Applied Mathematics Commons^™

Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva

College of Graduate Studies: Theses & Dissertations

Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator- prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.

Symmetry And Reductions Of Integrable Dynamical Systems: Peakon And The Toda Chain Systems, Vladimir Gerdjikov, Rossen Ivanov, Gaetano Vilasi

Articles

We are analyzing several types of dynamical systems which are both integrable and important for physical applications. The first type are the so-called peakon systems that appear in the singular solutions of the Camassa-Holm equation describing special types of water waves. The second type are Toda chain systems, that describe molecule interactions. Their complexifications model soliton interactions in the adiabatic approximation. We analyze the algebraic aspects of the Toda chains and describe their real Hamiltonian forms.

Relative Equilibria Of Isosceles Triatomic Molecules In Classical Approximation, Damaris Miriam Mckinley

Theses and Dissertations (Comprehensive)

In this thesis we study relative equilibria of di-atomic and isosceles tri-atomic molecules in classical approximations with repulsive-attractive interaction. For di-atomic systems we retrieve well-known results. The main contribution consists of the study of the existence and stability of relative equilibria in a three-atom system formed by two identical atoms of mass $m$ and a third of mass $m_3$, constrained in an isosceles configuration at all times.

Given the shape of the binary potential only, we discuss the existence of equilibria and relative equilibria. We represent the results in the form of energy-momentum diagrams. We find that fixing the masses …

Computational Models For Nanosecond Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Laser ablation in an ambient environment is becoming increasingly important in science and technology. It is used in applications ranging from chemical analysis via mass spectroscopy, to pulsed laser deposition and nanoparticle manufacturing. We describe numerical schemes for a multiphase hydrodynamic model of nanosecond laser ablation expressing energy, momentum, and mass conservation in the target material, as well as in the expanding plasma plume, along with collisional and radiative processes for laser-induced breakdown (plasma formation). Numerical simulations for copper in a helium background gas are presented and the efficiency of various ODE integrators is compared.

Generalist And Specialist Pollination Syndromes: When Are They Favoured? A Theoretical Approach To Predict The Conditions Under Which A Generalist Or Specialist Pollination Syndrome Is Favoured., Tyler L. Poppenwimer

Senior Independent Study Theses

No abstract provided.

Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

No abstract provided.

Elementary Differential Equations, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough.

An …

A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

Serious infections due to antibiotic-resistant bacteria are pervasive, and of particular concern within hospital units due to frequent interaction among health-care workers and patients. Such nosocomial infections are difficult to eliminate because of inconsistent disinfection procedures and frequent interactions among infected persons, and because ill-chosen antibiotic treatment strategies can lead to a growth of resistant bacterial strains. Clinical studies to address these concerns have several issues, but chief among them are the effects on the patients involved. Realistic simulation models offer an attractive alternative. This paper presents a hybrid simulation model of antibiotic resistant infections in a hospital ward, combining …

A Note On The Qualitative Behavior Of Some Second Order Nonlinear Equation, Juan E. Nápoles Valdes

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present two qualitative results concerning the solutions of some second order nonlinear equations, under suitable assumptions. The first result centers on the boundedness of the solutions while the second discusses the square integrability of the solutions. These results are obtained by extending and improving the current literature through sound mathematical analysis.

New Existence Results To Solution Of Fractional Boundary Value Problems, Rahmat Darzi, Bahar Mohammadzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we verify the existence of solution to boundary value problem of nonlinear fractional differential equation involving Caputo fractional derivatives. We obtain new existence results based on nonlinear alternative of Leray-Schauder type and Krasnoselskiis fixed point theorem. At the end, two illustrative examples have been presented.

Modelling The Role Of Cloud Density On The Removal Of Gaseous Pollutants And Particulate Matters From The Atmosphere, Shyam Sundar, Rajan K. Sharma, Ram Naresh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a six dimensional nonlinear mathematical model is proposed to study the effect of the density of cloud droplets (formed due to the presence of vapors in the atmosphere) on the removal of pollutants, both gaseous and particulate, from the atmosphere. We assume that there exist six nonlinearly interacting phases in the atmosphere i.e. the vapor phase, the phase of cloud droplets, the phase of raindrops, the phase of gaseous pollutants, the phase of particulate matters and the phase of gaseous pollutants absorbed in raindrops. It is further assumed that the dynamics of the system undergo ecological type …

Spread Of Malicious Objects In Computer Network: A Fuzzy Approach, Bimal K. Mishra, Apeksha Prajapati

Applications and Applied Mathematics: An International Journal (AAM)

We propose an e-epidemic fuzzy SEIQRS (Susceptible-Exposed-Infectious-Quarantine- Recovered-Susceptible) model for the transmission of malicious codes in a computer network. We have simulated the result for various parameters and analyzed the stability of the model. The efficiency of antivirus software and crashing of the nodes due to attack of malicious code is analyzed. Furthermore, initial simulation results illustrate the behavior of different classes for minimizing the infection in a computer network. It also reflects the positive impact of anti-virus software on malicious code propagation in a computer network. The basic reproduction number R0 f and its formulation is also discussed.

