PHD, Kent State University, 2024, College of Arts and Sciences / Department of Physics

The thermodynamics of N = 4 supersymmetric Yang-Mills theory in four dimensions (SYM4,4) is of great interest since, at finite-temperature, the weak-coupling limit of this theory has many similarities with quantum chromodynamics (QCD). Unlike QCD, however, in SYM4,4 it is possible to make use of the AdS/CFT correspondence between gravity in anti-de Sitter space (AdS) and the large-Nc limit of conformal field theories (CFT) on the boundary of AdS to obtain results for SYM4,4 thermodynamics in the strong coupling limit. The mathematical structure of SYM4,4 is similar to that of QCD, the difference is mostly in the number of degrees of freedom and the representations of fields. There are four Majorana fermions and six scalars and all the fields are in the adjoint representation. In the last decade or so the thermodynamics of SYM4,4 in a strong-coupling regime received a great deal of attention due to AdS/CFT where in SYM4,4 is mapped to its gravity dual. In this limit, the thermodynamics has been computed to the order λ−3/2, where λ = Nc g2 is the ‘t Hooft coupling. In the opposite sector of weak coupling, prior to our work, the free energy density of SYM4,4 was known to the order λ3/2. In this regime, calculations are performed using perturbative field theory methods. This weak-coupling expansion of SYM4,4 like QCD can pushed until λ5/2, after which non-perturbative effects come into play. In this SYM4,4 free energy density expansion interesting observations are made by constructing a generalized Pade which interpolates between strong and weak coupling expansion. The weak coupling expansion converges towards this Pade for λ ≲ 1 and the strong coupling for λ ≳ 10. The makes the weak and strong coupling expansion and their convergence in the intermediate region of 1 ≲ λ ≲ 10 of a great deal of interest. On the weak-coupling side the free energy density calculations in SYM4,4, like in QCD, are done and improved upon using various perturbative field t (open full item for complete abstract)

Committee: Michael Strickland Dr. (Advisor); Zhangbu Xu Dr. (Committee Member); Artem Zvavitch Dr. (Committee Member); Edgar Koojiman Dr. (Committee Member); Khandker Quader Dr. (Committee Member) Subjects: Nuclear Physics; Particle Physics; Physics

Doctor of Philosophy, The Ohio State University, 2023, Chemistry

Algebraic diagrammatic construction (ADC) theory has been found to be a relatively low-cost method with attractive features for the study of photochemical problems. However, because the original formulation of ADC is formulated with a single Slater determinant approximating the ground-state wavefunction, it is insufficient in reproducing accurate photochemical results for systems that exhibit strong correlation effects. In this thesis, I present new approximations in multireference algebraic diagrammatic construction (MR-ADC) theory for simulating electronic excitations of strongly-correlated molecular systems. First, I present the theory and implementation of new strict and extended second-order MR-ADC methods (MR-ADC(2) and MR-ADC(2)-X, respectively) and benchmark these methods for low-lying excited states in several small molecules, including the carbon dimer, ethylene, and butadiene. Next, I present an implementation of MR-ADC methods that incorporates the core-valence separation (CVS) approximation, providing efficient access to simulating core-excited states. The potential of CVS-MR-ADC for systems with multiconfigurational electronic structure is examined by calculating the K-edge XAS spectrum of the ozone molecule and the dissociation curve of core-excited molecular nitrogen. I conclude with an efficient implementation of CVS-MR-ADC, reformulated in terms of spin-free quantities, and present preliminary data on core-excitations in large chemical systems that were not computationally feasible using spin-orbital quantities.

