Applied Mathematics Commons^™

Numerical Computations Of Vortex Formation Length In Flow Past An Elliptical Cylinder, Matthew Karlson, Bogdan Nita, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the …

Optimal Allocation Of Two Resources In Annual Plants, David Mcmorris

Department of Mathematics: Dissertations, Theses, and Student Research

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Under the assumption that annual plants grow to maximize fitness, we can use techniques from optimal control theory to understand this process. We introduce two models for resource allocation in annual plants which extend classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits in annual plants. In each case, we use optimal control theory to determine the optimal resource allocation strategy for the plant …

Evaluating Driving Performance Of A Novel Behavior Planning Model On Connected Autonomous Vehicles, Keyur Shah

Honors Scholar Theses

Many current algorithms and approaches in autonomous driving attempt to solve the "trajectory generation" or "trajectory following” problems: given a target behavior (e.g. stay in the current lane at the speed limit or change lane), what trajectory should the vehicle follow, and what inputs should the driving agent apply to the throttle and brake to achieve this trajectory? In this work, we instead focus on the “behavior planning” problem—specifically, should an autonomous vehicle change lane or keep lane given the current state of the system?

In addition, current theory mainly focuses on single-vehicle systems, where vehicles do not communicate with …

The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Novel Mathematical Model Of The Trojan Y-Chromosome Strategy With Optimal Control, Christopher Turner

Electronic Theses and Dissertations

Invasive species are a prevalent problem all over the world. Controlling and eradicating an invasive species is an even more diffcult problem. The Trojan Y Chromosome (TYC) eradication strategy is one control method. This method alters the female to male sex ratio by introducing sex reversed males called supermales. These sex reversed males can only produce male progeny. Mathematical models of this strategy have shown that a population can be driven to extinction with a continuous supply of these sex reversed males. There are many different mathematical models of this strategy, but most have serious flaws, such as negative solutions …

Target Control Of Networked Systems, Isaac S. Klickstein

Mechanical Engineering ETDs

The control of complex networks is an emerging field yet it has already garnered interest from across the scientific disciplines, from robotics to sociology. It has quickly been noticed that many of the classical techniques from controls engineering, while applicable, are not as illuminating as they were for single systems of relatively small dimension. Instead, properties borrowed from graph theory provide equivalent but more practical conditions to guarantee controllability, reachability, observability, and other typical properties of interest to the controls engineer when dealing with large networked systems. This manuscript covers three topics investigated in detail by the author: (i) the …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Filtered-Dynamic-Inversion Control For Unknown Minimum-Phase Systems With Unknown Relative Degree, Sumit Suryakant Kamat

Theses and Dissertations--Mechanical and Aerospace Engineering

We present filtered-dynamic-inversion (FDI) control for unknown linear time-invariant systems that are multi-input multi-output and minimum phase with unknown-but-bounded relative degree. This FDI controller requires limited model information, specifically, knowledge of an upper bound on the relative degree and knowledge of the first nonzero Markov parameter. The FDI controller is a single-parameter high-parameter-stabilizing controller that is robust to uncertainty in the relative degree. We characterize the stability of the closed-loop system. We present numerical examples, where the FDI controller is implemented in feedback with mathematical and physical systems. The numerical examples demonstrate that the FDI controller for unknown relative degree …

Hybrid Electric Vehicle Energy Management Strategy With Consideration Of Battery Aging, Bin Zhou

Dissertations, Master's Theses and Master's Reports

The equivalent consumption minimization strategy (ECMS) is a well-known energy management strategy for Hybrid Electric Vehicles (HEV). ECMS is very computationally efficient since it yields an instantaneous optimal control. ECMS has been shown to minimize fuel consumption under certain conditions. But, minimizing the fuel consumption often leads to excessive battery damage. The objective of this dissertation is to develop a real-time implementable optimal energy management strategy which improves both the fuel economy and battery aging for Hybrid Electric Vehicles by using ECMS. This work introduces a new optimal control problem where the cost function includes terms for both fuel consumption …

Dynamics In A Respiratory Control Model With Two Delays, Saroj P. Pradhan, Ferenc Hartung, Janos Turi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we study ventilation patterns in a set of parameter dependent nonlinear delay equations with two transport delays modeling the human respiratory control system with peripheral and central control loops. We present a convergent numerical scheme suitable to perform simulations when all disturbances and system parameters are known, then we consider the numerical identifiability of various system parameters based on ventilation data. We are especially interested in the identification of the transport delays in the control loops because these parameters are not measurable directly, but they have a strong influence on system stability/instability.

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Controllability And Observability Of Time-Varying Linear Nabla Fractional Systems, Tilekbek Zhoroev

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Relaxation And Linear Programs On A Hybrid Control Model, Héctor Jasso-Fuentes, Jose-Luis Menaldi

Mathematics Faculty Research Publications

Some optimality results for hybrid control problems are presented. The hybrid model under study consists of two subdynamics, one of a standard type governed by an ordinary differential equation, and the other of a special type having a discrete evolution. We focus on the case when the interaction between the subdynamics takes place only when the state of the system reaches a given fixed region of the state space. The controller is able to apply two controls, each applied to one of the two subdynamics, whereas the state follows a composite evolution, of continuous type and discrete type. By the …

On Optimal Stopping And Impulse Control With Constraint, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

The optimal stopping and impulse control problems for a Markov-Feller process are considered when the controls are allowed only when a signal arrives. This is referred to as control problems with constraint. In [28, 29, 30], the HJB equation was solved and an optimal control (for the optimal stopping problem, the discounted impulse control problem and the ergodic impulse control problem, respectively) was obtained, under suitable conditions, including a setting on a compact metric state space. In this work, we extend most of the results to the situation where the state space of the Markov process is locally compact.

