Ordinary Differential Equations and Applied Dynamics Commons^™

(R2033) Resonant Curve Due To Perturbations Of Geo-Synchronous Satellite Including Effect Of Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Virendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have investigated resonant curve due to frequencies − angular rate of rotation of the Earth and the rate of change of Earth’s equatorial ellipticity parameter. Perturbation equations are used to convert the non-linear equations of motion of geo-synchronous satellite to the linear form. With the help of graphs, we have shown the effect of Earth’s equatorial ellipticity parameter on oscillatory amplitude and variation in orbital radius of satellite. By defining different perturbations, we have also drawn resonant curve due to frequencies steady-state orbital angular rate of satellite and the rate of change of Earth’s equatorial ellipticity …

(R2032) Modeling The Effect Of Sanitation Effort On The Spread Of Carrier-Dependent Infectious Diseases Due To Environmental Degradation, Ram Naresh, Sandhya Rani Verma, J. B. Shukla, Manju Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this present study, an SIS model is proposed and analyzed to study the effect of sanitation effort in controlling the spread of carrier-dependent infectious disease in a human habitat due to environmental degradation. The dynamics of the model consist of six dependent variables, the susceptible population density, infective population density, carrier population density, cumulative density of environmental degradation and the density of sanitation effort applied on carrier population and degraded environment. In the modeling process, the carrier population density and sanitation effort are modeled logistically and the degradation of the environment is assumed to be directly proportional to the …

(R2030) Generalized Quasilinearization Method For A Initial Value Problem On Time Scales, Şahap Çetin, Yalçın Yılmaz, Coşkun Yakar

Applications and Applied Mathematics: An International Journal (AAM)

We have investigated that the generalized quasilinearization method under some convenient conditions for nonlinear initial value problem (IVP) of dynamic equation on time scale constructed by monotone sequences of function by using comparison theorem that is the solution of linear IVP of dynamic equation on time scale which converge uniformly and monotonically to the unique solution of the original problem, and the convergence is quadratic.

Deep Hybrid Modeling Of Neuronal Dynamics Using Generative Adversarial Networks, Soheil Saghafi

Dissertations

Mechanistic modeling and machine learning methods are powerful techniques for approximating biological systems and making accurate predictions from data. However, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. This dissertation constructs Deep Hybrid Models that address these shortcomings by combining deep learning with mechanistic modeling. In particular, this dissertation uses Generative Adversarial Networks (GANs) to provide an inverse mapping of data to mechanistic models and identifies the distributions of mechanistic model parameters coherent to the data.

Chapter 1 provides background information on …

Complex-Valued Approach To Kuramoto-Like Oscillators, Jacqueline Bao Ngoc Doan

Electronic Thesis and Dissertation Repository

The Kuramoto Model (KM) is a nonlinear model widely used to model synchrony in a network of oscillators – from the synchrony of the flashing fireflies to the hand clapping in an auditorium. Recently, a modification of the KM (complex-valued KM) was introduced with an analytical solution expressed in terms of a matrix exponential, and consequentially, its eigensystem. Remarkably, the analytical KM and the original KM bear significant similarities, even with phase lag introduced, despite being determined by distinct systems. We found that this approach gives a geometric perspective of synchronization phenomena in terms of complex eigenmodes, which in turn …

Modeling The Immune Response To Immunotherapy And Triple Negative Breast Cancer In Mice, Dayton J. Syme, Angelica Davenport, Yun Lu, Anna G. Sorace, Nicholas G. Cogan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Generalized Differential Equation Models For Disease Interventions: A Novel Approach For Predicting Sexually Transmitted Disease Outbreaks, Scott Greenhalgh

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling The Dynamics Of Alcohol-Marijuana Co-Abuse In Virginia, Ana L. Vivas-Barber, James Tipton, Sujan Pant, Anne Fernando

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mathematical Model For Wound Healing In Reef-Building Coral Pocillopora Damicornis, Quintessa Hay, Luke Gardner, Eunice Pak, Liza M. Roger, Rebecca A. Segal, Anna Shaw, Nastassja A. Lewinski, Angela M. Reynolds

Biology and Medicine Through Mathematics Conference

No abstract provided.

