<p> [Co/Pd]<i>_n</i> multilayers with different number of repetitions n were deposited on Si substrates in order to study the magnetic properties and Hall resistivity in this system. The magnetic moment dependence on applied field was studied in parallel (in-plane) and perpendicular (out-of-plane) configurations. The [Co/Pd]<i>_n</i> multilayers with 2 and 3 repetitions, with thickness of the Co sublayer of 0.8 and 1.0 nm and thickness of the Pd sublayer of 1.3 and 2.0 nm, were found to have perpendicular magnetic anisotropy. The Hall resistivity dependence on applied field was measured at different temperatures. The Hall hysteresis loops confirm the perpendicular anisotropy of the multilayers, and indicate that the origin of the anomalous Hall effect (AHE) in this system, with low number of repetitions, is dominated by surface scattering.</p>

<p> Atomic resonances present a difficult chapter in the study of atomic structure. The calculation and measurement of these resonant states have provided a challenge for both theorists and experimentalists. This work focuses on the numerical calculation of the resonant states. Some years ago a method to calculate the resonant states of three-body atomic interactions was developed. This method involves solving the Faddeev equations using a Merkuriev cut and a Coulomb-Sturmian basis, and will be the method used for the calculations in this work. This method was used as an alternative to the more conventional methods of calculating atomic resonant states. At the time of its derivation, the method was used to calculate the narrow-width resonances of the electron-Positronium (e &ndash; Ps) system, which showed accurate results with respect to the calculations done by other groups using alternative methods. Additionally, the method saw an emergence of resonances (broad-width) which line-up to the system thresholds. We have come to call these broad-width resonances the threshold resonances. However, at the time, these threshold resonances proved too computationally intensive to make confident results. Now, with the assistance of better computational resources and an improved code, this problem is again addressed. </p><p> New calculations of the narrow-width and threshold resonances were completed which support the appearance of the threshold resonances in the e &ndash; Ps system. The threshold resonances were observed lining up at the first, second, and third two-body thresholds, a trend that is assumed to continue at even higher energies. Calculations were carried out for both the 1S and 3S states. After successfully making calculations of the e &ndash; Ps system resonant states, calculations were also carried out for the electron-Hydrogen (e&ndash;H) 1S and 3S resonances. The calculations for the e &ndash; H system were carried out for the threshold resonances emerging from the 1st threshold. Additionally, we propose an explanation for the emergence of the threshold resonances.</p>

<p> The likelihood that gravitational waves from stellar-size black holes spiraling into a supermassive black hole would be detectable by a space based gravitational wave observatory has spurred the interest in studying the extreme mass-ratio inspiral (EMRI) problem and black hole perturbation theory (BHP). In this approach, the smaller black hole is treated as a point particle and its trajectory deviates from a geodesic due to the interaction with its own field. This interaction is known as the gravitational self-force, and it includes both a damping force, commonly known as radiation reaction, as well as a conservative force. The computation of this force is complicated by the fact that the formal expression for the force due to a point particle diverges, requiring a careful regularization to find the finite self-force. </p><p> This dissertation focuses on the computation of the scalar, electromagnetic and gravitational self-force on accelerated particles. We begin with a discussion of the "MiSaTaQuWa" prescription for self-force renormalization (Mino, Sasaki, Takasugi 1999 and Quinn and Wald, 1999) along with the refinements made by Detweiler and Whiting (2003), and demonstrate how this prescription is equivalent to performing an angle average and renormalizing the mass of the particle. With this background, we shift to a discussion of the "mode-sum renormalization" technique developed by Barack and Ori (2000), who demonstrated that for particles moving along a geodesic in Schwarzschild spacetime (and later in Kerr spacetime), the regularization parameters can be described using only the leading and subleading terms (known as the A and B terms). We extend this to demonstrate that this is true for fields of spins 0, 1, and 2, for accelerated trajectories in arbitrary spacetimes. </p><p> Using these results, we discuss the renormalization of a charged point mass moving through an electrovac spacetime; extending previous studies to situations in which the gravitational and electromagnetic contributions are comparable. We renormalize by using the angle average plus mass renormalization in order to find the contribution from the coupling of the fields and encounter a striking result: Due to a remarkable cancellation, the coupling of the fields does not contribute to the renormalization. This means that the renormalized mass is obtained by subtracting (1) the purely electromagnetic contribution from a point charge moving along an accelerated trajectory and (2) the purely gravitational contribution of an electrically neutral point mass moving along the same trajectory. In terms of the mode-sum regularization, the same cancellation implies that the regularization parameters are merely the sums of their purely electromagnetic and gravitational values. </p><p> Finally, we consider the scalar self-force on a point charge orbiting a Schwarzschild black-hole following a non-Keplerian circular orbit. We utilize the techniques of Mano, Suzuki, and Takasugi (1996) for generating analytic solutions. With this tool, it is possible to generate a solution for the field as a series in the Fourier frequency, which allows researchers to naturally express the solutions in a post Newtonian series (see Shah et. al. 2014). We make use of a powerful insight by Hikida et. al.(2005), which allows us to perform the renormalization analytically. We investigate the details of this procedure and illuminate the mechanisms through which it works. We finish by demonstrating the power of this technique, showing how it is possible to obtain the post Newtonian expressions by only explicitly computing a handful of modes.</p>