Committee: Alexander Sokolov (Advisor); Bern Kohler (Committee Member); John Herbert (Committee Member) Subjects: Physical Chemistry

PHD, Kent State University, 2021, College of Arts and Sciences / Department of Physics

The goal of high-energy nuclear physics is to understand the dynamics and properties of the various forms and phases of the strongly-interacting matter. Heavy-ion collision experiments are performed to deposit a large energy density in a very small volume of space and generate a form of extremely hot matter called the quark-gluon plasma (QGP). The behavior of the generated matter shows signatures of collectivity allowing phenomenological models based on statistical or fluid dynamical descriptions to be used successfully to analyze the outcomes the experiments. However, the very short lifetime and the extreme conditions of the QGP call for the construction of theoretical models based on the physics of nonequilibrium systems. Understanding the properties of QGP requires the study of collective excitations in the emergent many-body dynamics of the quarks and gluons as the fundamental objects in the theory of quantum chromodynamics. In this dissertation, the collective excitations of the nonequilibrium QGP are studied by calculating the quark and gluon self-energies within the hard loop effective theory. By extracting the solutions of the gluon dispersion relation in the complex plane, the presence of unstable modes in the momentum-anisotropic QGP is studied. The quark self-energy is also used to calculate the rate of photon emission from QGP in the subsequent studies performed as part of this dissertation. Electromagnetic probes (photons and dileptons) are considered among the best observables for extracting information about the early stages of evolution of the strongly interacting matter produced in heavy-ion collisions. In contrast to the hadrons, the emitted photons and leptons are not distorted by a strong coupling to the medium and they can escape the system with much larger mean free paths. Since the dilepton and photon emission rates from QGP are directly affected by the momentum distribution of the partonic degrees of freedom, their emission patter (open full item for complete abstract)

Committee: Michael Strickland Dr. (Advisor); Declan Keane Dr. (Committee Member); Jonathan Selinger Dr. (Committee Member); Barry Dunietz Dr. (Committee Member); Gang Yu Dr. (Committee Member) Subjects: Nuclear Physics; Particle Physics; Physics

Bachelor of Science, Wittenberg University, 2020, Math

The objective of this thesis is to understand the systematic analytic treatment of the model presented in Anna Ghazaryan and Vahagn Manukian's journal article, “Coherent Structures in a Population Model for Mussel-Algae Interaction," which concentrates on the formation of mussel beds on soft sediments, like those found on cobble beaches. The study will investigate how the tidal flow of the water is the main structure that creates the mussel-algae interaction observed on soft sediments. With this investigation, the idea of fast-time and slow-time systems is explicated according to Geometric Singular Perturbation Theory, how Invariant Manifold Theory proves the existence of our solutions, the process of non-dimensionalization, and the re-scaling of the model. It will apply concepts found in nonlinear dynamics to discover equilibria and nullclines of the system. Finally, the study will discuss what the findings mean in context of the population model and the implications of tidal flow on other ecological relationships.

Committee: Adam Parker (Advisor); Alyssa Hoofnagle (Committee Member); Jeremiah Williams (Committee Member) Subjects: Applied Mathematics; Aquatic Sciences; Ecology; Mathematics

Doctor of Philosophy, The Ohio State University, 2021, Chemistry

The computational bottleneck of applying quantum chemistry methods has always been a significant obstacle to calculating the properties of condensed-phase systems. In this work we present accurate, scalable methods that push the dynamic range of ground- and excited-state quantum chemistry into the condensed-phase. First, we introduce an extension of symmetry-adapted perturbation theory that includes nonadditive (many-atom) dispersion effects that are essential in the description of large systems. Application of this approach to the study of π-π interactions has revealed that the dominant paradigm (based on low-order electrostatic multipoles) for understanding π-stacking is fundamentally flawed. We propose a reformulation of the electrostatic model of aromatic π-π interactions that is based on van der Waals forces, instead. Our work with π-stacking is exemplary of the utility that symmetry-adapted perturbation theory with many-body dispersion (SAPT+MBD) has as an interpretive tool, and our results suggest that it will be extremely useful in characterizing intermolecular interactions at the nanoscale. In the second part of this work, we introduce several efficient methods for solution-phase photochemistry. Contributions of this work include the implementation of a vibrational exciton model, a new root-homing algorithm based on level shifting, and introducing natural charge-transfer orbitals to combat spurious states in solution-phase time-dependent density functional theory (TDDFT). The vibrational exciton model is extremely scalable, and we use it to investigate the infrared spectrum of >200 surfactant molecules at the air/water interface. Our results have lead to insights into the nature of signal depletion in one-dimensional infrared spectra of self-aggregating molecules at interfaces. Our root-homing algorithm is robust to variational collapse, and shows promise in finding orbital-optimized excited states when the density of states becomes large. Lastly, our na (open full item for complete abstract)

