Applied Mathematics Commons^™

Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor

Articles

Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …

Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu

LSU New Orleans Theses and Dissertations

The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and …

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

On The Selection Of A Good Shape Parameter For Rbf Approximation And Its Application For Solving Pdes, Lei-Hsin Kuo

Dissertations

Meshless methods utilizing Radial Basis Functions~(RBFs) are a numerical method that require no mesh connections within the computational domain. They are useful for solving numerous real-world engineering problems. Over the past decades, after the 1970s, several RBFs have been developed and successfully applied to recover unknown functions and to solve Partial Differential Equations (PDEs).
However, some RBFs, such as Multiquadratic (MQ), Gaussian (GA), and Matern functions, contain a free variable, the shape parameter, c. Because c exerts a strong influence on the accuracy of numerical solutions, much effort has been devoted to developing methods for determining shape parameters which provide …

A Tent Pitching Scheme Motivated By Friedrichs Theory, Jay Gopalakrishnan, Peter Monk, Paulina Sepulveda

Mathematics and Statistics Faculty Publications and Presentations

Certain Friedrichs systems can be posed on Hilbert spaces normed with a graph norm. Functions in such spaces arising from advective problems are found to have traces with a weak continuity property at points where the inflow and outflow boundaries meet. Motivated by this continuity property, an explicit space-time finite element scheme of the tent pitching type, with spaces that conform to the continuity property, is designed. Numerical results for a model one-dimensional wave propagation problem are presented.

Generating Random Vectors Using Transformation With Multiple Roots And Its Applications, Qidi Peng, Henry Schellhorn, Lu Zhu

Applications and Applied Mathematics: An International Journal (AAM)

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach.

A Note On An M/M/S Queueing System With Two Reconnect And Two Redial Orbits, Amina A. Bouchentouf, Hanane Sakhi

Applications and Applied Mathematics: An International Journal (AAM)

A queueing system with two reconnect orbits, two redial (retrial) orbits, s servers and two independent Poisson streams of customers is considered. An arriving customer of type i, i = 1, 2 is handled by an available server, if there is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience and abandon after an exponentially distributed amount of time, the abandoned one may leave the system (lost customer) or move into one of the redial orbits, from which he makes a new …

Analysis Of Repairable M[X]/(G1,G2)/1 - Feedback Retrial G-Queue With Balking And Starting Failures Under At Most J Vacations, P. Rajadurai, M. C. Saravanarajan, V. M. Chandrasekaran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type …

Optimal Solution Of A Fully Fuzzy Linear Fractional Programming Problem By Using Graded Mean Integration Representation Method, Moumita Deb, P. K. De

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, the study of fully fuzzy linear fractional programming problem (FFLFPP) using graded mean integration representation method is discussed where all the parameters and variables are characterized by trapezoidal fuzzy numbers. A computational algorithm has been presented to obtain an optimal solution by applying simplex method. To demonstrate the applicability of the proposed approach, one numerical example is solved. Also to check the efficiency and feasibility of the proposed approach, we compare the results of examples by applying crisp numbers, triangular fuzzy numbers and trapezoidal fuzzy numbers.

Optimal Error Estimate Of Upwind Scheme On Adaptive Grid For Two Parameter Singular Perturbation Problem, J. Mohapatra, M. K. Mahalik

Applications and Applied Mathematics: An International Journal (AAM)

A singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved by an upwind finite difference operator on an appropriate non-uniform mesh constructed adaptively by equi-distributing a monitor function based on the solution. An error bound in the maximum norm is established theoretically with the error constants shown to be independent of both singular perturbation parameters. The normalized flux obtained via interpolating the polynomial from the numerical solution is also uniformly convergent. A numerical experiment illustrates in practice the result of convergence proved theoretically.

On Some Optimal Multiple Root-Finding Methods And Their Dynamics, Munish Kansal, V. Kanwar, Saurabh Bhatia

Applications and Applied Mathematics: An International Journal (AAM)

Finding multiple zeros of nonlinear functions pose many difficulties for many of the iterative methods. In this paper, we present an improved optimal class of higher-order methods for multiple roots having quartic convergence. The present approach of deriving an optimal class is based on weight function approach. In terms of computational cost, all the proposed methods require three functional evaluations per full iteration, so that their efficiency indices are 1.587 and, are optimal in the sense of Kung-Traub conjecture. It is found by way of illustrations that they are useful in high precision computing enviroments. Moreover, basins of attraction of …

Implicit-Explicit Higher-Order Time Integration Schemes For Computations Of Structural Dynamics With Fluid-Structure Interaction, José C. Pedro, Mapundi K. Banda, Precious Sibanda

Applications and Applied Mathematics: An International Journal (AAM)

In this paper higher order implicit Runge-Kutta schemes are applied to fluid-structure interaction (FSI) simulations. A staggered approach with a structural predictor is applied to an FSI problem. The equations governing the dynamics of the structure are integrated in time by the Explicit Single Diagonal Implicit Runge-Kutta (ESDIRK) schemes and the arbitrary high order finite volume scheme is taken as the fluid solver. The performance of the ESDIRK scheme of order of convergence three to five is tested. Comparative studies with other time integration schemes which have been successfully applied to FSI problems are undertaken. Comparisons to test the performance …

Period Decompositions For The Capacitated Lot Size Problem With Setup Times, Silvio Alexandre De Araujo, Bert De Reyck, Zeger Degraeve, Ioannis Fragkos, Raf Jans

Research Collection Lee Kong Chian School Of Business

We study the multi-item capacitated lot sizing problem with setup times. Based on two strong reformulations of the problem, we present a transformed reformulation and valid inequalities that speed up column generation and Lagrange relaxation. We demonstrate computationally how both ideas enhance the performance of our algorithm and show theoretically how they are related to dual space reduction techniques. We compare several solution methods and propose a new efficient hybrid scheme that combines column generation and Lagrange relaxation in a novel way. Computational experiments show that the proposed solution method for finding lower bounds is competitive with textbook approaches and …

Transition Orbits Of Walking Droplets, Joshua Parker

Physics

It was recently discovered that millimeter-sized droplets bouncing on the surface of an oscillating bath of the same fluid can couple with the surface waves it produces and begin walking across the fluid bath. These walkers have been shown to behave similarly to quantum particles; a few examples include single-particle diffraction, tunneling, and quantized orbits. Such behavior occurs because the drop and surface waves depend on each other to exist, making this the first and only known macroscopic pilot-wave system. In this paper, the quantized orbits between two identical drops are explored. By sending a perturbation to a pair of …

A Super Non-Dominated Point For Multi-Objective Transportation Problem, Abbas S. Bander, Vahid Morovati, Hadi Basirzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper a method to obtain a non-dominated point for the multi-objective transportation problem is presented. The superiority of this method over the other existing methods is that the presented non-dominated point is the closest solution to the ideal solution of that problem. The presented method does not need to have the ideal point and other parameters to find this solution. Also, the calculative load of this method is less than other methods in the literature.

Multiphysics Modeling To Enhance Understanding Of Microwave Heating Of Food In Domestic Ovens, Jiajia Chen

Department of Agricultural and Biological Systems Engineering: Dissertations, Theses, and Student Research

Nonuniform heating is the biggest issue in the microwave heating of prepared meals. Multiphysics based models are promising tools to improve microwave heating uniformity by properly designing the food product. However, limited availability of accurate temperature-dependent material properties, inadequate model prediction accuracy, and high computational power and complexity in model development are three gaps that greatly limited the application of these models in the food industry.

To fill in the gaps, firstly, we developed a multitemperature calibration protocol to measure temperature-dependent dielectric properties (dielectric constant and loss factor). The temperature-dependent dielectric and thermal (thermal conductivity and specific heat capacity) properties …

Time Integration Methods Of Fundamental Solutions And Approximate Fundamental Solutions For Nonlinear Elliptic Partial Differential Equations, Corey Leon Jones

Dissertations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

Efficient Thermal Image Segmentation Through Integration Of Nonlinear Enhancement With Unsupervised Active Contour Model, Fatema Albalooshi, Evan Krieger, Paheding Sidike, Vijayan K. Asari

Electrical and Computer Engineering Faculty Publications

Thermal images are exploited in many areas of pattern recognition applications. Infrared thermal image segmentation can be used for object detection by extracting regions of abnormal temperatures. However, the lack of texture and color information, low signal-to-noise ratio, and blurring effect of thermal images make segmenting infrared heat patterns a challenging task. Furthermore, many segmentation methods that are used in visible imagery may not be suitable for segmenting thermal imagery mainly due to their dissimilar intensity distributions.

Thus, a new method is proposed to improve the performance of image segmentation in thermal imagery. The proposed scheme efficiently utilizes nonlinear intensity …

Efficient General Computational Method For Estimation Of Standard Atmosphere Parameters, Nihad E. Daidzic Ph.D., Sc.D.

International Journal of Aviation, Aeronautics, and Aerospace

Knowledge of standard air temperature, pressure, density, speed of sound, and viscosity as a function of altitude is essential information in aircraft design, performance testing, pressure altimeter calibration, and several other aeronautical engineering and aviation science applications. A new efficient computational method for rapid calculations of standard atmospheric parameters up to 86 orthometric km is presented. Additionally, mass and weight of each standard atmospheric layer were calculated using a numerical integration method. The sum of all fractional masses and weights represents the total mass and weight of Earth’s atmosphere. The results obtained here agree well with measurements and models of …

Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene

Publications and Research

The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment …

Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond

Dartmouth Scholarship

Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …

Almost Sure Asymptotic Stabilization Of Differential Equations With Time-Varying Delay By Lévy Noise, Dezhi Liu, Weiqun Wang, Jose Luis Menaldi

Mathematics Faculty Research Publications

This paper aims to determine that the Lévy noise can stabilize the given differential equations with time-varying delay, which has generalized the Brownian motion case. An analysis is developed and sufficient conditions on the stabilization for stochastic differential equations with time-varying delay are presented. Our stabilization criteria is in terms of linear matrix inequalities (LMIs), whence the feedback controls can be designed more easily in practice.

Mathematical Modeling Of Emiliania Huxleyi And A Host-Specific Virus, Julia Middleton

Honors Theses

The world’s oceans provide the basis for life on the planet. One microscopic algae, the coccolithophores, and Emiliania huxleyi in particular, is a major source of carbon drawdown in the context of the global carbon cycle and account for a significant amount of the primary production in oceanic ecosystems. We know that the oceans are packed with marine viruses and they have an important role in the rise and fall of plankton populations but current mathematical models do not accurately account for virus-host interactions when predicting plankton blooms. Therefore I am using model optimization and comparison techniques to evaluate current …

One-Bit Compressive Sensing With Partial Support Information, Phillip North

CMC Senior Theses

This work develops novel algorithms for incorporating prior-support information into the field of One-Bit Compressed Sensing. Traditionally, Compressed Sensing is used for acquiring high-dimensional signals from few linear measurements. In applications, it is often the case that we have some knowledge of the structure of our signal(s) beforehand, and thus we would like to leverage it to attain more accurate and efficient recovery. Additionally, the Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization. Indeed, the field of One-Bit Compressive Sensing aims to recover a signal from measurements reduced to only their sign-bit. This …

Singular Value Computation And Subspace Clustering, Qiao Liang

Theses and Dissertations--Mathematics

In this dissertation we discuss two problems. In the first part, we consider the problem of computing a few extreme eigenvalues of a symmetric definite generalized eigenvalue problem or a few extreme singular values of a large and sparse matrix. The standard method of choice of computing a few extreme eigenvalues of a large symmetric matrix is the Lanczos or the implicitly restarted Lanczos method. These methods usually employ a shift-and-invert transformation to accelerate the speed of convergence, which is not practical for truly large problems. With this in mind, Golub and Ye proposes an inverse-free preconditioned Krylov subspace method, …

The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang

Theses and Dissertations--Mathematics

The problem of computing the matrix exponential e^tA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., e^tAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …