Applied Mathematics Commons^™

Research And Development Of The Positron Damping Rings For The Proposed International Linear Collider, And At Cern In Geneva, Switzerland For The Large Hadron Collider Atlas Experiment's Integrated Simulation Framework, Ryan Badman

Honors Capstone Projects - All

Abstract not available. Please download the full Capstone for abstract.

Simulations Of Surfactant Driven Thin Film Flow, Shreyas Kumar

HMC Senior Theses

This thesis is intended to fulfill the requirements of the Math and Physics departments at Harvey Mudd College. We begin with a brief introduction to the study of surfactant dynamics followed by some background on the experimental framework our work is related to. We then go through a derivation of the model we use, and explore in depth the nature of the Equation of State (EoS), the relationship between the surface tension on a fluid and the surfactant concentration. We consider the effect of using an empirical equation of state on the results of the simulations and compare the new …

Invisibility: A Mathematical Perspective, Austin G. Gomez

CMC Senior Theses

The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. …

Computational Fluid Dynamics (Cfd) Modeling Of A Laboratory Scale Coal Gasifier, Kiel S. Schultheiss

Electronic Theses and Dissertations

Furthering gasification technology is an essential part of advancing clean coal technologies. In order to seek insight into the appropriate operations for the formation of synthetic gas (syngas) a numerical simulation was performed to predict the phenomena of coal gasification in a laboratory scale entrained-flow coal gasifier. The mesh for the model was developed with ICEM CFD software and the chemical and physical phenomena were modeled using the fluid flow solver ANSYS FLUENT. Mesh independence was verified. The model was validated with experimental data from several studies performed on a laboratory scale gasifier.

Systematic examination of the model was performed …

Intelligent Feature Selection Techniques For Pattern Classification Of Time-Domain Signals, Corey Alexander Miller

Dissertations, Theses, and Masters Projects

Time-domain signals form the basis of analysis for a variety of applications, including those involving variable conditions or physical changes that result in degraded signal quality. Typical approaches to signal analysis fail under these conditions, as these types of changes often lie outside the scope of the domain's basic analytic theory and are too complex for modeling. Sophisticated signal processing techniques are required as a result. In this work, we develop a robust signal analysis technique that is suitable for a wide variety of time-domain signal analysis applications. Statistical pattern classification routines are applied to problems of interest involving a …

Validation Of Weak Form Thermal Analysis Algorithms Supporting Thermal Signature Generation, Elton Lewis Freeman

Masters Theses

Extremization of a weak form for the continuum energy conservation principle differential equation naturally implements fluid convection and radiation as flux Robin boundary conditions associated with unsteady heat transfer. Combining a spatial semi-discretization via finite element trial space basis functions with time-accurate integration generates a totally node-based algebraic statement for computing. Closure for gray body radiation is a newly derived node-based radiosity formulation generating piecewise discontinuous solutions, while that for natural-forced-mixed convection heat transfer is extracted from the literature. Algorithm performance, mathematically predicted by asymptotic convergence theory, is subsequently validated with data obtained in 24 hour diurnal field experiments for …

Molecular Dynamics Studies Of Water Flow In Carbon Nanotubes, Alexander D. Marshall

Electronic Thesis and Dissertation Repository

We present classical molecular dynamics (MD) simulations providing insight into the behaviour of water. We focus on confined water, the properties of which are often significantly different from the properties of bulk water.

First, we performed several simulations investigating the handling of long-range interactions in GROMACS [1], a MD simulation package. Selection of simulation protocols such as handling of long-range interactions is often overlooked, sometimes to the significant detriment of the final result [2, 3, 4]. Ensuring that the chosen simulation protocols are appropriate is a critical step in computer simulation.

Second, we performed MD simulations where water flowed between …

Preoperative Planning Of Robotics-Assisted Minimally Invasive Cardiac Surgery Under Uncertainty, Hamidreza Azimian

Electronic Thesis and Dissertation Repository

In this thesis, a computational framework for patient-specific preoperative planning of Robotics-Assisted Minimally Invasive Cardiac Surgery (RAMICS) is developed. It is expected that preoperative planning of RAMICS will improve the rate of success by considering robot kinematics, patient-specific thoracic anatomy, and procedure-specific intraoperative conditions. Given the significant anatomical features localized in the preoperative computed tomography images of a patient's thorax, port locations and robot orientations (with respect to the patient's body coordinate frame) are determined to optimize characteristics such as dexterity, reachability, tool approach angles and maneuverability. In this thesis, two approaches for preoperative planning of RAMICS are proposed that …

Phase Field Crystal Approach To The Solidification Of Ferromagnetic Materials, Niloufar Faghihi

Electronic Thesis and Dissertation Repository

The dependence of the magnetic hardness on the microstructure of magnetic solids is investigated, using a field theoretical approach, called the Magnetic Phase Field Crystal model. We constructed the free energy by extending the Phase Field Crystal (PFC) formalism and including terms to incorporate the ferromagnetic phase transition and the anisotropic magneto-elastic effects, i.e., the magnetostriction effect. Using this model we performed both analytical calculations and numerical simulations to study the coupling between the magnetic and elastic properties in ferromagnetic solids. By analytically minimizing the free energy, we calculated the equilibrium phases of the system to be liquid, non-magnetic …

