Applied Mathematics Commons^™

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data …

Switching Mechanism In The B-1revtilted Phase Of Bent-Core Liquid Crystals, Carlos J. García-Cervera, Tiziana Giorgi, Sookyung Joo, Xin Yang Lu

Mathematics & Statistics Faculty Publications

The B_1RevTilted is a uniformly smectic tilted columnar phase in which the macroscopic polarization can be reorientated via electric field. To study the effects on the reorientation mechanism of the various physical parameters, we analyze a local, and a non-local Landau-de Gennes-type energy functional. For the case of large columnar samples, we show that both energies give the same qualitative behavior, with a relevant role played by the terms that describe the interaction between polarization and nematic directors. We also obtain existence of the L²-gradient flow in metric spaces for the full local energy.

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 …}

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

A Partitioned Approach For Computing Fluid-Structure Interaction, With Application To Tumor Modeling And Simulation, Asim Timalsina

Mathematics & Statistics Theses & Dissertations

Modeling and Simulation plays a critical role in understanding complex physical and biological phenomena as it provides an efficient and controlled test environment, without the risk of costly experiments and clinical trials. In this dissertation, we present an extensive study of two such systems with integrated application: Fluid structure interaction (FSI) and virotherapy on tumor. Moreover, we substantiate a few preliminary results of FSI application on tumor.

The FSI problem comprises of fluid forces exerted on the solid body and the motion of the structure affecting the fluid flow. FSI problems are of great interest to applied industries, however they …

Scalable And Fully Distributed Localization In Large-Scale Sensor Networks, Miao Jin, Su Xia, Hongyi Wu, Xianfeng David Gu

Electrical & Computer Engineering Faculty Publications

This work proposes a novel connectivity-based localization algorithm, well suitable for large-scale sensor networks with complex shapes and a non-uniform nodal distribution. In contrast to current state-of-the-art connectivity-based localization methods, the proposed algorithm is highly scalable with linear computation and communication costs with respect to the size of the network; and fully distributed where each node only needs the information of its neighbors without cumbersome partitioning and merging process. The algorithm is theoretically guaranteed and numerically stable. Moreover, the algorithm can be readily extended to the localization of networks with a one-hop transmission range distance measurement, and the propagation of …

Fire, Ice, Water, And Dirt: A Simple Climate Model, John Kroll

Mathematics & Statistics Faculty Publications

A simple paleoclimate model was developed as a modeling exercise. The model is a lumped parameter system consisting of an ocean (water), land (dirt), glacier, and sea ice (ice) and driven by the sun (fire). In comparison with other such models, its uniqueness lies in its relative simplicity yet yielding good results. For nominal values of parameters, the system is very sensitive to small changes in the parameters, yielding equilibrium, steady oscillations, and catastrophes such as freezing or boiling oceans. However, stable solutions can be found, especially naturally oscillating solutions. For nominally realistic conditions, natural periods of order 100kyrs are …

Accounting For Locational, Temporal, And Physical Similarity Of Residential Sales In Mass Appraisal Modeling: The Development And Application Of Geographically, Temporally, And Characteristically Weighted Regression, Paul E. Bidanset, Michael Mccord, John R. Lombard, Peadar Davis, William J. Mccluskey

School of Public Service Faculty Publications

Geographically weighted regression (GWR) has been recognized in the assessment community as a viable automated valuation model (AVM) to help overcome, at least in part, modeling hurdles associated with location, such as spatial heterogeneity and spatial autocorrelation of error terms. Although previous researchers have adjusted the GWR weights matrix to also weight by time of sale or by structural similarity of properties in AVMs, the research described in this paper is the first that has done so by all three dimensions (i.e., location, structural similarity, and time of sale) simultaneously. Using 24 years of single-family residential sales in Fairfax, Virginia, …

On A Time Domain Boundary Integral Equation Formulation For Acoustic Scattering By Rigid Bodies In Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation. However, the constant mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the assumed uniform flow. A customary boundary condition for rigid surfaces is that the normal acoustic velocity be zero. In this paper, a careful study of the acoustic energy conservation equation is presented that shows such a boundary condition would in fact lead to source …

A Wasserstein Gradient Flow Approach To Poisson-Nernst-Planck Equations, David Kinderlehrer, Leinard Monsaingeon, Xiang Xu

Mathematics & Statistics Faculty Publications

The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial …

Multiplicative Noise Removal With A Sparsity-Aware Optimization Model, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus …

A New Formulation Of Time Boundary Integral Equation For Acoustic Wave Scattering In The Presence Of A Uniform Mean Flow, Fang Q. Hu, Michelle E. Pizzo, Douglas M. Nark

Mathematics & Statistics Faculty Publications

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In …

Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …

Heuristic And Exact Algorithms For The Two-Machine Just In Time Job Shop Scheduling Problem, Mohammed Al Salem, Leonardo Bedoya-Valencia, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

The problem addressed in this paper is the two-machine job shop scheduling problem when the objective is to minimize the total earliness and tardiness from a common due date (CDD) for a set of jobs when their weights equal 1 (unweighted problem). This objective became very significant after the introduction of the Just in Time manufacturing approach. A procedure to determine whether the CDD is restricted or unrestricted is developed and a semirestricted CDD is defined. Algorithms are introduced to find the optimal solution when the CDD is unrestricted and semirestricted. When the CDD is restricted, which is a much …

Global Strong Solutions Of The Full Navier-Stokes And Q-Tensor System For Nematic Liquid Crystal Flows In Two Dimensions, Cecilia Cavaterra, Elisabetta Rocca, Hao Wu, Xiang Xu

Mathematics & Statistics Faculty Publications

We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 …

Sawtooth Profile In Smectic A Liquid Crystals, Carlos J. Garcia-Cervera, Tiziana Giorgi, Sookyung Joo

Mathematics & Statistics Faculty Publications

We study the de Gennes free energy for smectic A liquid crystals over S^2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter a, and investigate the behaviors of the minimizers when the field strength is of order O (ε^-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and …

Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak

Mathematics & Statistics Faculty Publications

A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …

Accuracy Comparison Of Numerical Integration Algorithms For Real-Time Hybrid Simulations, Ganesh Anant Reddy

Civil & Environmental Engineering Theses & Dissertations

The use of accurate numerical integration algorithms is one of the key factors for a successful real-time hybrid simulation (RTHS). In RTHSs, explicit integration algorithms are preferred more than implicit methods since all calculations need to be completed within a given time step during simulation. Explicit methods require the use of effective stiffness and damping for experimental substructures, which are incorporated into the calculation of the integration parameters. In general, those values that are greater than the expected stiffness and damping of the experimental substructure are used to ensure the stability of simulation. If a rate-dependent and nonlinear experimental substructure …

The Effect Of Noise On The Response Of A Vertical Cantilever Beam Energy Harvester, Michael I. Friswell, Onur Bilgen, S. Faruque Ali, Grzegorz Litak, Sondipon Adhikari

Mechanical & Aerospace Engineering Faculty Publications

An energy harvesting concept has been proposed comprising a piezoelectric patch on a vertical cantilever beam with a tip mass. The cantilever beam is excited in the transverse direction at its base. This device is highly nonlinear with two potential wells for large tip masses, when the beam is buckled. For the pre-buckled case considered here, the stiffness is low and hence the displacement response is large, leading to multiple solutions to harmonic excitation that are exploited in the harvesting device. To maximise the energy harvested in systems with multiple solutions the higher amplitude response should be preferred. This paper …

Estimating Cost Adjustments Required To Accomplish Target Savings In Chronic Disease Management Interventions: A Simulation Study, Rafael Diaz, Joshua G. Behr, Bruce S. Britton

VMASC Publications

Chronic diseases are persistent ailments that are not preventable or curable with medication or vaccination. Many of the leading chronic conditions in industrialized societies may be related to lifestyle choices. The prevalence of these chronic conditions significantly affects the health, suffering, and longevity of patients. This paper demonstrates the utility of system dynamics as an approach to model and simulate the behavior of key cost factors in the implementation of population health management interventions. The study uses modeling and simulation as an evaluative method to identify potential savings stemming from an intervention within a well-defined population group. The model is …

Modeling And Simulation Of Molecular Couette Flows And Related Flows, Wei Li

Mathematics & Statistics Theses & Dissertations

In this thesis, molecular Couette flow is clearly defined and the modeling and simulation of this kind of flow is systematically investigated. First, the integral equations for the velocity of gaseous Couette flow and related flows are derived from linearized Boltzmann BGK equation with Maxwell boundary condition and solved with high precision by using Chebyshev collocation and chunk-based collocation methods. The velocity profiles of gaseous Couette flows and related flows with a wide range of Knudsen number and the Maxwell boundary condition of various accommodation ratios are obtained. Moreover, the order of convergence of the numerical methods is also discussed …

Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Duality Of The Weak Parallelogram Laws On Banach Spaces, Charles Benjamin Harris

Mathematics & Statistics Theses & Dissertations

The first chapter of this thesis concerns the stability and convergence of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation

u'(t) + ∫^t₀ β (t--s) Au(s) ds = 0, t ≥ 0, u( 0) = u_0,

which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space and β(t) is locally integrable, nonnegative, nonincreasing, convex, with -- β'(t) and β''(t) convex. We establish …

Generating Combinatorial Objects- A New Perspective, Alexander Chizoma Nwala

Computer Science Theses & Dissertations

Combinatorics is the science of "possibilities." This definition, while not formal is a fair statement because all too often, in order to gain insight into the solution of many counting problems, we explore the possibilities. In some cases we seek to know how many options, while in other cases we seek to enumerate or list the options. Irrespective of the scenario, combinatorics plays a vital role today. In many instances such as exploring the options for choosing a new password for a combination lock, we employ combinatorics. In considering the possible license plate permutations for a state, or to see …

Analyzing Cholera Dynamics In Homogeneous And Heterogeneous Environments, Drew Posny

Mathematics & Statistics Theses & Dissertations

Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. Mathematical models play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. This dissertation is concerned with mathematical modeling and analysis of cholera dynamics. First, we study an autonomous model in a homogeneous environment with added controls that involves both direct …

Modeling And Simulation Of Shape Changes Of Red Blood Cells In Shear Flow, John Gounley

Mathematics & Statistics Theses & Dissertations

A description of the biomechanical character of red blood cells is given, along with an introduction to current computational schemes which use deformable capsules to simulate red blood cell shape change. A comprehensive two- and three-dimensional framework for the fluid-structure interaction between a deformable capsule and an ambient flow is provided. This framework is based on the immersed boundary method, using lattice Boltzmann and finite element methods for the fluid and structure, respectively. The characteristic response and recovery times of viscoelastic circular and spherical capsules are compared, and their dependence on simulation parameters is shown. The shape recovery of biconcave …

Graph Partitioning Using Matrix Values For Preconditioning Symmetric Positive Definite Systems, Eugenr Vecharynski, Yousef Saad, Masha Sosonkina

Computational Modeling & Simulation Engineering Faculty Publications

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel matrix-vector multiplication, and typically disregard the information on the coefficients of the matrix. This information, however, may have a significant impact on the quality of the preconditioning procedure used within the chosen iterative scheme. In the present paper, we suggest a spectral partitioning algorithm, which takes into account the information on the matrix coefficients and constructs partitions with respect to the objective of enhancing the quality …

Data Mining Based Hybridization Of Meta-Raps, Fatemah Al-Duoli, Ghaith Rabadi

Engineering Management & Systems Engineering Faculty Publications

Though metaheuristics have been frequently employed to improve the performance of data mining algorithms, the opposite is not true. This paper discusses the process of employing a data mining algorithm to improve the performance of a metaheuristic algorithm. The targeted algorithms to be hybridized are the Meta-heuristic for Randomized Priority Search (Meta-RaPS) and an algorithm used to create an Inductive Decision Tree. This hybridization focuses on using a decision tree to perform on-line tuning of the parameters in Meta-RaPS. The process makes use of the information collected during the iterative construction and improvement phases Meta-RaPS performs. The data mining algorithm …

Lattice-Boltzmann Simulations Of The Thermally Driven 2d Square Cavity At High Rayleigh Numbers, Dario Contrino, Pierre Lallemand, Pietro Asinari, Li-Shi Luo

Mathematics & Statistics Faculty Publications

The thermal lattice Boltzmann equation (TLBE) with multiple-relaxation-times (MRT) collision model is used to simulate the steady thermal convective flows in the two-dimensional square cavity with differentially heated vertical walls at high Rayleigh numbers. The MRT-TLBE consists of two sets of distribution functions, i.e., a D2Q9 model for the mass-momentum equations and a D2Q5 model for the temperature equation. The dimensionless flow parameters are the following: the Prandtl number Pr = 0.71 and the Rayleigh number Ra = 10⁶, 10⁷, and 10⁸. The D2Q9 + D2Q5 MRT-TLBE is shown to be second-order accurate and …

Topics In Electromagnetic, Acoustic, And Potential Scattering Theory, Umaporn Nuntaplook

Mathematics & Statistics Theses & Dissertations

With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves — is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering …