Dynamic Systems Commons^™

Algorithm For Calculating The Parameters Of A Multi-Position Electromagnetic Linear Mechatronic Module, Nazarov Khayriddin Nuritdinovich, Matyokubov Nurbek Rustamovich, Temurbek Omonboyevich Rakhimov

Chemical Technology, Control and Management

Currently, in the world in the field of science, engineering and technology, including in mechatronics and robotics, the creation of multi-coordinate mechatronic systems that perform power and control functions is becoming of paramount importance, this is due to a number of important positive qualities of the systems, such as simplicity and compactness of the design, the possibility of obtaining significant efforts, high accuracy and stability of the establishment of fixed positions, ease of control and high reliability. This article presents the calculation of the parameters of multi-position mechatronic modules based on linear execution elements. In the construction of this model, …

Convergence Properties Of Solutions Of A Length-Structured Density-Dependent Model For Fish, Geigh Zollicoffer

Rose-Hulman Undergraduate Mathematics Journal

We numerically study solutions to a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We make conjectures about the convergence properties of solutions to this equation, and give numerical simulations which support these conjectures. We also study the distribution of biomass in the different age classes as a function of the total biomass.

(R1508) Stability And Zero Velocity Curves In The Perturbed Restricted Problem Of 2 + 2 Bodies, Rajiv Aggarwal, Dinesh Kumar, Bhavneet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The present study investigates the existence and linear stability of the equilibrium points in the restricted problem of 2+2 bodies including the effect of small perturbations epsilon-1 and espilon-2 in the Coriolis and centrifugal forces respectively. The less massive primary is considered as a straight segment and the more massive primary a point mass. The equations of motion of the infinitesimal bodies are derived.We obtain fourteen equilibrium points of the model, out of which six are collinear and rest non-collinear with the centers of the primaries. The position of the equilibrium points are affected by the small perturbation in centrifugal …

(R1464) Stability Of The Artificial Equilibrium Points In The Low-Thrust Restricted Three-Body Problem With Variable Mass, Amit Mittal, Krishan Pal, Pravata Kumar Behera, Deepak Mittal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we have investigated the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem with variable mass. In this model of the low-thrust restricted three-body problem, we have considered both the primaries as point masses. The mass of the spacecraft varies with time according to Jeans’ law (1928). We have introduced a new concept for creating the AEPs in the restricted three-body problem with variable mass using continuous constant acceleration. We have derived the equations of motion of the spacecraft after using the space-time transformations of Meshcherskii. The AEPs have been created …

A Quantum Mechanics Approach For The Dynamics Of An Immigration, Emigration Fission Model, Leon Arriola

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimal Control Techniques In Addiction Modeling, Leigh Pearcy, William Christopher Strickland, Suzanne Lenhart

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Stability Of Explicit And Implicit Discrete Epidemic Models: Applications To Swine Flu Outbreak, Elvan Akin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Pancreatic Cancer Microenvironment In Search Of Control Targets, Daniel Plaugher

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Neural Network Controller Vs Pulse Control To Achieve Complete Eradication Of Cancer Cells In A Mathematical Model, Joel A. Quevedo, Sergio A. Puga, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Chemoimmunotherapy Treatment Strategies On A Mathematical Model Of Cancer Evolution, Sandra M. Lopez, Yolocuauhtli Salazar, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Model For Osteosarcoma Progression And Treatments, Trang M. Le

Doctoral Dissertations

Cancer is a complex disease where every tumor has its own characteristics, and thus different tumors may respond differently to the same treatments. Osteosarcoma, which is a rare type of cancer with poor prognosis, is especially characterized by its high heteogeneity. Therefore, it is important to study the progression of osteosarcoma tumors in different groups of patients with distinct characteristics. The immune system has been reported to play an important role in the development of various cancers with some immune cells having anti-tumor effects and others having pro-tumor effects. With recent advances in digital cytometry methods, which are techniques to …

