Applied Mathematics Commons^™

Mathematical Analysis And Applications Of Logistic Differential Equation, Eva Arnold, Monika Neda

Festival of Communities: UG Symposium (Posters)

Logistic differential equation has a way to measure the proportionality of various resources with respect to time. This equation has been used in many research areas, such as, biology, medicine, psychology, economics, etc. A mathematical description, analysis and solution of the logistic type differential equation is studied. Besides the mathematical part, the poster will contain biological examples, graphs of the direction fields for different parameter settings and logistic plots for specific species population. The logistic growth function will also be applied to learning curves in area of psychology, as a rate at which performance improves.

Oral Presentation: The Universe In A Box, Jason Jaacks

Festival of Communities: UG Symposium (Posters)

When and how galaxies formed throughout the history of the Universe is one of the most fundamental questions of astronomy and astrophysics. As technology improves, astronomers are able to push the frontier of galaxy observation to a period when the Universe was less than 1 billion years old. This is when the first galaxies are beginning to form. However, beyond the limits of observational technology lies data fundamental to our complete understanding of these processes. Using state-of-the-art cosmological hydrodynamic computer codes combined with access to the nation’s largest and fastest supercomputers, we are able to simulate the formation and evolution …

Dynamic Decision Making And Race Games, Shipra De

Calvert Undergraduate Research Awards

Frequent criticism in dynamic decision making research pertains to the overly complex nature of the decision tasks used in experimentation. To address such concerns we study dynamic decision making with respect to the simple race game Hog, which has a computable optimal decision strategy. In the two-player game of Hog, individuals compete to be the first to reach a designated threshold of points. Players alternate rolling a desired quantity of dice. If the number one appears on any of the dice, the player receives no points for his turn; otherwise, the sum of the numbers appearing on the dice is …

A Mathematical Approach For Optimizing The Casino Slot Floor: A Linear Programming Application, Kasra Christopher Ghaharian

UNLV Theses, Dissertations, Professional Papers, and Capstones

Linear programming is a tool that has been successfully applied to various problems across many different industries and businesses. However, it appears that casino operators may have overlooked this useful and proven method. At most casino properties the bulk of gaming revenues are derived from slot machines. It is therefore imperative for casino operators to effectively manage and cultivate the performance of this department. A primary task for the casino operator is planning and deciding the mix of slot machines in order to maximize performance.

This paper presents the task of optimizing the casino slot floor as a linear programming …

Conservation Based Uncertainty Propagation In Dynamic Systems, Lillian J. Ratliff

UNLV Theses, Dissertations, Professional Papers, and Capstones

Uncertainty is present in our everyday decision making process as well as our understanding of the structure of the universe. As a result an intense and mathematically rigorous study of how uncertainty propagates in the dynamic systems present in our lives is warranted and arguably necessary. In this thesis we examine existing methods for uncertainty propagation in dynamic systems and present the results of a literature survey that justifies the development of a conservation based method of uncertainty propagation. Conservation methods are physics based and physics drives our understanding of the physical world. Thus, it makes perfect sense to formulate …

Efficient Simulation Of Fluid Flow, David Hannasch, Monika Neda

Undergraduate Research Opportunities Program (UROP)

We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop.

Statistical Inferences For Functions Of Parameters Of Several Pareto And Exponential Populations With Application In Data Traffic, Sumith Gunasekera

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, we discuss the usability and applicability of three statistical inferential frameworks--namely, the Classical Method, which is sometimes referred to as the Conventional or the Frequentist Method, based on the approximate large sample approach, the Generalized Variable Method based on the exact generalized p -value approach, and the Bayesian Method based on prior densities--for solving existing problems in the area of parametric estimation. These inference procedures are discussed through Pareto and exponential distributions that are widely used to model positive random variables relevant to social, scientific, actuarial, insurance, finance, investments, banking, and many other types of observable phenomena. …

An H-Adaptive Finite-Element Technique For Constructing 3d Wind Fields, Darrell Pepper, Xiuling Wang

Mechanical Engineering Faculty Research

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions …

Modeling Redox-Based Magnetohydrodynamics In Three-Dimensional Microfluidic Channels, Hussameddine S. Kabbani, Aihua Wang, Xiaobing Luo, Shizhi Qian

Mechanical Engineering Faculty Research

RedOx-based magnetohydrodynamic MHD[1] flows in three-dimensional microfluidic channels are investigated theoretically with a coupled mathematical model consisting of the Nernst-Planck equations for the concentrations of ionic species, the local electroneutrality condition for the electric potential, and the Navier-Stokes equations for the flow field. A potential difference is externally applied across two planar electrodes positioned along the opposing walls of a microchannel that is filled with a dilute RedOx electrolyte solution, and a Faradaic current transmitted through the solution results. The entire device is positioned under a magnetic field which can be provided by either a permanent magnet or an electromagnet. …

Traveling Waves In A Suspension Bridge System, Robert A. Ain

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we study the traveling waves in a Lazer-McKenna suspension bridge system which is governed by two coupled nonlinear beam and wave equations. The Lazer-McKenna suspension bridge system describes the vertical deflections in the roadbed and supporting cable of a suspension bridge. Based on some basic analysis on the system, we are able to compute traveling waves numerically by using MAPLE. Multiple large-amplitude traveling waves are obtained. The graphs of various traveling waves are displayed and discussed.

