Ordinary Differential Equations and Applied Dynamics Commons^™

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 …

Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

Resonance In The Motion Of A Geocentric Satellite Due To Poynting-Robertson Drag And Equatorial Ellipticity Of The Earth, Charanpreet Kaur, Binay K. Sharma, Sushil Yadav

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of resonance in a motion of a geocentric satellite is numerically investigated under the consolidated gravitational forces of the Sun, the Earth including Earth’s equatorial ellipticity parameter and Poynting-Robertson (P-R) drag. We are presuming that bodies lying on an ecliptic plane are the Sun and the Earth, and satellite on orbital plane. Resonance is monitored between satellite’s mean motion and average angular velocity of the Earth around the Sun, and also between satellite’s mean motion and equatorial ellipticity parameter of the Earth. We also perform a systematic and thorough analysis in an attempt to understand …

Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _

Applications and Applied Mathematics: An International Journal (AAM)

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

Spectral Tau-Jacobi Algorithm For Space Fractional Advection-Dispersion Problem, Amany S. Mohamed, Mahmoud M. Mokhtar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use the shifted Jacobi polynomials to approximate the solution of the space fractional advection-dispersion. The method is based on the Jacobi operational matrices of fractional derivative and integration. A double shifted Jacobi expansion is used as an approximating polynomial. We apply this method to solve linear and nonlinear term FDEs by using initial and boundary conditions.

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

Biology and Medicine Through Mathematics Conference

No abstract provided.

Seasonal Variation Of Nutrient Loading In A Stoichiometric Producer-Consumer System, Lale Asik, Jackson Kulik, Kevin R. Long, Angela Peace

Biology and Medicine Through Mathematics Conference

No abstract provided.

Understanding The Role Of Macrophages In Lung Inflammation Through Mathematical Modeling, Sarah B. Minucci

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Quantifying The Contribution Of Environmental Pathways To The Transmission Of Clostridium Difficile, Lindsey R. Fox, Cara Sulyok, Judy Day, Cristina Lanzas, Suzanne Lenhart

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Pbpk Model Of Low-Concentration Vitamin D Supplementation In The Absence Of Sunlight, Colton Sawyer

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Spraying Strategies For Controlling Re-Infestation By Chagas Disease Vectors, Bismark Oduro, Winfried Just, Mario Grijalva

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Study Of Pair Formation Disease Models With A Two Phase Infection, Berlinda Rosa Batista

Biology and Medicine Through Mathematics Conference

No abstract provided.

Β Cell Network Dysfunction In Pancreatic Islets By Silencing Hub Cells, Janita Patwardhan, Bradford E. Peercy

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Pharmacokinetic Model Of Lead Absorption And Calcium Competitive Dynamics, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun

Dissertations, Theses, and Capstone Projects

The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.

Hrushovski first proposed an algorithm for computing the differential …

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

Masters Theses & Specialist Projects

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that …

Modelling Non-Linear Functional Responses In Competitive Biological Systems., Nickolas Goncharenko

Western Research Forum

One of the most versatile and well understood models in mathematical biology is the Competitive Lotka Volterra (CLV) model, which describes the behaviour of any number of exclusively competitive species (that is each species competes directly with every other species). Despite it's success in describing many phenomenon in biology, chemistry and physics the CLV model cannot describe any non-linear environmental effects (including resource limitation and immune response of a host due to infection). The reason for this is the theory monotone dynamical systems, which was codeveloped with the CLV model, does not apply when this non-linear effect is introduced. For …

Classification Of Solutions Of Non-Homogeneous Non-Linear Second Order Neutral Delay Dynamic Equations With Positive And Negative Coefficients, N. Sikender, P. Rami Reddy, M. Chenna Krishna Reddy, S. V. Sailaja

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we have studied the non-homogeneous non-linear second order neutral delay dynamic equations with positive and negative coefficients of the form classified all solutions of this type equations and obtained conditions for the existence or non-existence of solutions into four classes and these four classes are mutually disjoint. Examples are included to illustrate the validation of the main results.

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …

Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

CODEE Journal

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera

Williams Honors College, Honors Research Projects

Coherency strains appear in interacting atomic monolayers due to differing bond lengths, which can arise from different materials or geometries. Examples include extended monolayers interacting with a substrate and the interacting walls of a multi-walled carbon nanotube. These strains can induce various equilibrium configurations, which we will analyze by means of a phenomenological model that incorporates forces from bond stretching and bending within each layer and the weak van der Waals interactions connecting the separate layers. We vary the strengths of each interaction to explore their effects on equilibrium structures, and the specific case of a two-walled carbon nanotube is …