Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

A reliability centered maintenance decision system for a discrete part manufacturing facility

This thesis develops and validates the framework of a specialized maintenance decision support system for a discrete part manufacturing facility. Its construction utilizes a modular approach based on the fundamental philosophy of Reliability Centered Maintenance (RCM). The proposed architecture uniquely integrates System Decomposition, System Evaluation, Failure Analysis, Logic Tree Analysis, and Maintenance Planning modules. It presents an ideal solution to the unique maintenance inadequacies of modern discrete part manufacturing systems. Well established techniques are incorporated as building blocks of the system's modules. These include Failure Mode Effect and Criticality Analysis (FMECA), Logic Tree Analysis (LTA), Theory of Constraints (TOC), and an Expert System (ES). A Maintenance Information System (MIS) performs the system's support functions. Validation was performed by field testing of the system at a Miami based manufacturing facility. Such a maintenance support system potentially reduces downtime losses and contributes to higher product quality output. Ultimately improved profitability is the final outcome. ^

Exotic meson decay widths using lattice quantum chromodynamics

Most experiments in particle physics are scattering experiments, the analysis of which leads to masses, scattering phases, decay widths and other properties of one or multi-particle systems. Until the advent of Lattice Quantum Chromodynamics (LQCD) it was difficult to compare experimental results on low energy hadron-hadron scattering processes to the predictions of QCD, the current theory of strong interactions. The reason being, at low energies the QCD coupling constant becomes large and the perturbation expansion for scattering; amplitudes does not converge. To overcome this, one puts the theory onto a lattice, imposes a momentum cutoff, and computes the integral numerically. For particle masses, predictions of LQCD agree with experiment, but the area of decay widths is largely unexplored. ^ LQCD provides ab initio access to unusual hadrons like exotic mesons that are predicted to contain real gluonic structure. To study decays of these type resonances the energy spectra of a two-particle decay state in a finite volume of dimension L can be related to the associated scattering phase shift δ(k) at momentum k through exact formulae derived by Lüscher. Because the spectra can be computed using numerical Monte Carlo techniques, the scattering phases can thus be determined using Lüscher's formulae, and the corresponding decay widths can be found by fitting Breit-Wigner functions. ^ Results of such a decay width calculation for an exotic hybrid( h) meson (JPC = 1-+) are presented for the decay channel h → πa 1. This calculation employed Lüscher's formulae and an approximation of LQCD called the quenched approximation. Energy spectra for the h and πa1 systems were extracted using eigenvalues of a correlation matrix, and the corresponding scattering phase shifts were determined for a discrete set of πa1 momenta. Although the number of phase shift data points was sparse, fits to a Breit-Wigner model were made, resulting in a decay width of about 60 MeV. ^

A fresh look at decision making in international investment choices: Firm international coherence and home-host country relatedness

Understanding how decisions for international investments are made and how this affects the overall pattern of investments and firm’s performance is of particular importance both in strategy and international business research. This dissertation introduced first home-host country relatedness (HHCR) as the degree to which countries are efficiently combined within the investment portfolios of firms. It theorized and demonstrated that HHCR will vary with the motivation for investments along at least two key dimensions: the nature of foreign investments and the connectedness of potential host countries to the rest of the world. Drawing on cognitive psychology and decision-making research, it developed a theory of strategic decision making proposing that strategic solutions are chosen close to a convenient anchor. Building on research on memory imprinting, it also proposed that managers tend to rely on older knowledge representation. In the context of international investment decisions, managers use their home countries as an anchor and are more likely to choose as a site for foreign investments host countries that are ‘close’ to the home country. These decisions are also likely to rely more strongly on closeness to time invariant country factors of historic and geographic nature rather than time-variant institutions. Empirical tests using comprehensive investments data by all public multinational companies (MNC) worldwide, or over 15,000 MNCs with over half a million subsidiaries, support the claims. Finally, the dissertation introduced the concept of International Coherence (IC) defined as the degree to which an MNE’s network comprises countries that are related. It was hypothesized that maintaining a high level of coherence is important for firm performance and will enhance it. Also, the presence of international coherence mitigates some of the negative effects of unrelated product diversification. Empirical tests using data on foreign investments of over 20,000 public firms, while also developing a home-host country relatedness index for up to 24,300 home-host pairs, provided support for the theory advanced.

Ab initio quantum chemical studies on neutral-radical reactions of ethynyl (C2H) and cyano (CN) with unsaturated hydrocarbons

An Ab Initio/RRKM study of the reaction mechanism and product branching ratios of neutral-radical ethynyl (C2H) and cyano (CN) radical species with unsaturated hydrocarbons is performed. The reactions studied apply to cold conditions such as planetary atmospheres including Titan, the Interstellar Medium (ISM), icy bodies and molecular clouds. The reactions of C2H and CN additions to gaseous unsaturated hydrocarbons are an active area of study. NASA's Cassini/Huygens mission found a high concentration of C2H and CN from photolysis of ethyne (C2H2) and hydrogen cyanide (HCN), respectively, in the organic haze layers of the atmosphere of Titan. The reactions involved in the atmospheric chemistry of Titan lead to a vast array of larger, more complex intermediates and products and may also serve as a chemical model of Earth's primordial atmospheric conditions. The C2H and CN additions are rapid and exothermic, and often occur barrierlessly to various carbon sites of unsaturated hydrocarbons. The reaction mechanism is proposed on the basis of the resulting potential energy surface (PES) that includes all the possible intermediates and transition states that can occur, and all the products that lie on the surface. The B3LYP/6-311g(d,p) level of theory is employed to determine optimized electronic structures, moments of inertia, vibrational frequencies, and zero-point energy. They are followed by single point higher-level CCSD(T)/cc-vtz calculations, including extrapolations to complete basis sets (CBS) of the reactants and products. A microcanonical RRKM study predicts single-collision (zero-pressure limit) rate constants of all reaction paths on the potential energy surface, which is then used to compute the branching ratios of the products that result. These theoretical calculations are conducted either jointly or in parallel to experimental work to elucidate the chemical composition of Titan's atmosphere, the ISM, and cold celestial bodies.<.

Investigation of generation -recombination noise and related processes in aluminum gallium arsenide TEGFETs and Hall structures with quantum wells

Experimental and theoretical studies regarding noise processes in various kinds of AlGaAs/GaAs heterostructures with a quantum well are reported. The measurement processes, involving a Fast Fourier Transform and analog wave analyzer in the frequency range from 10 Hz to 1 MHz, a computerized data storage and processing system, and cryostat in the temperature range from 78 K to 300 K are described in detail. The current noise spectra are obtained with the “three-point method”, using a Quan-Tech and avalanche noise source for calibration. ^ The properties of both GaAs and AlGaAs materials and field effect transistors, based on the two-dimensional electron gas in the interface quantum well, are discussed. Extensive measurements are performed in three types of heterostructures, viz., Hall structures with a large spacer layer, modulation-doped non-gated FETs, and more standard gated FETs; all structures are grown by MBE techniques. ^ The Hall structures show Lorentzian generation-recombination noise spectra with near temperature independent relaxation times. This noise is attributed to g-r processes in the 2D electron gas. For the TEGFET structures, we observe several Lorentzian g-r noise components which have strongly temperature dependent relaxation times. This noise is attributed to trapping processes in the doped AlGaAs layer. The trap level energies are determined from an Arrhenius plot of log (τT2) versus 1/T as well as from the plateau values. The theory to interpret these measurements and to extract the defect level data is reviewed and further developed. Good agreement with the data is found for all reported devices. ^

Noise in gallium nitride-based quantum well structures used for nanometer devices in the frequency range 1 Hz--3 Mhz and temperature range 77K--324K