Committee: John Herbert (Advisor); Heather Allen (Committee Member); Sherwin Singer (Committee Member); Barbara Ryden (Committee Member) Subjects: Physical Chemistry

Doctor of Philosophy, The Ohio State University, 2016, Chemistry

We discuss the development and application of a number of fragmentation methods focused on understanding of intermolecular interactions in different systems. The advantage of fragmentation methods is to avoid the exponential growth of required computational power for the most advanced and accurate quantum chemistry theories which preclude the application in systems with large number of atoms and molecules. In those fragmentation methods, the full chemical system is partitioned into different subsystems, circumventing the exponential scaling computational cost. How this partitioning is performed and applied appropriately is the principal emphasis of this work. One of the fragmentation methods developed by our group, called extended XSAPT, combines an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large non-covalent assemblies such as molecular and ionic clusters, supramolecular complexes, clathrates, or DNA--drug complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically-meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and the empirical atom-atom dispersion potentials are introduced here in an attempt to improve this situation. Comparison to high-level ab initio benchmarks for biologically-related dimers, water clusters, halide--water clusters, supremolecular complexes, methane clathrate hydrates, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as third to fifth order with respect to monomer size, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of (open full item for complete abstract)

Committee: John Herbert (Advisor); Sherwin Singer (Committee Member); Marcos Sotomayor (Committee Member) Subjects: Chemistry; Physical Chemistry

Doctor of Philosophy, University of Akron, 2014, Chemical Engineering

The main objective of our work is to construct a meaningful and robust connection between molecular simulation and theory in the framework of an Equation of State (EOS). We propose to evaluate the repulsive, dispersive and electrostatic parameters of the Helmholtz free energy by comparing to the corresponding contributions from simulation. To this end, we employ Thermodynamic Perturbation Theory (TPT) to establish the bridge between the theory and simulation for the repulsive and attractive interactions of real molecular fluids. For the electrostatic interactions, a novel procedure is presented to mimic the long-range interactions between partial charges by an effective short-range association potential. The resulting EOS captures general force field characteristics, such as transferability, and provides satisfactory agreement with the molecular simulation for bulk fluid properties. We also improved the predictability in the critical region by comparing the performance of the Renormalization Group (RG) Theory with a third-order TPT. We extend our methodology to inhomogeneous fluids via the adaptation of the classical Density Functional Theory (DFT). For the first time, the microstructure of fused and soft chains, as a representative of realistic molecular conformations, is studied for confined fluid and interfaces. In doing so, we develop a monomer functional that can reproduce the microstructure of the soft spheres for a wide temperature and density range. The transition from monomers to chains is carried out by using the Statistical Associating Fluid Theory (SAFT). The current state-of-the-art for the chain functional, in the framework of the SAFT approach, is further improved to take into account the fused nature of molecules. We have also released the widely-used Mean Field approximation and developed a non-local dispersion functional for the attractive interactions. Normal and branched alkanes, Ethers, 1-alkanols, Nitriles, water and carbon dioxide are studied (open full item for complete abstract)

Committee: J. Richard Elliott Dr. (Advisor); David Perry Dr. (Committee Member); Lu-Kwang Ju Dr. (Committee Member); Jie Zheng Dr. (Committee Member); Ernian Pan Dr. (Committee Member) Subjects: Chemical Engineering

Doctor of Philosophy, The Ohio State University, 2011, Chemistry

Construction of accurate potential energy (PE) surfaces for molecular systems is one of the primary tasks performed by theoretical physical chemists. Once in hand, these PE functions can be used to study the dynamics and spectroscopies, as well as the structures and properties of molecular systems. This study focuses on approximating many-body electronic induction in order to improve the accuracy of existing potentials and improve the efficiency of {em{ab initio}} methods in order to allow “on-the-fly” energy and force evaluations in dynamical calculations. The majority of the work reported here focuses on the solvated electron. We initiate a study aimed at understanding the effects of explicitly including the (ultrafast) electron--solvent electronic induction, or polarization. We construct a single electron potential in which the coarse grained electronic degrees of freedom of the solvent are treated self-consistently along with the electronic wave function. Predictions of the binding energy of an excess electron in water clusters obtained using this potential compare well to {em{ab initio}} electronic structure theories. Subsequently, this potential was used to investigate the behavior of the excess electron in liquid water. The explicit treatment of induction appears to have a minimal impact on the structure and solvation dynamics of the excess electron (in the ground state) but does have a large impact on the vertical detachment energy and the optical absorption spectrum. In these latter cases there is an abrupt change in the charge distribution of the excess electron. In such cases the electronic response from the solvent can be large and should be taken into account. The electronic response of the solvent occurs on the time scale of electronic excitation. This introduces technical complications when solving for orthogonal eigenstates of this system since the model Hamiltonian is state dependent. We describe a simple meth (open full item for complete abstract)

Committee: John Herbert (Advisor); Sherwin Singer (Committee Member); Anne McCoy (Committee Member) Subjects: Chemistry; Physical Chemistry; Physics

Doctor of Philosophy, The Ohio State University, 2022, Mechanical Engineering

Global regulatory targets for reducing CO2 emissions along with the customer demand is driving the automotive sector towards energy efficient transportation. Powertrain electrification offers great potential to improve the fuel economy due to the extra control flexibility compared to vehicles with a single power source. The benefits of the electrification can be significantly reduced when auxiliaries such as the vehicle climate control system directly competes with the powertrain for battery energy, reducing the range and energy efficiency. Connected and Automated Vehicles (CAVs) can increase the energy savings by allowing to switch from instantaneous optimization to predictive optimization by leveraging information from advanced navigation systems, Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) communication. In this work, two energy optimization problems for CAVs are studied. First is to jointly optimize the vehicle and powertrain dynamics and the second is to optimize the vehicle climate control system. The focus of this work is to combine the Dynamic Programming (DP), Approximate Dynamic Programming (ADP) and perturbation theory based approaches to solve the energy optimization problems with variations in external inputs and parameters that affects the plant model, objective function or constraints. To this end, mathematical methods are used to develop two novel algorithms that compensates for mismatches between nominal and estimated parameters. The first approach develops a cost correction scheme to evaluate the sensitivity of the value function to parameters, with the ultimate goal of correcting the original optimization problem online with the observed parameters. Two case-studies are considered with variations in vehicle payload and auxiliary power load. Second, a novel algorithm for solving dynamic optimization problem is developed to apply closed-loop corrections to solution of the original optimization problem without the need to (open full item for complete abstract)

Committee: Marcello Canova (Advisor); Abhishek Gupta (Committee Member); Stephanie Stockar (Committee Member) Subjects: Engineering; Mechanical Engineering

Master of Science, University of Akron, 2020, Applied Mathematics

In this thesis we study the longitudinal motion of a light viscoelastic rod carrying a heavy particle. We will fix the leftmost side of our rod and then discretize our rod into K light blocks with one heavy block on the rightmost end where ε is the ratio of the mass of a light block to the mass of the heavy block and ε << 1. We then focus on the simplest case, K = 1. We will then show that in this case we cannot use regular asymptotic expansions to approximate the solutions to the resulting system of differential equations. We instead use a singular perturbation approach from [1] to analyze our problem. We then show that our initial value problem can be transformed into an integral equation and that this integral equation is satisfied by an approximate solution on a compact domain. We then conclude that this approximate solution is an approximate solution to the original initial value problem and we will get estimates on the solutions that are uniform in time and in ε. We then study the outer problem numerically for a non-monotonic function. We will linearize our system about its fixed points and study, using the Stable Manifold Theorem, the stability of the fixed points.

Committee: J. Patrick Wilber (Advisor); Truyen Nguyen (Committee Member); Lingxing Yao (Committee Member) Subjects: Applied Mathematics

Doctor of Philosophy, The Ohio State University, 2020, Geodetic Science

To improve on the understanding of Earth dynamics, a perturbation theory aimed at geopotential recovery, based on purely kinematic state vectors, is implemented. The method was originally proposed in the study by Xu (2008). It is a perturbation method based on Cartesian coordinates that is not subject to singularities that burden most conventional methods of gravity recovery from satellite-to-satellite tracking. The principal focus of the theory is to make the gravity recovery process more efficient, for example, by reducing the number of nuisance parameters associated with arc endpoint conditions in the estimation process. The theory aims to do this by maximizing the benefits of pure kinematic tracking by GNSS over long arcs. However, the practical feasibility of this theory has never been tested numerically. In this study, the formulation of the perturbation theory is first modified to make it numerically practicable. It is then shown, with realistic simulations, that Xu's original goal of an iterative solution is not achievable under the constraints imposed by numerical integration error. As such, a non-iterative alternative approach is implemented, instead. Finally, the principles of this modified procedure are applied to the Schneider (1968) model, improving the original model by an order of magnitude for high-low satellite-to-satellite tracking (SST). The new model is also adapted to the processing of low-low SST, and a combination thereof, i.e. GRACE-like missions. In validating the linearized model for multiple-day-long arcs, it is revealed (through simulated GRACE-like orbits) to be at least as accurate as (or in some cases better than) the GRACE K-band range-rate nominal precision of 0.1 μm/s. Further application of the model to simulated recovery of spherical harmonic coefficients is shown to achieve accuracies commensurate to other models in practice today.

Committee: Michael Durand (Advisor); Christopher Jekeli (Advisor); Steven Lower (Committee Member) Subjects: Applied Mathematics; Earth; Geophysical; Geophysics; Statistics

Doctor of Philosophy, The Ohio State University, 1972, Graduate School

Committee: Not Provided (Other) Subjects: Physics

Doctor of Philosophy, The Ohio State University, 2015, Mathematics

The concept of singular shocks was introduced in a series of papers in the 1980s, by Keyfitz and Kranzer, in order to solve Riemann problems for a class of equations which cannot be solved using classical solutions. Classical solutions for Riemann problems are measurable functions composed of regular shocks and rarefactions, and singular shocks are distributions involving delta measures that are weak limits of approximate viscous solutions. During the past decades, many abstract theories of singular shocks were developed, and many examples of this type of solution in problems modeling physical phenomena were discovered. We study singular shocks as self-similar zero-viscosity limits via the viscous regularization ut+f(u)x=εtuxx for two systems of conservation laws. The first system models incompressible two-phase fluid flow in one space dimension, and the second one is the Keyfitz-Kranzer system. Singular shocks for both systems have been analyzed in the literature, and the results are enhanced in this dissertation. We improve and apply theorems from Geometric Singular Perturbation Theory, including Fenichel's Theorems, the Exchange Lemma, and the Corner Lemma, to prove existence and convergence of viscous profiles for singular shocks for those two examples. We also derive estimates for the growth rates of the unbounded viscous solutions. In particular, it is demonstrated that, although viscous solutions for these two systems both have shock layers of widths of order ε, they tend to infinity in quantitatively different manners. For the two-phase flow model, the maximum value of the solution is of order log(1/ε), while for the Keyfitz-Kranzer system, the maximum value is of order 1/ε2.

Committee: Barbara Keyfitz (Advisor); Ovidiu Costin (Committee Member); Saleh Tanveer (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2006, Physics

We present state-of-the-art unquenched lattice QCD results for B meson semileptonic decay, B → π l ν, form factors. We use gauge configurations prepared by the MILC collaboration, which include the effects of the sea quarks, the s quark and two very light quarks (u and d). We employ the nonrelativistic NRQCD action to simulate the heavy b quark and a highly improved staggered quark action (AsqTad) to simulate the sea and valence light quarks. To reduce the uncertainties, we perform matching of the heavy-light current with these highly improved actions through one loop. The perturbative matching accounts for the effects of mixing with dimension 4 operators that are 풪(1/M) and 풪(a). We extrapolate the form factors f+(q2) and f0(q2) to their values at the physical pion mass using chiral perturbation theory formulas. Integrating this result, we obtain ∫16 GeV2q2max [dΓ/dq2]dq2 / |Vub|2 = 1.46(35) ps-1. Combining this with a preliminary average by the Heavy Flavor Averaging Group (HFAG'05) of recent branching fraction data for exclusive B semileptonic decays from the BaBar, Belle and CLEO collaborations, leads to |Vub| = 4.22(30)(51) × 10-3.