Study Of Vortex Ring Dynamics In The Nonlinear Schrödinger Equation Utilizing Gpu-Accelerated High-Order Compact Numerical Integrators, Ronald Meyer Caplan

CGU Theses & Dissertations

We numerically study the dynamics and interactions of vortex rings in the nonlinear Schrödinger equation (NLSE). Single ring dynamics for both bright and dark vortex rings are explored including their traverse velocity, stability, and perturbations resulting in quadrupole oscillations. Multi-ring dynamics of dark vortex rings are investigated, including scattering and merging of two colliding rings, leapfrogging interactions of co-traveling rings, as well as co-moving steady-state multi-ring ensembles. Simulations of choreographed multi-ring setups are also performed, leading to intriguing interaction dynamics.

Due to the inherent lack of a close form solution for vortex rings and the dimensionality where they live, efficient …

Energy Functional For Nuclear Masses, Michael Giovanni Bertolli

Doctoral Dissertations

An energy functional is formulated for mass calculations of nuclei across the nuclear chart with major-shell occupations as the relevant degrees of freedom. The functional is based on Hohenberg-Kohn theory. Motivation for its form comes from both phenomenology and relevant microscopic systems, such as the three-level Lipkin Model. A global fit of the 17-parameter functional to nuclear masses yields a root- mean-square deviation of χ[chi] = 1.31 MeV, on the order of other mass models. The construction of the energy functional includes the development of a systematic method for selecting and testing possible functional terms. Nuclear radii are computed within …

Transverse Waves In Simulated Liquid Rocket Engines With Arbitrary Headwall Injection, Charles Toufic Haddad

Masters Theses

This work introduces a closed-form analytical solution for the transverse vorticoacoustic wave in a circular cylinder with arbitrary headwall injection. This particular configuration mimics the conditions leading to the onset of traveling radial and tangential waves in a simple liquid rocket engine (LRE). Assuming a short cylindrical chamber with an injecting headwall, regular perturbations are used to linearize the problem’s mass, momentum, energy, ideal gas and isentropic relations. A Helmholtz decomposition is subsequently applied to the first-order disturbance equations, thus giving rise to a compressible, inviscid and acoustic set that is responsible for driving the unsteady motion and to an …

Paleomagnetism And Investigation Of 40 Ma Lavas, Liverpool Range, New South Whales, Australia, Nathan M. Padilla

Physics

The main focus of this project is the continued study of a reversal of the earth’s magnetic field recorded from lavas in the Liverpool Range of New South Whales, Australia. This reverse-to-normal transition, recently dated at ~40 Ma, was first reported in Nature in 1986. [2] In March 2011 some 200+ cores were drilled from several sections about the volcanic range—Jemmy’s Creek, Bald Hill, Rock Creek, Yarraman, and Coolah Tops Road. Here we focus on paleomagnetic findings from samples drilled from the most extensive section, that being along the trail near Jemmy’s Creek. Results from alternating field demagnetization show the …

Electronic Excitations In Ytio3 Using Tddft And Electronic Structure Using A Multiresolution Framework, William Scott Thornton

Doctoral Dissertations

We performed ab initio studies of the electronic excitation spectra of the ferro- magnetic, Mott-insulator YTiO3 using density functional theory (DFT) and time- dependent density functional theory (TDDFT). In the ground state description, we included a Hubbard U to account for the strong correlations present within the d states on the cation. The excitation spectra was calculated using TDDFT linear response formalism in both the optical limit and the limit of large wavevector transfer. In order to identify the local d-d transitions in the response, we also computed the density response of YTiO3 using a novel technique where the basis …

Perfectly Matched Layer Absorbing Boundary Conditions For The Discrete Velocity Boltzmann-Bgk Equation, Elena Craig

Mathematics & Statistics Theses & Dissertations

Perfectly Matched Layer (PML) absorbing boundary conditions were first proposed by Berenger in 1994 for the Maxwell's equations of electromagnetics. Since Hu first applied the method to Euler's equations in 1996, progress made in the application of PML to Computational Aeroacoustics (CAA) includes linearized Euler equations with non-uniform mean flow, non-linear Euler equations, flows with an arbitrary mean flow direction, and non-linear clavier-Stokes equations. Although Boltzmann-BGK methods have appeared in the literature and have been shown capable of simulating aeroacoustics phenomena, very little has been done to develop absorbing boundary conditions for these methods. The purpose of this work was …

Simulations Of Surfactant Spreading, Jeffrey Wong

HMC Senior Theses

Thin liquid films driven by surface tension gradients are studied in diverse applications, including the spreading of a droplet and fluid flow in the lung. The nonlinear partial differential equations that govern thin films are difficult to solve analytically, and must be approached through numerical simulations. We describe the development of a numerical solver designed to solve a variety of thin film problems in two dimensions. Validation of the solver includes grid refinement studies and comparison to previous results for thin film problems. In addition, we apply the solver to a model of surfactant spreading and make comparisons with theoretical …