Electronic noise has been investigated in AlxGa1−x N/GaN Modulation-Doped Field Effect Transistors (MODFETs) of submicron dimensions, grown for us by MBE (Molecular Beam Epitaxy) techniques at Virginia Commonwealth University by Dr. H. Morkoç and coworkers. Some 20 devices were grown on a GaN substrate, four of which have leads bonded to source (S), drain (D), and gate (G) pads, respectively. Conduction takes place in the quasi-2D layer of the junction (xy plane) which is perpendicular to the quantum well (z-direction) of average triangular width ∼3 nm. A non-doped intrinsic buffer layer of ∼5 nm separates the Si-doped donors in the AlxGa1−xN layer from the 2D-transistor plane, which affords a very high electron mobility, thus enabling high-speed devices. Since all contacts (S, D, and G) must reach through the AlxGa1−xN layer to connect internally to the 2D plane, parallel conduction through this layer is a feature of all modulation-doped devices. While the shunting effect may account for no more than a few percent of the current IDS, it is responsible for most excess noise, over and above thermal noise of the device. ^ The excess noise has been analyzed as a sum of Lorentzian spectra and 1/f noise. The Lorentzian noise has been ascribed to trapping of the carriers in the AlxGa1−xN layer. A detailed, multitrapping generation-recombination noise theory is presented, which shows that an exponential relationship exists for the time constants obtained from the spectral components as a function of 1/kT. The trap depths have been obtained from Arrhenius plots of log (τT2) vs. 1000/T. Comparison with previous noise results for GaAs devices shows that: (a) many more trapping levels are present in these nitride-based devices; (b) the traps are deeper (farther below the conduction band) than for GaAs. Furthermore, the magnitude of the noise is strongly dependent on the level of depletion of the AlxGa1−xN donor layer, which can be altered by a negative or positive gate bias VGS. ^ Altogether, these frontier nitride-based devices are promising for bluish light optoelectronic devices and lasers; however, the noise, though well understood, indicates that the purity of the constituent layers should be greatly improved for future technological applications. ^

Personal autonomy in discharge planning decision -making in mentally alert hospitalized elderly individuals: The social workers' perspective

This study was conducted to understand (a) hospital social workers' perspectives about patients' personal autonomy and self-determination, (b) their experiences, and (c) their beliefs and behaviors. The study used the maximum variation sampling strategy to select hospitals and hospital social work respondents. Individual interviews were conducted with 31 medical/surgical and mental health hospital social workers who worked in 13 hospitals. The data suggest the following four points. First, the hospital setting as an outside influence as it relates to illness and safety, and its four categories, mentally alert patients, family members, health care professionals, and social work respondents, seems to enhance or diminish patients' autonomy in discharge planning decision making. Second, respondents report they believe patients must be safe both inside and outside the hospital. In theory, respondents support autonomy and self-determination, respect patients' wishes, and believe patients are the decision makers. However, in practice, respondents respect autonomy and self-determination to a point. Third, a model, The Patient's Decision in Discharge Planning: A Continuum, is presented where a safe discharge plan is at one end of a continuum, while an unsafe discharge plan is at the other end. Respondents respect personal autonomy and the patient's self-determination to a point. This point is likely to be located in a gray area where the patient's decision crosses from one end of the continuum to the other. When patients decide on an unsafe discharge plan, workers' interventions range from autonomy to paternalism. And fourth, the hospital setting as an outside influence may not offer the best opportunity for patients to make decisions (a) because of beliefs family members and health care professionals hold about the value of patient self-determination, and (b) because patients may not feel free to make decisions in an environment where they are surrounded by family members, health care professionals, and social work respondents who have power and who think they know best. Workers need to continue to educate elderly patients about their right to self-determination in the hospital setting. ^