<p> The compelling astrophysical evidence for dark matter on one hand and the experimental evidence for neutrino masses on the other, demands modifications beyond the Standard Model. Therefore, building new models by extending the symmetries and particle content of the Standard Model is being pursued to remedy these problems. In this thesis, various models along with their predictions are presented. First, a gauge SU(2)<i>_N</i> extension of the Standard Model, under which all of the Standard Model particles are singlet is introduced. The inverse seesaw mechanism is implemented for neutrino mass, with the new gauge boson as a dark matter candidate. The second paper is a gauge B-L extension of the Standard Model which breaks down to <b> Z</b>₃, and it includes a long-lived dark matter candidate. The next model assumes that leptons do not couple directly to Higgs, and one loop mass generation is considered with important consequences, including Higgs decay, muon anomalous magnetic moment, etc. We then look at a U(1) gauge extension of the supersymmetric Standard Model, which has no &mu; term, and the Higgs boson's mass supersymmetric constraint is relaxed. The next model is a gauge B-L extension of the Standard Model with radiative seesaw neutrino mass and multipartite dark matter. We then consider another gauge U(1) extension under which quarks and leptons of each family may transform differently, while flavor-changing interactions are suitably suppressed. The next paper has an unbroken gauge SU(2) symmetry, which becomes confining at keV scale. We discuss the cosmological constraints and the implications for future <i>e</i>⁺<i>e</i>^&ndash; colliders. Finally, an alternative left-right model is proposed with an automatic residual <i>Z</i>₂ &times; <i>Z</i>₃ symmetry, such that dark matter has two components, i.e., one Dirac fermion and one complex scalar.</p><p>

During my thesis work I have investigated the problem of polyelectrolyte characterization and in particular how to interpret the experimental data to obtain the mass and gyration radius of short polyelectrolytes. This is usually a challenging problem for experimentalists to deal with. For example, the interpretation of the static light scattering data to obtain the gyration radius becomes increasingly inaccurate as the size of the chain becomes very much smaller then the light wavelength. Also, the interpretation of membrane osmomometry data is complicated by the leakage of the solute of low molecular weight polymers and so forth. There are, however, a number of approaches to deal with these problems. In the first chapter of my thesis I obtained a crossover formula of the second virial coefficient of polyelectrolytes that correctly reproduces the perturbative and asymptotic polymer regimes in addition to the salt concentration dependence at high-to-medium salt concentrations. This formula will then be combined with similar crossover formula for the radius of gyration to interpret the later from the second virial coefficient measurement. On the technical side of the story, the crossover formula was obtained by combining the renormalization group equation (to the first nontrivial order in epsilon) with the direct d=3 computation of the perturbative expansion (to the second order in the two coupling constants) obtained from double inverse Laplace transform. The second chapter of my dissertation is about the translocation phenomena. Translocation is a phenomena of threading a polymer through narrow pores and/or channels. This is very promising technique to measure the molecular weight of every individual polymer in the solution. Indeed, the polymer chain threading through the pore blocks the flow of electric current that also flows through the pore. By the duration of the current blockade the length of polymer chain can be obtained. Unfortunately, there are a number of problems this approach encounters. One of them is that the only so far practically obtainable nanometer-size pore is the alpha hemolysine one which has a complicated internal layout—a spherical (more or less) vestibule. This nasty feature makes current blockade vs time data harder to interpret. There is a way to bypass this problem. Recently a number of research groups began to modify the pore via the directed mutagenesis to reduce the time the chain spends in the vestibule. In my work I theoretically investigated translocation of the polyelectrolyte chain through a spherical cavity with tunable charge. The results provide some guidelines on how to reduce the influence of the vestibule on the translocation time if we are to modify the chain in addition to the decorating the pore with charges. This work includes a number of interesting techniques. It is based on the self-consistent field theory which gives us nonlinear Schroedinger and Poisson-Boltzmann equations. These equations are then solved numerically via a finite difference schemes. Lets point out possible extensions of this work. The SCFT technique is a primary computational tool for polyelectrolyte brushes and melts. Those things can be useful for the rapidly developing technology of pore gating, brush filtration and brush lubrication, just to name a few.

<p> In this thesis, we investigate theoretically a new model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of arbitrary valences, and then beyond, where correlation effects are systematically taken into account in a loop expansion. In particular, we compute exactly various one-loop quantities, including electrostatic potentials, ion distributions, and chemical potentials, not only for symmetric (1; 1) electrolyte but also for asymmetric (2; 1) electrolyte, and make use of these quantities to address charge regulation at the one-loop level. We find that correlation effects give rise to various phase transitions in the adsorption of ions, and present phase diagrams for (1; 1) and (2; 1) electrolytes, whose distinct behaviors suggest that charge regulation, at the one-loop level, is no longer universal but depends crucially on the valency of the ions.</p>

<p> We analyze branching polymers, called dendrimers, grafted to a flat surface, called a brush, which perfectly fill space above the surface, called a melt, with continuously defined branching profiles. The profiles we consider are representative of traditionally branching and statistically branching dendrimers. Using the ansatz of a parabolic monomer interaction pressure, derived from the polymer brush system and appropriated through an analogy to a time dependent mass in a gravitational potential, analytical solutions for the hight of a monomer from the grafting surface as a function of its position on the polymer chain were found. We were then able to numerically solve for the density of free ends as a function of height. Within our ansatz, there exists a degeneracy of the free energy with respect to an individual dendrimers maximal height. We find that the dendrimer melt brush consists of dendrimers shaped like buoys located at all heights attached to the grafting surface by a highly stretched web of monomers.</p>

<p>Electron systems in the quantum Hall regime change from a liquid state to a Wigner crystal state as the filling factor is lowered below approximately 1/5. This phase transition can be studied with theoretical methods by comparing the ground-state energies of the quantum liquid and the quantum Wigner crystal. Past studies have not included realistic effects such as finite thickness, Landau-level mixing, and disorder on the electron system. We expand upon the classic work by Maki and Zotos to calculate Wigner crystal energies that include a finite thickness of the two-dimensional electron lattice. </p>

<p> Self-propelled particles (SPPs) are particles who, by themselves, are able to generate persistent motion by converting energy from an ambient reservoir into work. Collections of such particles form a class of intrinsically out-of-equilibrium fluids called active fluids which have energy input and dissipation at the scale of the particle constituents. Despite their non-equilibrium nature, large scale, cohesive structures will often spontaneously emerge. These structures can manifest in microscopic realizations such as collective cell motility but also in much larger objects like flocks of birds. In this work we apply the powerful tools of non-equilibrium statistical mechanics to study SPPs both at the single particle level and for collections of interacting particles. </p><p> The primary non-equilibrium characteristic of a SPP is the persistent correlation in its direction of motion. In the first theme, we address the following question: What is the effect of the details of the decorrelation process on long time properties of SPPs? This question is addressed in 2 parts. First, we compare the response of active Brownian particles and run-and-tumble particles when subject to external torques. Second, we investigate the nature of the non-equilibrium steady state by constructing the Smoluchowski equation. The second topic comes with the added feature that it allows us to address the validity of different approximation techniques available to deal with correlated stochastic processes. </p><p> In the second theme we construct a theoretical framework to characterize the non-equilibrium steady states of interacting SPPs. Starting from a microscopic model of self-propelled hard spheres we use tools of non-equilibrium statistical mechanics and the kinetic theory of hard spheres to derive a Smoluchowski equation for interacting active Brownian particles. We illustrate the utility of the statistical mechanics framework developed with two applications. First, we derive the steady state pressure of the hard sphere active fluid in terms of the microscopic parameters and second, we identify the critical density for the onset of motility-induced phase separation in this system. We show that both these quantities agree well with overdamped simulations of active Brownian particles with excluded volume interactions given by steeply repulsive potentials. The results presented in this section can be used to incorporate excluded volume effects in diverse models of self-propelled particles. </p><p> The final theme is an application of the self-propelled particle model to systems of motile cells. Some cells are able to deform the substrate they are adhered to and at the same time are able to sense and respond to their mechanical environment. For a collection of cells this can lead to a elastic interaction between them. In this study the cells are modeled as self-propelled &ldquo;force dipoles&rdquo; that deform the surface. We find that a combination of only activity and the medium mediated elastic interaction is enough to form the collective swarming, clustering, and streaming seen in some experiments. The numerical phenomenology is then rationalized using a mean-field hydrodynamic theory.</p><p>

<p> Standard Quantum Mechanics, although successful in terms of calculating and predicting results, is inherently diffcult to understand and can suffer from misinterpretation. Entropic Dynamics is an epistemic approach to quantum mechanics based on logical inference. It incorporates the probabilities that naturally arise in situations in which there is missing information. It is the author's opinion that an advantage of this approach is that it provides a clearer mental image with which to picture quantum mechanics. This may provide an alternate means of presenting quantum mechanics to students. After a theory is presented to students, an instructor will then work through the paradigmatic examples that demonstrate the theory. In this thesis, we will be applying Entropic Dynamics to some of those paradigmatic examples. We begin by reviewing probability theory and Bayesian statistics as tools necessary for the development of Entropic Dynamics. We then review the topic of entropy, building from an early thermodynamic interpretation to the informational interpretation used here. The development of Entropic Dynamics involves describing a particle in terms of a probability density, and then following the time evolution of the probability density based on diffusion-like motion and the maximization of entropy. At this point, the review portion of the thesis is complete. </p><p> We then move on to applying Entropic Dynamics to several of the paradigmatic examples used to explain quantum mechanics. The rst of these is wave packet expansion. The second is interference, which is the basis behind many of the important phenomena in quantum mechanics. The third is the double slit experiment, which provides some interesting insight into the subject of interference. In particular, we look at the way in which minima can occur without a mechanism for destructive interference, since probabilities only add. The idea of probability flow is very apparent at this point in the discussion. The next example is that of the harmonic oscillator. This leads to an interesting insight concerning rotation and angular momentum as it corresponds to the flow of probability. The last example explored is that of entanglement. The discussion begins with a review of EPR, but then comes to the interesting conclusion that many of the problems inherent in the traditional approach to entanglement do not exist in Entropic Dynamics. The last topic covered in this thesis consists of some remarks concerning the state of education research as it pertains to quantum mechanics and the ways in which Entropic Dynamics might address them.</p><p>