Application Of Meshless Methods For Thermal Analysis, Darrell Pepper, Bozidar Sarler

Mechanical Engineering Faculty Research

Many numerical and analytical schemes exist for solving heat transfer problems. The meshless method is a particularly attractive method that is receiving attention in the engineering and scientific modeling communities. The meshless method is simple, accurate, and requires no polygonalisation. In this study, we focus on the application of meshless methods using radial basis functions (RBFs) — which are simple to implement — for thermal problems. Radial basis functions are the natural generalization of univariate polynomial splines to a multivariate setting that work for arbitrary geometry with high dimensions. RBF functions depend only on the distance from some center point. …

A Fast And Simple Algorithm For Computing M Shortest Paths In Stage Graph, M. Sherwood, Laxmi P. Gewali, Henry Selvaraj, Venkatesan Muthukumar

Electrical & Computer Engineering Faculty Research

We consider the problem of computing m shortest paths between a source node s and a target node t in a stage graph. Polynomial time algorithms known to solve this problem use complicated data structures. This paper proposes a very simple algorithm for computing all m shortest paths in a stage graph efficiently. The proposed algorithm does not use any complicated data structure and can be implemented in a straightforward way by using only array data structure. This problem appears as a sub-problem for planning risk reduced multiple k-legged trajectories for aerial vehicles.

A Fast And Simple Algorithm For Computing M-Shortest Paths In State Graph, M. Sherwood, Laxmi P. Gewali, Henry Selvaraj, Venkatesan Muthukumar

Electrical & Computer Engineering Faculty Research

We consider the problem of computing m shortest paths between a source node s and a target node t in a stage graph. Polynomial time algorithms known to solve this problem use complicated data structures. This paper proposes a very simple algorithm for computing all m shortest paths in a stage graph efficiently. The proposed algorithm does not use any complicated data structure and can be implemented in a straightforward way by using only array data structure. This problem appears as a sub-problem for planning risk reduced multiple k-legged trajectories for aerial vehicles.

Real-Time Travel Time Estimation Using Macroscopic Traffic Flow Models, Pushkin Kachroo, Kaan Ozbay, Antoine G. Hobeika

Electrical & Computer Engineering Faculty Research

This paper presents the estimation of travel time on highways based on macroscopic modelling. The focus is on real-time values as compared to average or static values. The macroscopic models are used for distributed and time/space lumped settings and corresponding travel time estimation functions and algorithms are developed. The implications of these algorithms for the implementation of various incident management and traffic control strategies are also discussed.

Overview Of Fuzzy Logic, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The presentation includes a brief introduction to fuzzy logic and fuzzy logic controllers. These concepts are illustrated by an example of an autonomous vehicle controller.

Comparison Of Two Distributed Fuzzy Logic Controllers For Flexible-Link Manipulators, Linda Z. Shi, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The paper suggests that fuzzy logic controllers present a computationally efficient and robust alternative to conventional controllers. The paper presents two possible structures for the distributed fuzzy logic controller of a single-link flexible manipulator. A linear quadratic regulator method is used to prove the effectiveness of fuzzy logic controllers.

Design Of Fuzzy Logic Controllers For Optimal Performance, Mohamed Trabia

Mechanical Engineering Faculty Presentations

While fuzzy logic controllers are generally robust, the performance of a system whose behavior is not well understood, or that has a large number of coupled inputs and outputs, may be less than optimal. In this paper, nonlinear programming techniques are used to improve the performance of a fuzzy logic controller for navigating an autonomous vehicle.

Alternative Principal Components Regression Procedures For Dendrohydrologic Reconstructions, Hugo G. Hidalgo, Thomas C. Piechota, John A. Dracup

Civil and Environmental Engineering and Construction Faculty Research

Streamflow reconstruction using tree ring information (dendrohydrology) has traditionally used principal components analysis (PCA) and stepwise regression to form a transfer function. However, PCA has several procedural choices that may result in very different reconstructions. This study assesses the different procedures in PCA-based regression and suggests alternative procedures for selection of variables and principal components. Cross-validation statistics are presented as an alternative for independently testing and identifying the optimal model. The objective is to use these statistics as a measure of the model's performance to find a conceptually acceptable model with a low prediction error and the fewest number of …

Validation Of Waimss Incident Duration Estimation Model, Wei Wu, Pushkin Kachroo, Kaan Ozbay

Electrical & Computer Engineering Faculty Research

This paper presents an effort to validate the traffic incident duration estimation model of WAIMSS (wide area incident management support system). Duration estimation model of WAIMSS predicts the incident duration based on an estimation tree which was calibrated using incident data collected in Northern Virginia. Due to the limited sample size, a full scale test of the distribution, mean and variance of incident duration was performed only for the root node of the estimation tree, white only mean tests were executed at all other nodes whenever a data subset was available. Further studies were also conducted on the model error …

Investigating The Use Of Kalman Filtering Approaches For Dynamic Origin-Destination Trip Table Estimation, Pushkin Kachroo, Kaan Ozbay, Arvind Narayanan

Electrical & Computer Engineering Faculty Research

This paper studies the applicability of Kalman filtering approaches for network wide traveler origin-destination estimation from link traffic volumes. The paper evaluates the modeling assumptions of the Kalman filters and examines the implications of such assumptions.

A Mathmatical Model Of Primary Productivity And Limnological Patterns In Lake Mead, Lorne G. Everett

Publications (WR)

The temporal and spatial changes in chemical and biological properties of Lake Mead have been investigated, thereby indicating the sources of water pollution and the time of highest pollution potential. Planktonic organisms have been shown to indicate the presence of water problems. Macro- and micro-nutrient analyses have shown that primary productivity is not inhibited by limiting concentrations. A mathematical model has been developed, tested with one set of independent data, and shown worthy of management utility. Although the model works very well for the Lake Mead area, the physical reality of the Multiple Linear Regression equation should be tested on …