Deprofessionalization of curriculum decision -making

The purpose of this study was to analyze the evolution of Florida state level policy efforts and to assess the responding educational policy development and implementation at the local school district level. The focus of this study was the secondary language arts curriculum in Miami-Dade County Public Schools. ^ Data was collected using document analysis as a source of meaning making out of the language sets proffered by agencies at each level. A matrix was created based on Klein's levels of curriculum decision-making and Functional Process Theory categories of policy formation. The matrix allowed the researcher to code and classify specific information in terms accountability/high-stakes testing; authority; outside influences; and operational/structural organization. ^ Federal policy documents provided a background and impetus for much of what originated at the State level. The State then produced policy directives which were accepted by the District and specific policy directives and guidelines for practice. No evidence was found indicating the involvement of any other agencies in the development, transmission or implementation of the State level initiated policies. ^ After analyzing the evolutionary process, it became clear that state policy directives were never challenged or discussed. Rather, they were accepted as standards to be met and as such, school districts complied. Policy implementation is shown to be a top-down phenomenon. No evidence was found indicating a dialogue between state and local systems, rather the state, as the source of authority, issued specifically worded policy directives and the district complied. Finally, this study recognizes that outside influences play an important role in shaping the education reform policy in the state of Florida. The federal government, through NCLB and other initiatives created a climate which led almost naturally to the creation of the Florida A+ Plan. Similarly, the concern of the business community, always interested in the production of competent workers, continued to support efforts at raising the minimum skill level of Florida high school graduates. ^ Suggestions are made for future research including the examination of local school sites in order to assess the overall nature of the school experience rather than rely upon performance indicators mandated by state policy. ^

A decision support framework for infrastructure maintenance investment decision-making

Infrastructure management agencies are facing multiple challenges, including aging infrastructure, reduction in capacity of existing infrastructure, and availability of limited funds. Therefore, decision makers are required to think innovatively and develop inventive ways of using available funds. Maintenance investment decisions are generally made based on physical condition only. It is important to understand that spending money on public infrastructure is synonymous with spending money on people themselves. This also requires consideration of decision parameters, in addition to physical condition, such as strategic importance, socioeconomic contribution and infrastructure utilization. Consideration of multiple decision parameters for infrastructure maintenance investments can be beneficial in case of limited funding. Given this motivation, this dissertation presents a prototype decision support framework to evaluate trade-off, among competing infrastructures, that are candidates for infrastructure maintenance, repair and rehabilitation investments. Decision parameters' performances measured through various factors are combined to determine the integrated state of an infrastructure using Multi-Attribute Utility Theory (MAUT). The integrated state, cost and benefit estimates of probable maintenance actions are utilized alongside expert opinion to develop transition probability and reward matrices for each probable maintenance action for a particular candidate infrastructure. These matrices are then used as an input to the Markov Decision Process (MDP) for the finite-stage dynamic programming model to perform project (candidate)-level analysis to determine optimized maintenance strategies based on reward maximization. The outcomes of project (candidate)-level analysis are then utilized to perform network-level analysis taking the portfolio management approach to determine a suitable portfolio under budgetary constraints. The major decision support outcomes of the prototype framework include performance trend curves, decision logic maps, and a network-level maintenance investment plan for the upcoming years. The framework has been implemented with a set of bridges considered as a network with the assistance of the Pima County DOT, AZ. It is expected that the concept of this prototype framework can help infrastructure management agencies better manage their available funds for maintenance.

Deprofessionalization of curriculum decision-making

The purpose of this study was to analyze the evolution of Florida state level policy efforts and to assess the responding educational policy development and implementation at the local school district level. The focus of this study was the secondary language arts curriculum in Miami-Dade County Public Schools. Data was collected using document analysis as a source of meaning making out of the language sets proffered by agencies at each level. A matrix was created based on Klein's levels of curriculum decision-making and Functional Process Theory categories of policy formation. The matrix allowed the researcher to code and classify specific information in terms accountability/high-stakes testing; authority; outside influences; and operational/structural organization. Federal policy documents provided a background and impetus for much of what originated at the State level. The State then produced policy directives which were accepted by the District and specific policy directives and guidelines for practice. No evidence was found indicating the involvement of any other agencies in the development, transmission or implementation of the State level initiated policies. After analyzing the evolutionary process, it became clear that state policy directives were never challenged or discussed. Rather, they were accepted as standards to be met and as such, school districts complied. Policy implementation is shown to be a top-down phenomenon. No evidence was found indicating a dialogue between state and local systems, rather the state, as the source of authority, issued specifically worded policy directives and the district complied. Finally, this study recognizes that outside influences play an important role in shaping the education reform policy in the state of Florida. The federal government, through NCLB and other initiatives created a climate which led almost naturally to the creation of the Florida A+ Plan. Similarly, the concern of the business community, always interested in the production of competent workers, continued to support efforts at raising the minimum skill level of Florida high school graduates. Suggestions are made for future research including the examination of local school sites in order to assess the overall nature of the school experience rather than rely upon performance indicators mandated by state policy.