Navigating Around Convex Sets, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We review some basic results of convex analysis and geometry in Rn in the context of formulating a differential equation to track the distance between an observer flying outside a convex set K and K itself.

Maximizing And Modeling Malonyl-Coa Production In Escherichia Coli, Tatiana Thompson Silveira Mello

LSU Master's Theses

In E. coli, fatty acid synthesis is catalyzed by the enzyme acetyl-CoA carboxylase (ACC), which converts acetyl-CoA into malonyl-CoA. Malonyl-CoA is a major building block for numerous of bioproducts. Multiple parameters regulate the homeostatic cellular concentration of malonyl-CoA, keeping it at a very low level. Understanding how these parameters affect the bacterial production of malonyl-CoA is fundamental to maximizing it and its bioproducts. To this end, competing pathways consuming malonyl-CoA can be eliminated, and optimal nutritional and environmental conditions can be provided to the fermentation broth. Most previous studies utilized genetic modifications, expensive consumables, and high-cost quantification methods, making …

A Fuzzy Two-Warehouse Inventory Model For Single Deteriorating Item With Selling-Price-Dependent Demand And Shortage Under Partial-Backlogged Condition, S. K. Indrajitsingha, P. N. Samanta, U. K. Misra

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have developed an inventory model for a single deteriorating item with two separate storage facilities (one is owned warehouse (OW) and the other a rented warehouse (RW)) and in which demand is selling- price dependent. Shortage is allowed and is partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. It is assumed that the holding cost of the rented warehouse is higher than that of owned warehouse. As demand, selling- price, holding- cost, shortage, lost- sale, deterioration- rate are uncertain in nature, we consider them as …

Analysis Of An Eco-Epidemiological Model Under Optimal Control Measures For Infected Prey, Alfred Hugo, Emanuel Simanjilo

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the analysis of an eco-epidemiological model with optimal control strategies for infected prey. A model is proposed and analyzed qualitatively using the stability theory of the differential equations. A local and global study of the model is performed around the disease-free equilibrium and the endemic equilibrium to analyze the global stability using the Lyapunov function. The time-dependent control is introduced into the system to determine the best strategy for controlling the disease. The results obtained suggested the separation of the infected population plays a vital role in disease elimination.

A New Successive Linearization Approach For Solving Nonlinear Programming Problems, Inci Albayrak, Mustafa Sivri, Gizem Temelcan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we focused on general nonlinear programming (NLP) problems having m nonlinear (or linear) algebraic inequality (or equality or mixed) constraints with a nonlinear (or linear) algebraic objective function in n variables. We proposed a new two-phase-successive linearization approach for solving NLP problems. Aim of this proposed approach is to find a solution of the NLP problem, based on optimal solution of linear programming (LP) problems, satisfying the nonlinear constraints oversensitively. This approach leads to novel methods. Numerical examples are given to illustrate the approach.

Exact Feedback Linearization Of Systems With State-Space Modulation And Demodulation, Nikolaos I. Xiros Deng

LSU New Orleans Theses and Dissertations

The control theory of nonlinear systems has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. In several key areas, such as aerospace, chemical and petrochemical industries, bioengineering, and robotics, a new practical application for this tool appears every day. System nonlinearity is characterized when at least one component or subsystem is nonlinear. Classical methods used in the study of linear systems, particularly superposition, are not usually applied to the nonlinear systems. It is necessary to use other methods to study the control of these systems. …

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the …

Traffic Signal Consensus Control, Gerardo Lafferriere

TREC Final Reports

We introduce a model for traffic signal management based on network consensus control principles. The underlying principle in a consensus approach is that traffic signal cycles are adjusted in a distributed way so as to achieve desirable ratios of queue lengths throughout the street network. This approach tends to reduce traffic congestion due to queue saturation at any particular city block and it appears less susceptible to congestion due to unexpected traffic loads on the street grid. We developed simulation tools based on the MATLAB computing environment to analyze the use of the mathematical consensus approach to manage the signal …

A Decentralized Network Consensus Control Approach For Urban Traffic Signal Optimization, Gerardo Lafferriere

TREC Project Briefs

Automobile traffic congestion in urban areas is a worsening problem that comes with significant economic and social costs. This report offers a new approach to urban congestion management through traffic signal control.

Numerical Simulations For Optimal Control Of A Cancer Cell Model With Delay, Jessica S. Lugo

Murray State Theses and Dissertations

Mathematical models are often created to analyze the complicated behavior of many physical systems. One such system is that of the interaction between cancer cells, the immune system, and various treatments such as chemotherapy, radiation, and immunotherapy. Using models that depict these relationships gives researchers insight on the dynamics of this complicated system and possibly ideas for improved treatment schedules.

The model presented here gives the relationship of cancer cells in development phases with immune cells and cycle-specific chemotherapy treatment. This model includes a constant delay term in the mitotic phase. Optimal control theory is used to minimize the cost …

Stabilize Chaotic Flows In A Coupled Triple-Loop Thermosyphon System, Haley N. Anderson

Honors College Theses

This study addresses the control of chaotic dynamic systems represented by three coupled Lorenz systems. In application, Lorenz systems are commonly used to describe the one-dimensional motion of fluids in a tube when heated below and cooled above. This system, in particular, reflects the fluid motion in a coupled triple-loop thermosyphon system. The goal is to derive a system of nonlinear differential equations to help us study various flow patterns governed by such a high-dimensional nonlinear model numerically. Once the driving parameter (Rayleigh number) values are identified corresponding to the chaotic regime, a minimal number of proportional controllers are designed …

Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …