Applied Mathematics Commons^™

Modeling Nonlinear Heat Transfer For A Pin-On-Disc Sliding System, Brian A. Boardman

Theses and Dissertations

The objective of this research is to develop a numerical method to characterize heat transfer and wear rates for samples of Vascomax® 300, or Maraging 300, steel. A pin-on-disc experiment was conducted in which samples were exposed to a high-pressure, high-speed, sliding contact environment. This sliding contact generates frictional heating that influences the temperature distribution and wear characteristics of the test samples. A two-dimensional nonlinear heat transfer equation is discretized and solved via a second-order explicit finite difference scheme to predict the transient temperature distribution of the pin. This schematic is used to predict the removal of material from the …

Correlation Coefficients For A Study With Repeated Measures, Guogen Shan, Hua Zhang, Tao Jiang

Environmental & Global Health Faculty Research

Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlation calculation are compared: (1) Pearson correlation; (2) correlation of subject means; (3) partial correlation for subject effect; (4) partial correlation for visit effect; and (5) a mixed model approach. Pearson correlation coefficient is traditionally used in a cross-sectional study. Pearson correlation is close to the correlations computed from mixed-effects models that consider the correlation structure, but Pearson correlation may not be theoretically appropriate in …

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

Emirates Journal for Engineering Research

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.

Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, Raghad Kadhim Salih

Emirates Journal for Engineering Research

A proposed method is presented to solve n^th order linear retarded Volterra integro-differential equations (RVIDE's) numerically by using fourth-order block and Weddle methods. Comparison between numerical and exact results has been given in numerical examples for conciliated the accuracy of the results of the proposed scheme.

A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez

Honors Program: Senior Projects (Public)

Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.

Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on …

A Demographic Model Of An Endangered Florida Native Bromeliad (Tillandsia Utriculata), Zoe S. Brookover, Alexandra M. Campbell, Brian D. Christman, Sydney L. Davis, Erin N. Bodine

Spora: A Journal of Biomathematics

The large, long-lived, epiphytic bromeliad Tillandsia utriculata is currently listed as state-endangered in Florida due to significant population reduction from predation by an invasive weevil, Metamasius callizona. We have developed a novel demographic model of a population of T. utriculata in Myakka River State Park (MRSP) in Sarasota, Florida using a stage-structured matrix model. Analysis of the model revealed conditions for population viability over a variety of parameter scenarios. Model analysis showed that without weevil predation the minimum germination rate required for population viability is low (4–16%), and that given a viable population at structural equilibrium we would expect …

High-Order Adaptive Synchrosqueezing Transform, Jawaher Alzahrani

Dissertations

The prevalence of the separation of multicomponent non-stationary signals across many elds of research makes this concept an important subject of study. The synchrosqueezing transform (SST) is a particular type of reassignment method. It aims to separate and recover the components of a multicomponent non-stationary signal. The short time Fourier transform (STFT)-based SST (FSST) and the continuous wavelet transform (CWT)based SST (WSST) have been used in engineering and medical data analysis applications. The current study introduces the dierent versions of FSST and WSST to estimate instantaneous frequency (IF) and to recover components. It has a good concentration and reconstruction for …

Finding Music In Chaos: Designing And Composing With Virtual Instruments Inspired By Chaotic Equations, Landon P. Viator

LSU Doctoral Dissertations

Using chaos theory to design novel audio synthesis engines has been explored little in computer music. This could be because of the difficulty of obtaining harmonic tones or the likelihood of chaos-based synthesis engines to explode, which then requires re-instantiating of the engine to proceed with sound production. This process is not desirable when composing because of the time wasted fixing the synthesis engine instead of the composer being able to focus completely on the creative aspects of composition. One way to remedy these issues is to connect chaotic equations to individual parts of the synthesis engine instead of relying …

Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

To predict how the Pavement Condition Index will change over time, practitioners use a complex empirical formula derived in the 1980s. In this paper, we provide a possible theoretical explanation for this formula, an explanation based on general ideas of invariance. In general, the existence of a theoretical explanation makes a formula more reliable; thus, we hope that our explanation will make predictions of road quality more reliable.

New (Simplified) Derivation Of Nash's Bargaining Solution, Nguyen Hoang Phuong, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

According to the Nobelist John Nash, if a group of people wants to selects one of the alternatives in which all of them get a better deal than in a status quo situations, then they should select the alternative that maximizes the product of their utilities. In this paper, we provide a new (simplified) derivation of this result, a derivation which is not only simpler -- it also does not require that the preference relation between different alternatives be linear.

Towards Making Fuzzy Techniques More Adequate For Combining Knowledge Of Several Experts, Nguyen Hoang Phuong, Vladik Kreinovich

Departmental Technical Reports (CS)

In medical and other applications, expert often use rules with several conditions, each of which involve a quantity within the domain of expertise of a different expert. In such situations, to estimate the degree of confidence that all these conditions are satisfied, we need to combine opinions of several experts -- i.e., in fuzzy techniques, combine membership functions corresponding to different experts. In each area of expertise, different experts may have somewhat different membership functions describing the same natural-language ("fuzzy") term like small. It is desirable to present the user with all possible conclusions corresponding to all these membership functions. …

Why Mean, Variance, Moments, Correlation, Skewness Etc. – Invariance-Based Explanations, Olga Kosheleva, Laxman Bokati, Vladik Kreinovich

Departmental Technical Reports (CS)

In principle, we can use many different characteristics of a probability distribution. However, in practice, a few of such characteristics are mostly used: mean, variance, moments, correlation, etc. Why these characteristics and not others? The fact that these characteristics have been successfully used indicates that there must be some reason for their selection. In this paper, we show that the selection of these characteristics can be explained by the fact that these characteristics are invariant with respect to natural transformations -- while other possible characteristics are not invariant.

Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty

Mathematics and Statistics Faculty Publications

The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and liftedgraphic matroids introduced earlier by Zaslavsky. For each biased graph (G, B) Zaslavsky defined a unique lift matroid L(G, B) and a unique frame matroid F(G, B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B, L, F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there …

Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an …

Responsive Economic Model Predictive Control For Next-Generation Manufacturing, Helen Durand

Chemical Engineering and Materials Science Faculty Research Publications

There is an increasing push to make automated systems capable of carrying out tasks which humans perform, such as driving, speech recognition, and anomaly detection. Automated systems, therefore, are increasingly required to respond to unexpected conditions. Two types of unexpected conditions of relevance in the chemical process industries are anomalous conditions and the responses of operators and engineers to controller behavior. Enhancing responsiveness of an advanced control design known as economic model predictive control (EMPC) (which uses predictions of future process behavior to determine an economically optimal manner in which to operate a process) to unexpected conditions of these types …

A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the …

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.

A Tutorial Of The Immersed Interface Method, Sheng Xu

Science Seminars

The immersed interface method is a computational methodology to solve differential equations with non-smooth solutions across interfaces. In this talk, Dr. Xu will use a simple example to demonstrate the main ingredients and features of this method. He will then present the application of the method to the simulation of fluid flows and make the connection of the application with the simple example.

This talk is a tutorial of the method for undergraduate students.

Come at 3:30pm for refreshments, speaker at 4:00pm

Direct Ellipsoidal Fitting Of Discrete Multi-Dimensional Data, Madeline Hamilton

SMU Journal of Undergraduate Research

Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the equation of ellipsoid for the boundary of such multi-dimensional discrete distribution. In this approach, the equation of an ellipsoid is reconstructed using a set of matrix equations from low-dimensional projections of the input data. We provide a Mathematica program realizing the full implementation of the ellipsoid reconstruction algorithm in an arbitrary number of dimensions. To demonstrate its many potential uses, the direct reconstruction method is applied to quasi-Gaussian statistical …

Informal Professional Development On Twitter: Exploring The Online Communities Of Mathematics Educators, Jaymie Ruddock

SMU Journal of Undergraduate Research

Professional development in its most traditional form is a classroom setting with a lecturer and an overwhelming amount of information. It is no surprise, then, that informal professional development away from institutions and on the teacher's own terms is a growing phenomenon due to an increased presence of educators on social media. These communities of educators use hashtags to broadcast to each other, with general hashtags such as #edchat having the broadest audience. However, many math educators usethe hashtags #ITeachMath and #MTBoS, communities I was interested in learning more about. I built a python script that used Tweepy to connect …