Adaptive Multirate Infinitesimal Time Integration, Alex Fish

Mathematics Theses and Dissertations

As multiphysics simulations grow in complexity and application scientists desire more accurate results, computational costs increase greatly. Time integrators typically cater to the most restrictive physical processes of a given simulation\add{,} which can be unnecessarily computationally expensive for the less restrictive physical processes. Multirate time integrators are a way to combat this increase in computational costs by efficiently solving systems of ordinary differential equations that contain physical processes which evolve at different rates by assigning different time step sizes to the different processes. Adaptivity is a technique for further increasing efficiency in time integration by automatically growing and shrinking the …

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie

Spora: A Journal of Biomathematics

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti.

Swarm Intelligence For Solving Some Nonlinear Differential Equations, Ahmed Elzaghal, Mohammed Mohammed Elgamal, Ahmed H. Eltanboly

Mansoura Engineering Journal

The Euler method is a well-known numerical technique employed for solving initial value problems of ordinary differential equations. The solution obtained through Euler's method is subject to significant inaccuracies, which tend to amplify with each successive iteration. The Particle Swarm Optimization (PSO) algorithm is a highly effective method for finding optimal solutions to both linear and nonlinear optimization problems. In this particular investigation, the PSO technique was utilized to solve initial value problems associated with ordinary differential equations. The Euler method, on the other hand, employs equidistant grid points to approximate solutions, which can result in significant errors and a …

Multipatch Stochastic Epidemic Model For The Dynamics Of A Tick-Borne Disease, Milliward Maliyoni, Holly D. Gaff, Keshlan S. Govinder, Faraimunashe Chirove

Biological Sciences Faculty Publications

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the …

Innovations In Drop Shape Analysis Using Deep Learning And Solving The Young-Laplace Equation For An Axisymmetric Pendant Drop, Andres P. Hyer

Theses and Dissertations

Axisymmetric Drop Shape Analysis (ADSA) is a technique commonly used to determine surface or interfacial tension. Applications of traditional ASDA methods to process analytical technologies are limited by computational speed and image quality. Here, we address these limitations using a novel machine learning approach to analysis. With a convolutional neural network (CNN), we were able to achieve an experimental fit precision of (+/-) 0.122 mN/m in predicting the surface tension of drop images at a rate of 1.5 ms^-1 versus 7.7 s^-1, which is more than 5,000 times faster than the traditional method. The results are validated on real images …

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

HMC Senior Theses

Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …

Dynamical Aspects In (4+1)-Body Problems, Ryan Gauthier

Theses and Dissertations (Comprehensive)

The n-body problem models a system of n-point masses that attract each other via some binary interaction. The (n + 1)-body problem assumes that one of the masses is located at the origin of the coordinate system. For example, an (n+1)-body problem is an ideal model for Saturn, seen as the central mass, and one of its outer rings. A relative equilibrium (RE) is a special solution of the (n+1)-body problem where the non-central bodies rotate rigidly about the centre of mass. In rotating coordinates, these solutions become equilibria.

In this thesis we study dynamical aspects of planar (4 + …

Numerical Solutions Of Singular Nonlinear Ordinary Differential Equations Using Said-Ball Polynomials, Mobarek A. Assabaai, Ahmed Kherd

Emirates Journal for Engineering Research

In this article, the collocation method based on Said-Ball polynomials have been used to solve the singular nonlinear ordinary differential equations of various orders numerically. An operational matrix forms of these ordinary differential equations are obtained from Said-Ball polynomial with variated relations of solution and different derivatives. The presented method reduces the given problem to a system of nonlinear algebraic equations, which removed the singularity of ordinary differential equations. Resulting system is solved using Newton's iteration method to get the coefficients of Said-Ball polynomials. We obtained approximate solutions of the problem under study. Numerical results have been obtained and compared …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .

Applications and Applied Mathematics: An International Journal (AAM)

Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …

(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …

(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …

(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah

Applications and Applied Mathematics: An International Journal (AAM)

In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …

(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which …

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel Adara

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.