Ab Initio Quantum Chemical Studies on Neutral-Radical Reactions of Ethynyl (C2H) and Cyano (CN) with Unsaturated Hydrocarbons

An Ab Initio/RRKM study of the reaction mechanism and product branching ratios of neutral-radical ethynyl (C2H) and cyano (CN) radical species with unsaturated hydrocarbons is performed. The reactions studied apply to cold conditions such as planetary atmospheres including Titan, the Interstellar Medium (ISM), icy bodies and molecular clouds. The reactions of C2H and CN additions to gaseous unsaturated hydrocarbons are an active area of study. NASA’s Cassini/Huygens mission found a high concentration of C2H and CN from photolysis of ethyne (C2H2) and hydrogen cyanide (HCN), respectively, in the organic haze layers of the atmosphere of Titan. The reactions involved in the atmospheric chemistry of Titan lead to a vast array of larger, more complex intermediates and products and may also serve as a chemical model of Earth’s primordial atmospheric conditions. The C2H and CN additions are rapid and exothermic, and often occur barrierlessly to various carbon sites of unsaturated hydrocarbons. The reaction mechanism is proposed on the basis of the resulting potential energy surface (PES) that includes all the possible intermediates and transition states that can occur, and all the products that lie on the surface. The B3LYP/6-311g(d,p) level of theory is employed to determine optimized electronic structures, moments of inertia, vibrational frequencies, and zero-point energy. They are followed by single point higher-level CCSD(T)/cc-vtz calculations, including extrapolations to complete basis sets (CBS) of the reactants and products. A microcanonical RRKM study predicts single-collision (zero-pressure limit) rate constants of all reaction paths on the potential energy surface, which is then used to compute the branching ratios of the products that result. These theoretical calculations are conducted either jointly or in parallel to experimental work to elucidate the chemical composition of Titan’s atmosphere, the ISM, and cold celestial bodies.

Twelve Certain Men: The Impact of Emotional Appraisals on Juror Decision-Making

Our jury system is predicated upon the expectation that jurors engage in systematic processing when considering evidence and making decisions. They are instructed to interpret facts and apply the appropriate law in a fair, dispassionate manner, free of all bias, including that of emotion. However, emotions containing an element of certainty (e.g., anger and happiness, which require little cognitive effort in determining their source) can often lead people to engage in superficial, heuristic-based processing. Compare this to uncertain emotions (e.g., hope and fear, which require people to seek out explanations for their emotional arousal), which instead has the potential to lead them to engage in deeper, more systematic processing. The purpose of the current research is in part to confirm past research (Tiedens & Linton, 2001; Semmler & Brewer, 2002) that uncertain emotions (like fear) can influence decision-making towards a more systematic style of processing, whereas more certain emotional states (like anger) will lead to a more heuristic style of processing. Studies One, Two, and Three build upon this prior research with the goal of improving methodological rigor through the use of film clips to reliably induce emotions, with awareness of testimonial details serving as measures of processing style. The ultimate objective of the current research was to explore this effect in Study Four by inducing either fear, anger, or neutral emotion in mock jurors, half of whom then followed along with a trial transcript featuring eight testimonial inconsistencies, while the other participants followed along with an error-free version of the same transcript. Overall rates of detection for these inconsistencies was expected to be higher for the uncertain/fearful participants due to their more effortful processing compared to certain/angry participants. These expectations were not fulfilled, with significant main effects only for the transcript version (with or without inconsistencies) on overall inconsistency detection rates. There are a number of plausible explanations for these results, so further investigation is needed.