Applied Mathematics Commons^™

Problems In Chemical Graph Theory Related To The Merrifield-Simmons And Hosoya Topological Indices, William B. O'Reilly

Electronic Theses and Dissertations

In some sense, chemical graph theory applies graph theory to various physical sciences. This interdisciplinary field has significant applications to structure property relationships, as well as mathematical modeling. In particular, we focus on two important indices widely used in chemical graph theory, the Merrifield-Simmons index and Hosoya index. The Merrifield-Simmons index and the Hosoya index are two well-known topological indices used in mathematical chemistry for characterizing specific properties of chemical compounds. Substantial research has been done on the two indices in terms of enumerative problems and extremal questions. In this thesis, we survey known extremal results and consider the generalized …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

Relative Energy Comparison For Various Water Clusters Using Mp2, Df-Mp2, And Ccsd(T):Mp2 Methods, Qihang Wang

Honors Theses

The study of water clusters is an important area of research in many disciplines, such as biology, physical chemistry, and environmental studies. However, due to the difficulty in studying larger water clusters, such as clathrate hydrates, it is beneficial to obtain accurate descriptions of smaller water clusters to use as models for larger systems via computational methods. By starting with small water clusters, such as (H2O)₆, and moving into larger systems it is possible to build up data on various water structures that can determine the energetics of the various geometries within a certain number of water molecules. …

Development Of Synthetic Coal Char Simulant For Microwave Conversion Studies: A Computationally-Driven Approach, Kevin A. Hager

Graduate Theses, Dissertations, and Problem Reports

Recent experimental demonstration of new reaction windows for coal char/methane reactions that are less energy-intensive, provides innovation for modular reactors. However, the correlation of the exact mechanism for the enhancement of these reaction windows is not certain. This study investigates the simplification of these experimental studies by developing a well-characterized coal char simulant. The approach involves using a computational approach to screen macroscopic composition to replicate the dielectric and compositional response of actual char. This study is focused on PRB coal char. A discrete element method (DEM) technique was used to simulate the packing of coal chars to give the …

Model-Form Uncertainty Quantification For Predictive Probabilistic Graphical Models, Jinchao Feng

Doctoral Dissertations

In this thesis, we focus on Uncertainty Quantification and Sensitivity Analysis, which can provide performance guarantees for predictive models built with both aleatoric and epistemic uncertainties, as well as data, and identify which components in a model have the most influence on predictions of our quantities of interest. In the first part (Chapter 2), we propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, …

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

Computational Investigation Of Energetic Materials: Influence Of Intramolecular And Intermolecular Interactions On Sensitivity, Ashley Lauren Shoaf

Chemistry & Biochemistry Theses & Dissertations

The development of novel high energy density materials (HEDMs) with superior energetic properties depends on characterizing how and why detonation occurs. Detonation is highly energetic and a nearly instantaneous process, making experimental studies challenging; thus, computational modeling through density functional theory (DFT) and molecular dynamics (MD) can be used to propose weakened, or activated, bonds that break to initiate explosive decomposition, termed trigger bonds. Bond activation is characterized by the Wiberg bond index (WBI), a measure of interatomic electron density. Trigger bonds in HEDMs are commonly found in explosophores, functional groups that contribute to energetic potential such as X-NO_{2 …}

Investigation Of Volatile Organic Compounds (Vocs) Detected At Vapor Intrusion Sites, Mohammadyousef Roghani

Theses and Dissertations--Civil Engineering

This dissertation investigates unexplained vapor intrusion field data sets that have been observed at hazardous waste sites, including: 1) non-linear soil gas concentration trends between the VOC source (i.e. contaminated groundwater plume) and the ground surface; and, 2) alternative pathways that serve as entry points for vapors to infiltrate into buildings and serve to increase VOC exposure risks as compared to the classic vapor intrusion model, which primarily considered foundation cracks as the route for vapor entry. The overall hypothesis of this research is that theoretical knowledge of fate and transport processes can be systematically applied to vapor intrusion field …

Diffusion And Adsorption Coefficients Of Aromatic Hydrocarbons In Gas Chromatography Capillary Columns, Gabriela Navarro Tovar

Electronic Thesis and Dissertation Repository

This study focuses on a mathematical description of aromatic species elution peaks from a gas chromatographic BPX5 capillary column. Using the chromatographic peaks, statistical moments are calculated for toluene, naphthalene, phenol and 2-naphthol. This thesis reports two modelling approaches involving laminar gas flow, distribution coefficients (K_s) and diffusion coefficients in the stationary phase (D_s).

Firstly, a model with equilibrium adsorption is considered to describe symmetric peaks for toluene and naphthalene. Moreover, a model with non-equilibrium adsorption is proposed to describe asymmetric peaks of phenol and 2-napthol. In addition to the K_s and D …

Isotropic Oscillator Under A Magnetic And Spatially Varying Electric Field, David L. Frost Mr., Frank Hagelberg

Undergraduate Honors Theses

We investigate the energy levels of a particle confined in the isotropic oscillator potential with a magnetic and spatially varying electric field. Here we are able to exactly solve the Schrodinger equation, using matrix methods, for the first excited states. To this end we find that the spatial gradient of the electric field acts as a magnetic field in certain circumstances. Here we present the changes in the energy levels as functions of the electric field, and other parameters.

A Molecular Simulation Study On Micelle Fragmentation And Wetting In Nano-Confined Channels, Mona Habibi

Electronic Thesis and Dissertation Repository

We performed coarse-grained molecular-dynamics (MD) simulations to study the structural and dynamical properties of surfactant micelles in equilibrium and under Poiseuille-like flow in a nano-confined geometry. We used the MARTINI force-field to model the interactions between water molecules, counter-ions, and sodium dodecyl sulfate (SDS) surfactants. SDS surfactant was chosen as the standard model because of its potential application in drug delivery systems. First, we focused on the self-assembly of SDS in equilibrium. To form stable spherical mi- celles, we ran simulations in the isothermal-isobaric ensemble (NPT) on a system of free SDS surfactants, counter-ions and water molecules. We studied the …

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Structure Vs. Properties Using Chemical Graph Theory, Tabitha N. Williford

Electronic Theses and Dissertations

Chemical graph theory began as a way for mathematicians to bring together the areas of the Physical Sciences and Mathematics. Through its use, mathematicians are able to model chemical systems, predict their properties as well as structure-property relationships. In this dissertation, we consider two questions involving chemical graph theory and its applications. We first look at tree-like polyphenyl systems, which form an important family of compounds in Chemistry, particularly in Material Science. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are …

Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings

Doctoral Dissertations

An in-depth understanding of a wide range of physical, chemical, atmospheric and biological processes can only be achieved after the structure and dynamics of interfaces and the interfacial behavior of aqueous species, such as ions, are thoroughly studied and understood. This dissertation describes computational studies conducted to gain a more comprehensive understanding of such interfaces and the behavior of ions in the bulk and interfacial regions of the (1) air/water interface, and (2) alkane/water interfaces.

At the air/water interface the effect of counterion (sodium cations) charge and the influence of ion pairing on anion (chloride) propensity for the air/water interface …

Novel Algorithms And Instrumentation For Vibrational Spectroscopic Methods Of Analysis, Mohamed F. Abdelkader

Chemistry & Biochemistry Theses & Dissertations

Raman spectroscopy is a form of vibrational spectroscopy that has been increasingly applied to qualitative analysis of chemicals, explosives, pharmaceuticals, and fuels due to its non-invasive and non-destructive nature; its ease of sampling; and its high molecular specificity. These characteristics of Raman spectroscopy also facilitate its use for both in-line and at-line analysis. The principle limitation of Raman spectroscopy is optical interference arising from both analyte and non-analyte fluorescence. In this dissertation, a solution to this problem is presented in the form of a novel spectrometer design which operates in a sequentially shifted excitation mode to eliminate fluorescence backgrounds, fixed …

Atmospheric Transport And Diffusion Modeling Of Rocket Exhaust, Chad A. Burel

Theses and Dissertations

Space launches at Vandenberg Air Force Base (VAFB) and the Cape Canaveral Air Station (CCAS) produce exhaust from the solid rocket boosters and liquid hypergolic fuels containing several toxic substances including hydrogen chloride and hydrazine. In order to estimate the health risk that would be imposed upon the public by proposed launches, range safety officials rely on the Rocket Exhaust Effluent Diffusion Model to predict where the exhaust chemicals will go after the launch and how strong the concentrations will be. The original REEDM program averaged the meteorological parameters (wind speed, wind direction, shear, etc.) across the entire mixing level …

A Numerical Method For The Solution Of The Schrödinger Equation By A Trial Wavefunction Improvement Formula, Chun-Sheng Ko

Masters Theses

A numerical method and corresponding computer algorithm for solving the one-dimensional radial Schrödinger equation to any desired accuracy is developed. The method uses a finite difference scheme in which an initial trial wavefunction is digitalized over a lattice covering the region of integration. The values of a rough solution are then altered at each lattice point by a simple improvement formula decreasing the value of the variational energy until the desired minimum is reached. The accuracy of these solutions depends only on the grid size. This method is characterized and tested with a harmonic oscillator potential. Practical evaluations and applications …