeat the experimental properties of Gibbs free energies and interfacial tensions. With the hydrocarbon models as the backbone, poly(acrylic acid) (PAA) and polystyrene (PS) models were constructed. Their side chains were represented by one COOH (carboxylic acid) and three BZ beads, respectively. Before testing the PAA and PS models, their monomer models, propionic acid and ethylbenzene, were created and validated, to confirm that the cross interactions between hydrocarbon and COOH beads, and between hydrocarbon and BZ beads could be accurately predicted by the Lorentz-Berthelot (LB) combining rules. Then the experimental properties, density of polymers at 300 K and glass transition temperatures, and the conformations of their all-atom models in solvent mixtures of water and dimethylformamide (DMF) were reproduced by the CG models. The CG PAA and PS models were further used to build the bottlebrush copolymers of PAA-PS and to predict the structures of PAA-PA in different compositions of binary solvents water/DMF. Although CG models are useful in understanding the phenomena at large time- or length- scales, atomistic information is lost. Backmapping is usually involved in reconstructing atomistic models from their CG models. Here, four machine learning (ML) algorithms, artificial neural networks (ANN), k-nearest neighbor (kNN), gaussian process regression (GPR), and random forest (RF) were developed to improve the accuracy of the backmapped all-atom structures. These optimized four ML models showed R2 scores of more than 0.99 when testing the backmapping against four representative molecules: furan, benzene, naphthalene, graphene. / Doctor of Philosophy / Polymers have a wide range of applications from packaging, foams, coating to pipes, tanks and even medical devices and biosensors. To improve the properties of these materials it is important to understand their structure and features responsible for controlling their properties at the molecular-level. Molecular dynamic (MD) simulations are a powerful tool to study their structures and properties at microscopic level. However, studying the molecular-level conformations of polymers and their architectures usually requires large time- or length-scales, which is challenging for the all-atom MD simulations because of the high computational cost. Coarse-grained (CG) MD simulations can be used to study these soft-materials as they represent atomistic groups with beads, enabling the reduction of the system sizes drastically, and allowing the use of large timesteps in MD simulations. In MD simulations, force-fields (FF) that describe the intramolecular and intermolecular interactions determine the performance of simulations. Here, we firstly optimized the FF parameters for hydrocarbons. With the optimized CG hydrocarbon models, two representative CG polymer models, poly(acrylic acid) (PAA) and polystyrene (PS) were built by using hydrocarbons as the backbones of polymers. Furthermore, the PAA and PS chains were grafted on a linear hydrocarbon backbone to form a bottlebrush copolymer. Although CG MD models are useful in studying the complex process of polymers, the atomic detailed information is lost. To reconstruct accurate atomistic structures, backmapping by using machine learning (ML) algorithms was performed. The performance of the ML models was better than that of the existing backmapping packages built in Visual Molecular Dynamics (VMD).

Anyone who has eaten spicy foods has experienced the adverse effects of capsaicin, the pungent chemical found in hot chili that causes a burning sensation. The specific action of capsaicin occurs by the activation of receptors in sensory neurons. This thesis investigates the interaction of capsaicin with model cell membranes representing the structure of neurons. In particular, we are interested in the changes induced by capsaicin to the structure and dynamics of membranes. Molecular dynamics simulations are used to study the molecular interactions. The first part of this study evaluates different molecular representations for capsaicin in an 1-octanol/water system. This inhomogeneous system is commonly used to determine the partition of compounds between hydrophilic and hydrophobic environments, as that found in biological membranes. The results of these simulations validate the OPLS united-atom force field as a reasonable molecular representation of capsaicin, as it describes the behavior of capsaicin both quantitatively and qualitatively in 1-octanol/water mixtures. In the second part, simulations are performed for capsaicin and model cell membranes consisting of dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylethanolamine, two of the most commonly found lipids. Simulations investigated capsaicin in the aqueous and lipid phases. The results provide insight into the changes to the bilayers caused by capsaicin. Bilayers containing dipalmitoylphosphatidylethanolamine showed lower permeabilities to capsaicin than those composed of pure dipalmitoylphosphatidylcholine. Temperature is found to be an important factor in the permeability of capsaicin in the bilayer. Capsaicin in the bilayer concentrated in a region beneath the lipid/water interface, in which favorable hydrophilic and lipophilic interactions occur. The structure of the bilayer is not significantly changed at the concentrations of capsaicin considered. One important result from the simulations indicates that the interfacial density decreases with increasing capsaicin concentration in the bilayer, supporting the experimental observations of increased permeability in bilayers exposed to capsaicin. / Master of Science

Alzheimer's disease is the leading cause of senile dementia in the elderly, and as life expectancy increases across the globe, incidence of the disease is continually increasing. Current estimates place the number of cases at 25-30 million worldwide, with more than 5.4 million of these occurring in the United States. While the exact cause of the disease remains a mystery, it has become clear that the amyloid β-peptide (Aβ) is central to disease pathogenesis. The aggregation and deposition of this peptide in the brain is known to give rise to the hallmark lesions associated with Alzheimer's disease, but its exact mechanism of toxicity remains largely uncharacterized. Molecular dynamics (MD) simulations have achieved great success in exploring molecular events with atomic resolution, predicting and explaining phenomena that are otherwise obscured from even the most sensitive experimental techniques. Due to the difficulty of obtaining high-quality structural data of Aβ and its toxic assemblies, MD simulations can be an especially useful tool in understanding the progression of Alzheimer's disease on a molecular level. The work contained herein describes the interactions of Aβ monomers and oligomers with lipid bilayers to understand the mechanism by which Aβ exerts its toxicity. Also explored is the mechanism by which flavonoid antioxidants may prevent Aβ self-association and destabilize toxic aggregates, providing insight into the chemical features that give rise to this therapeutic effect. / Ph. D.