Modeling Of Bacillus Spores: Inactivation And Outgrowth, Alexis X. Hurst

Theses and Dissertations

This research models and analyzes the thermochemical damage produced in Bacillus spores by short, high-temperature exposures as well the repair process within damaged Bacillus spores. Thermochemical damage in spores is significantly due to reaction with water, hydrolysis reactions. Applying heat to the spore causes absorbed and chemically bound water molecules become mobile within the spore. These mobile water molecules react by hydrolysis reactions to degrade DNA and enzyme molecules in the spore. In order to survive the thermal inactivation, the spore must repair the damaged DNA during spore germination. The DNA repair process, as well as other germination functions, is …

Analytical Computation Of Proper Orthogonal Decomposition Modes And N-Width Approximations For The Heat Equation With Boundary Control, Tasha N. Fernandez

Masters Theses

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the …

Nonlinear Acoustics Of Piston-Driven Gas-Column Oscillations, Andrew William Wilson

Masters Theses

The piston-driven oscillator is traditionally modeled by directly applying boundary conditions to the acoustic wave equations; with better models re-deriving the wave equations but retaining nonlinear and viscous effects. These better models are required as the acoustic solution exhibits singularity near the natural frequencies of the cavity, with an unbounded (and therefore unphysical) solution. Recently, a technique has been developed to model general pressure oscillations in propulsion systems and combustion devices. Here, it is shown that this technique applies equally well to the piston-driven gas-column oscillator; and that the piston experiment provides strong evidence for the validity of the general …

Theoretical Models For Wall Injected Duct Flows, Tony Saad

Doctoral Dissertations

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by …

Applications Of Pattern Classification To Time-Domain Signals, Crystal Ann Bertoncini

Dissertations, Theses, and Masters Projects

Many different kinds of physics are used in sensors that produce time-domain signals, such as ultrasonics, acoustics, seismology, and electromagnetics. The waveforms generated by these sensors are used to measure events or detect flaws in applications ranging from industrial to medical and defense-related domains. Interpreting the signals is challenging because of the complicated physics of the interaction of the fields with the materials and structures under study. often the method of interpreting the signal varies by the application, but automatic detection of events in signals is always useful in order to attain results quickly with less human error. One method …

Chaotic Scattering In An Open Vase-Shaped Cavity: Topological, Numerical, And Experimental Results, Jaison Allen Novick

Dissertations, Theses, and Masters Projects

We present a study of trajectories in a two-dimensional, open, vase-shaped cavity in the absence of forces The classical trajectories freely propagate between elastic collisions. Bound trajectories, regular scattering trajectories, and chaotic scattering trajectories are present in the vase. Most importantly, we find that classical trajectories passing through the vase's mouth escape without return. In our simulations, we propagate bursts of trajectories from point sources located along the vase walls. We record the time for escaping trajectories to pass through the vase's neck. Constructing a plot of escape time versus the initial launch angle for the chaotic trajectories reveals a …

A New Application Of The Channel Packet Method For Low Energy 1-D Elastic Scattering, Clint M. Zeringue

Theses and Dissertations

An algorithm is presented which uses the channel packet method (CPM) to simulate low-energy, wave-packet propagation and compute S-matrix elements. A four-by-four matrix containing the momentum, expansion coefficients of the reactants and products is introduced to account for initial and final states having both positive and negative momentum. The approach does not consider scattering from one side or the other, rather it considers both incoming and outgoing wave packets from the left and right simultaneously. Therefore, during one simulation all four S-matrix elements, and elements, S_+k,-K, S_{-k, +k}, S_{+k, +k} and S_-k,-k are computed. …

Dynamic Phase Steepening In Alfven Waves, Stephen R. Granade

Honors Theses

Our solar system contains more activity and complexity than can be seen through a telescope. One such "invisible" phenomenon is the solar wind, created by a steady stream of particles blasted away from the sun in all directions. The sun's donut-shaped magnetic field lines channel this stream. Particles moving along the field lines perform an intricate helical dance, with ions winding one way and electrons the other.

The solar wind shapes and is shaped by the magnetic fields of the planets and the sun. If left undisturbed by outside influences, the earth's magnetic field, like the sun's, would resemble a …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

On A Moving Boundary Problem Of Transitional Ballistics, Jen-Ing G. Hwang

Mathematics & Statistics Theses & Dissertations

A major problem which arises in computer simulation of the firing of a gun weapon is the development of numerical schemes which effectively account for the physics of projectile motion. The chief difficulty is that away from the projectile the calculation is ordinarily accomplished on a fixed numerical grid, whereas due to projectile movement some cells of the grid near the projectile undergo volume changes as the calculation proceeds. A local finite volume scheme is developed which accounts for the expansion or compression of cells fore-and-aft of the projectile. Through the process of numerical experiment, the effectiveness of the scheme …