Committee: Junko Shigemitsu (Advisor); Eric Braaten (Other); Klaus Honscheid (Other); Richard Furnstahl (Other) Subjects:

Doctor of Philosophy, The Ohio State University, 2004, Physics

The leading correction from interactions to the transition temperature Tc for Bose-Einstein condensation can be obtained from a nonperturbative calculation in the critical O(N) scalar field theory in 3 dimensions with N=2. We show that the linear delta expansion can be applied to this problem in such a way that in the large-N limit it converges to the exact analytic result. If the principal of minimal sensitivity is used to optimize the convergence rate, the errors seem to decrease exponentially with the order in the delta expansion. For N=2, we calculate the shift in Tc to fifth order in delta. The results are consistent with slow convergence to the results of recent lattice Monte Carlo calculations. The convergence can be accelerated by using a resummation method proposed by Kleinert et al. called variational perturbation theory.

Committee: Eric Braaten (Advisor) Subjects:

Doctor of Philosophy, The Ohio State University, 2002, Physics

The nontrivial topological structure of the QCD gauge vacuum generates a CP breaking term in the QCD Lagrangian. However, measurements of the neutron electric dipole moment have demonstrated that the term's coefficient is unnaturally small, a dilemma known as the strong CP problem. A massless up quark has long been seen as a potential solution, as the term could then be absorbed through the resulting freedom to perform arbitrary chiral rotations on the up quark field. Through the light-quark-mass ratio mu/md, leading order Chiral Perturbation Theory appears to rule this scenario out. However, the Kaplan-Manohar ambiguity demonstrates that certain strong next-to-leading order corrections are indistinguishable from the effects of an up quark mass. Only a direct calculation of the Gasser-Leutwyler coefficient combination 2L8 - L5 can resolve the issue. New theoretical insights into partial quenched Chiral Perturbation Theory have revealed that a calculation of the low-energy constants of the partially quenched chiral Lagrangian is equivalent to a determination of the physical Gasser-Leutwyler coefficients. The coefficient combination in question is directly accessible through the pion mass's dependence on the valence quark mass, a dependence ripe for determination via Lattice Quantum Chromodynamics. We carry out such a partially quenched lattice calculation using Nf = 3 staggered fermions and the recently developed smearing technique known as hypercubic blocking. Through the use of several ensembles, we make a quantitative assessment of our systematic error. We find 2L8 - L5 = (0.22 ± 0.14 ) × 10-3, which corresponds to a light-quark-mass ratio of mu/md = 0.408 ± 0.035. Thus, our study rules out the massless-up-quark solution to the strong CP problem. This is the first calculation of its type to use a physical number of light quarks, Nf = 3, and the first determination of L8 - L5 to include a comprehensive study of statistical error.

Committee: Junko Shigemitsu (Advisor) Subjects:

Doctor of Philosophy, The Ohio State University, 2002, Mathematics

A variety of experimental and modeling studies have been performed to investigate wave propagation in networks of thalamic neurons and their relationship to spindle sleep rhythms. It is believed that spindle oscillations result from the reciprocal interaction between thalamocortical (TC) and thalamic reticular (RE) neurons. We consider a reduced one-layer network of synaptically coupled, mutually inhibitory TC cells modeled by a system of singularly perturbed integral-differential equations. Geometric singular perturbation methods are used to prove the existence of a locally unique slow wave pulse that propagates along the network. By seeking a slow pulse solution, we are able to reformulate the problem to finding a heteroclinic orbit in a three-dimensional system of ordinary differential equations with two additional constraints on the location of the orbit at two distinct points in time.

Committee: David Terman (Advisor) Subjects:

Doctor of Philosophy, Case Western Reserve University, 2009, Physics

This thesis presents a study of the phonons and related properties in two sets of nitride compounds, whose properties are until now relatively poorly known. The Zn-IV-N2 group of compounds with the group IV elements Si, Ge and Sn, form a series analogous to the well known III-N nitride series with group III element Al, Ga, In. Structurally, they can be derived by doubling the period of III-V compounds in the plane in two directions and replacing the group-III elements with Zn and a group-IV element in a particular ordered pattern. Even though they are similar to the well-known III-V nitride compounds, the study of the properties of these materials is in its early stages. The phonons in these materials and their relation to the phonons in the corresponding group-III nitrides are of fundamental interest. They are also of practical interest because the phonon related spectra such as infrared absorption and Raman spectroscopy are sensitive to the structural quality of the material and can thus be used to quantify the degree of crystalline perfection of real samples. First-principles calculations of the phonons and related ground state properties of these compounds were carried out using Density Functional Perturbation Theory (DFPT) with the Local Density Approximation (LDA) for exchange and correlation and using a pseudopotential plane wave implementation which was developed by several authors over the last decades. The main focus of our study is on the phonons at the center of the Brillouin zone because the latter are most directly related to commonly used spectroscopies to probe the vibrations in a solid: infrared reflectivity and Raman spectroscopy. For a semiconducting or insulating compound, a splitting occurs between transverse and longitudinal phonons at the Γ-point because of the long-range nature of electrostatic forces. The concepts required to handle this problem are reviewed. Our discussion emphasizes how the various quantities required are related to variou (open full item for complete abstract)

Committee: Walter R. L. Lambrecht (Committee Chair); Philip L. Taylor (Committee Member); Kathleen Kash (Committee Member); Pirouz Pirouz (Committee Member) Subjects: Physics

Doctor of Philosophy, University of Akron, 2012, Chemical Engineering

This dissertation pursues four research studies based on enhancing the combination of discontinuous molecular dynamics simulation (DMD) and thermodynamic perturbation theory (TPT) as the foundation of an efficient methodology for molecular modeling with chemical engineering applications. The general hypothesis is that molecular simulation can be accelerated through the judicious application of thermodynamic theories. The first part of this dissertation relates to the variation of zeroth, first, and second order TPT trends for polymers with many molecular architectures including linear, ring, and branch structures. The TPT trends have been analyzed with respect to molecular weight and each TPT contribution approaches an asymptote at long chain limit. This means that we could rely on theory and correlation that could explain such behavior without the need for simulation at infinite chain length and behaviors at intermediate chain lengths can be inferred effectively by interpolation. The second part of this work is about the excess entropy of mixing for polymer solutions with different molecular structures. Polymeric mixtures of hydrocarbons and alcohols have been simulated with discontinuous potential models to characterize the Helmholtz energy of the repulsive reference fluids. This quantity is equivalent to the athermal mixture entropy. The asymptotic trends indicate that branches and rings are softer than n-alkanes. In other words, the excess entropy is larger for straight chains than for branched and/or ring hydrocarbons with the same number of carbons. We also observe trends that lead to precise characterizations and accurate predictions of the entropic contribution to the χ parameter (χS) of Flory-Huggins theory for mixtures of all sizes, shapes, and compositions of molecular structures.Knowing these general trends permits interpolation and computation at multiple state points without need of additional simulations. The third part of the dissertation considers t (open full item for complete abstract)

Committee: J. Richard Elliott Dr. (Advisor); Jutta Luettmer-Strathmann Dr. (Committee Member); Hendrik Heinz Dr. (Committee Member); Jie Zheng Dr. (Committee Member); Ernian Pan Dr. (Committee Member); Ligyun Liu Dr. (Committee Member) Subjects: Chemical Engineering

BA, Oberlin College, 2013, Mathematics

The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis.

Committee: Jim Walsh (Advisor) Subjects: Climate Change; Mathematics