Euler's Three-Body Problem, Sylvio R. Bistafa

Euleriana

In physics and astronomy, Euler's three-body problem is to solve for the motion of a body that is acted upon by the gravitational field of two other bodies. This problem is named after Leonhard Euler (1707-1783), who discussed it in memoirs published in the 1760s. In these publications, Euler found that the parameter that controls the relative distances among three collinear bodies is given by a quintic equation. Later on, in 1772, Lagrange dealt with the same problem, and demonstrated that for any three masses with circular orbits, there are two special constant-pattern solutions, one where the three bodies remain …

Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

Smooth Global Approximation For Continuous Data Assimilation, Kenneth R. Brown

Theses and Dissertations

This thesis develops the finite element method, constructs local approximation operators, and bounds their error. Global approximation operators are then constructed with a partition of unity. Finally, an application of these operators to data assimilation of the two-dimensional Navier-Stokes equations is presented, showing convergence of an algorithm in all Sobolev topologies.

Outcomes Of Aspheric Primaries In Robe’S Circular Restricted Three-Body Problem, Bhavneet Kaur, Shipra Chauhan, Dinesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We consider the Robe’s restricted three-body problem in which the bigger primary is assumed to be a hydrostatic equilibrium figure as an oblate spheroid filled with a homogeneous incompressible fluid, around which a circular motion is described by the second primary, that is a finite straight segment. The aim of this note is to investigate the effect of oblateness and length parameters on the motion of an infinitesimal body that lies inside the bigger primary. The locations of the equilibrium points are approximated by the series expansions and it is found that two collinear equilibrium points lying on the line …

An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, Vanessa Maybruck

Honors Student Research

Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like …

Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra

LSU Doctoral Dissertations

This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …

Lexicographic Sensitivity Functions For Nonsmooth Models In Mathematical Biology, Matthew D. Ackley

Electronic Theses and Dissertations

Systems of ordinary differential equations (ODEs) may be used to model a wide variety of real-world phenomena in biology and engineering. Classical sensitivity theory is well-established and concerns itself with quantifying the responsiveness of such models to changes in parameter values. By performing a sensitivity analysis, a variety of insights can be gained into a model (and hence, the real-world system that it represents); in particular, the information gained can uncover a system's most important aspects, for use in design, control or optimization of the system. However, while the results of such analysis are desirable, the approach that classical theory …

Population And Evolution Dynamics In Predator-Prey Systems With Anti-Predation Responses, Yang Wang

Electronic Thesis and Dissertation Repository

This thesis studies the impact of anti-predation strategy on the population dynamics of predator-prey interactions. This work includes three research projects.

In the first project, we study a system of delay differential equations by considering both benefit and cost of anti-predation response, as well as a time delay in the transfer of biomass from the prey to the predator after predation. We reveal some insights on how the anti-predation response level and the biomass transfer delay jointly affect the population dynamics; we also show how the nonlinearity in the predation term mediated by the fear effect affects the long term …

Lecture 07: Nonlinear Preconditioning Methods And Applications, Xiao-Chuan Cai

Mathematical Sciences Spring Lecture Series

We consider solving system of nonlinear algebraic equations arising from the discretization of partial differential equations. Inexact Newton is a popular technique for such problems. When the nonlinearities in the system are well-balanced, Newton's method works well, but when a small number of nonlinear functions in the system are much more nonlinear than the others, Newton may converge slowly or even stagnate. In such a situation, we introduce some nonlinear preconditioners to balance the nonlinearities in the system. The preconditioners are often constructed using a combination of some domain decomposition methods and nonlinear elimination methods. For the nonlinearly preconditioned problem, …

The Fundamental Limit Theorem Of Countable Markov Chains, Nathanael Gentry

Senior Honors Theses

In 1906, the Russian probabilist A.A. Markov proved that the independence of a sequence of random variables is not a necessary condition for a law of large numbers to exist on that sequence. Markov's sequences -- today known as Markov chains -- touch several deep results in dynamical systems theory and have found wide application in bibliometrics, linguistics, artificial intelligence, and statistical mechanics. After developing the appropriate background, we prove a modern formulation of the law of large numbers (fundamental theorem) for simple countable Markov chains and develop an elementary notion of ergodicity. Then, we apply these chain convergence results …

Modelling The Transition From Homogeneous To Columnar States In Locust Hopper Bands, Miguel Velez

HMC Senior Theses

Many biological systems form structured swarms, for instance in locusts, whose swarms are known as hopper bands. There is growing interest in applying mathematical models to understand the emergence and dynamics of these biological and social systems. We model the locusts of a hopper band as point particles interacting through repulsive and attractive social "forces" on a one dimensional periodic domain. The primary goal of this work is to modify this well studied modelling framework to be more biological by restricting repulsion to act locally between near neighbors, while attraction acts globally between all individuals. This is a biologically motivated …

Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes

HMC Senior Theses

Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.

Expanding Social Network Modeling Software And Agent Models For Diffusion Processes, Patrick Vaden Shepherd

Theses and Dissertations--Computer Science

In an increasingly digitally interconnected world, the study of social networks and their dynamics is burgeoning. Anthropologically, the ubiquity of online social networks has had striking implications for the condition of large portions of humanity. This technology has facilitated content creation of virtually all sorts, information sharing on an unprecedented scale, and connections and communities among people with similar interests and skills. The first part of my research is a social network evolution and visualization engine. Built on top of existing technologies, my software is designed to provide abstractions from the underlying libraries, drive real-time network evolution based on user-defined …

Thermodynamic Entropy Of A Magnetized Ree-Eyring Particle-Fluid Motion With Irreversibility Process: A Mathematical Paradigm, M. M. Bhatti, Sara I. Abdelsalam

Basic Science Engineering

This article deals with the entropy generation and irreversibility process under the effects of partial slip on magnetic dusty liquid induced by peristaltic wave through a porous channel. The Ree-Eyring fluid model has been used for a governing flow. Mathematical modelling is based on Ohm's law, continuity equation, Darcy law and momentum equation. Analytical solutions are presented for fluid and particle phase. The effects of different pertinent parameters are considered for Newtonian and non-Newtonian cases. Numerical integration has been carried out using a computational software to analyse the pumping characteristics. The behaviour of velocity profile, trapping mechanism, entropy generation, Bejan …

Leveraging Elasticity To Uncover The Role Of Rabinowitsch Suspension Through A Wavelike Conduit: Consolidated Blood Suspension Application, Sara I. Abdelsalam, A. Z. Zaher

Basic Science Engineering

The present work presents a mathematical investigation of a Rabinowitsch suspension fluid through elastic walls with heat transfer under the effect of electroosmotic forces (EOFs). The governing equations contain empirical stress-strain equations of the Rabinowitsch fluid model and equations of fluid motion along with heat transfer. It is of interest in this work to study the effects of EOFs, which are rigid spherical particles that are suspended in the Rabinowitsch fluid, the Grashof parameter, heat source, and elasticity on the shear stress of the Rabinowitsch fluid model and flow quantities. The solutions are achieved by taking long wavelength approximation with …

Modeling Coupled Disease-Behavior Dynamics Of Sars-Cov-2 Using Influence Networks, Juliana C. Taube

Honors Projects

SARS-CoV-2, the virus that causes COVID-19, has caused significant human morbidity and mortality since its emergence in late 2019. Not only have over three million people died, but humans have been forced to change their behavior in a variety of ways, including limiting their contacts, social distancing, and wearing masks. Early infectious disease models, like the classical SIR model by Kermack and McKendrick, do not account for differing contact structures and behavior. More recent work has demonstrated that contact structures and behavior can considerably impact disease dynamics. We construct a coupled disease-behavior dynamical model for SARS-CoV-2 by incorporating heterogeneous contact …