Numerical Solution Of Fuzzy Arbitrary Order Predator-Prey Equations, Smita Tapaswini, S. Chakraverty

Applications and Applied Mathematics: An International Journal (AAM)

This paper seeks to investigate the numerical solution of fuzzy arbitrary order predator-prey equations using the Homotopy Perturbation Method (HPM). Fuzziness in the initial conditions is taken to mean convex normalised fuzzy sets viz. triangular fuzzy number. Comparisons are made between crisp solution given by others and fuzzy solution in special cases. The results obtained are depicted in plots and tables to demonstrate the efficacy and powerfulness of the methodology.

Global Dynamics Of A Water-Borne Disease Model With Multiple Transmission Pathways, Prasanta K. Mondal, T. K. Kar

Applications and Applied Mathematics: An International Journal (AAM)

We propose and analyze a water born disease model introducing water-to-person and person-toperson transmission and saturated incidence. The disease-free equilibrium and the existence criterion of endemic equilibrium are investigated. Trans critical bifurcation at the disease-free equilibrium is obtained when the basic reproductive number is one. The local stability of both the equilibria is shown and a Lyapunov functional approach is also applied to explore the global stability of the system around the equilibria. We display the effects of pathogen contaminated water and infection through contact on the system dynamics in the absence of person-to-person contact as well as in the …

An Exponential Matrix Method For Numerical Solutions Of Hantavirus Infection Model, Şuayip Yüzbaşi, Mehmet Sezer

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new matrix method based on exponential polynomials and collocation points is proposed to obtain approximate solutions of Hantavirus infection model corresponding to a class of systems of nonlinear ordinary differential equations. The method converts the model problem into a system of nonlinear algebraic equations by means of the matrix operations and the collocation points. The reliability and efficiency of the proposed scheme is demonstrated by the numerical applications and all numerical computations have been made by using a computer program written in Maple.

Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using …

Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi

Scripps Senior Theses

Malaria is a preventable and treatable blood-borne disease whose complications can be fatal. Although many interventions exist in order to reduce the impacts of malaria, the optimal method of distributing these interventions in a geographical area with limited resources must be determined. This thesis refines a model that uses an integer linear program and a compartmental model of epidemiology called an SIR model of ordinary differential equations. The objective of the model is to find an intervention strategy over multiple time steps and multiple geographic regions that minimizes the number of days people spend infected with malaria. In this paper, …

Minimizing Travel Time Through Multiple Media With Various Borders, Tonja Miick

Masters Theses & Specialist Projects

This thesis consists of two main chapters along with an introduction and
conclusion. In the introduction, we address the inspiration for the thesis, which
originates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address …

A Comparison And Catalog Of Intrinsic Tumor Growth Models, Elizabeth A. Sarapata

HMC Senior Theses

Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global …

A Study Of Nonlinear Dynamics In Mathematical Biology, Joseph Ferrara

UNF Graduate Theses and Dissertations

We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.

On The Peakon And Soliton Solutions Of An Integrable Pde With Cubic Nonlinearities, Rossen Ivanov, Tony Lyons

Conference papers

The interest in the singular solutions (peakons) has been inspired by the Camassa-Holm (CH) equation and its peakons. An integrable peakon equation with cubic nonlinearities was first discovered by Qiao. Another integrable equation with cubic nonlinearities was introduced by V. Novikov . We investigate the peakon and soliton solutions of the Qiao equation.

On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk

Applications and Applied Mathematics: An International Journal (AAM)

The numerical solution of a mixed linear integro delay differential-difference equation with piecewise interval is presented using the Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving a mixed linear integro delay differential difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms a mixed linear integro delay differential-difference equations and the given conditions into a matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system …

On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar

Applications and Applied Mathematics: An International Journal (AAM)

Dichotomic maps are used to check the stability of ordinary differential equations and difference equations. In this paper, this method is extended to dynamic equations on time scales; the stability and asymptotic stability to the trivial solution of the first order system of dynamic equations are examined using dichotomic and strictly dichotomic maps. This method, in dynamic equations, also involves Lyapunov’s direct method.

Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The …

G-Strands, Darryl Holm, Rossen Ivanov, James Percival

Articles

A G-strand is a map g(t,s): RxR --> G for a Lie group G that follows from Hamilton's principle for a certain class of G-invariant Lagrangians. The SO(3)-strand is the G-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3)_K-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the SO(3) …

Cyclic Universe With An Inflationary Phase From A Cosmological Model With Real Gas Quintessence, Rossen Ivanov, Emil Prodanov

Articles

Phase-plane stability analysis of a dynamical system describing the Universe as a two-fraction uid containing baryonic dust and real virial gas quintessence is presented. Existence of a stable periodic solution experiencing in ationary periods is shown. A van der Waals quintessence model is revisited and cyclic Universe solution again found.

Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.

Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.

Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …