Applied Mathematics Commons^™

Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong

Mathematics & Statistics Theses & Dissertations

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs …

A Computational Model Of Arterial Thrombus Mechanics In Stenotic Channels, Elise Kole Aspray

Theses and Dissertations

Platelet aggregation is one of the major components of blood clotting. The proximal cause of most heart attacks and many strokes is the rapid formation of a blood clot (thrombus) in response to the rupture or erosion of an arterial atherosclerotic plaque. In the context of a stenotic artery (i.e., an artery whose lumen is partially blocked by the plaque) understanding how the thrombus forms presents additional challenges because of the extremely high shear rates and stresses present as a consequence of the constriction. In this dissertation, we use a two-phase continuum model to investigate the stability of an existing …

High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman

Mathematics & Statistics Theses & Dissertations

High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L₂ stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …

Finding New Limit Points Of Mahler Measure By Methods Of Missing Data Restoration, Jean-Marc Sac-Epee J.M Sac-Epee, Souad El Otmani, Armand Maul, Georges Rhin

BAU Journal - Science and Technology

It is well known that the set of Mahler measures of single variable polynomial has limit points of which a list established by D. Boyd and M. Mossinghoff has been extended through approaches based on genetic algorithms. In this paper, we wish to further extend the list of known limit points by adapting a method of missing data restoration.

Geometric Quantizations Related To The Laplace Eigenspectra Of Compact Riemannian Symmetric Spaces Via Borel-Weil-Bott Theory, Camilo Montoya

FIU Electronic Theses and Dissertations

The purpose of this thesis is to suggest a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization. This is done by associating to each compact Riemannian symmetric space, via Marsden-Weinstein reduction, a generalized flag manifold which covers the space parametrizing all of its maximal totally geodesic tori. In the process we notice a direct relation between the Satake diagram of the symmetric space and the painted Dynkin diagram of its associated flag manifold. We consider in detail the examples of the classical simply-connected …

Universal Biological Motions For Educational Robot Theatre And Games, Rajesh Venkatachalapathy, Martin Zwick, Adam Slowik, Kai Brooks, Mikhail Mayers, Roman Minko, Tyler Hull, Bliss Brass, Marek Perkowski

Systems Science Faculty Publications and Presentations

Paper presents a concept that is new to robotics education and social robotics. It is based on theatrical games, in motions for social robots and animatronic robots. Presented here motion model is based on Drift Differential Model from biology and Fokker-Planck equations. This model is used in various areas of science to describe many types of motion. The model was successfully verified on various simulated mobile robots and a motion game of three robots called "Mouse and Cheese."

Dpp: Deep Predictor For Price Movement From Candlestick Charts, Chih-Chieh Hung, Ying-Ju (Tessa) Chen

Mathematics Faculty Publications

Forecasting the stock market prices is complicated and challenging since the price movement is affected by many factors such as releasing market news about earnings and profits, international and domestic economic situation, political events, monetary policy, major abrupt affairs, etc. In this work, a novel framework: deep predictor for price movement (DPP) using candlestick charts in the stock historical data is proposed. This framework comprises three steps: 1. decomposing a given candlestick chart into sub-charts; 2. using CNN-autoencoder to acquire the best representation of sub-charts; 3. applying RNN to predict the price movements from a collection of sub-chart representations. An …

Grizzly Bears Mortalities And The Survival Of The Species, Courtney Swanson

Senior Seminars and Capstones

In this paper we aim to understand what is happening in the grizzly bear population mortalities from the year 2010 to 2020. We are performing Classical and Regression Tree (CART) methods and Correspondence Analysis on data provided by the U.S. Geological Survey (USGS). We found certain variables in the data set to be important through CART methods. Correspondence Analysis then allowed us to compare these variables to determine their relationships and association to one another. Most of the grizzly bear deaths are human caused and mainly over land and resources such as food and habitat. This aligns with some of …

Mathematical Modelling & Simulation Of Large And Small Scale Structures In Star Formation, Gianfranco Bino

Electronic Thesis and Dissertation Repository

This thesis aims to study the magnetic and evolutionary properties of stellar objects from the prestellar phase up to and including the late protostellar phase. Many of the properties governing star formation are linked to the core’s physical properties and the magnetic field highly dictates much of the core’s stability.

The thesis begins with the implementation of a fully analytic magnetic field model used to study the magnetic properties governing the prestellar core FeSt 1-457. The model is a direct result of Maxwell’s equations and yields a central-to-surface magnetic field ratio in the equatorial plane in cylindrical coordinates. The model …

Numerical Calculation Of Lyapunov Stable Solutions Of The Hyperbolic Systems, Dilfuza Ne'matova, Aziza Akbarova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

We give numerical examples demonstrating and confirming the theoretical results obtained for systems of two linear hyperbolic equations.

Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The structure of partially ordered sets of degrees of negative representability of linear orders with endomorphisms is studied. For these structures, the existence of incomparable, maximum and minimum degrees, infinite chains and antichains is established,and also considered connections with the concepts of reducibility of enumerations, splittable degrees and positive representetions.

Optimal Stopping Problems For A Family Of Continuous-Time Markov Processes, Héctor Jasso-Fuentes, Jose-Luis Menaldi, Fidel Vásquez-Rojas

Mathematics Faculty Research Publications

In this paper we study the well-know optimal stopping problem applied to a general family of continuous-time Markov process. The approach to follow is merely analytic and it is based on the characterization of stopping problems through the study of a certain variational inequality; namely one solution of this inequality will coincide with the optimal value of the stopping problem. In addition, by means of this characterization, it is possible to find the so-named continuation region, and as a byproduct obtaining the optimal stopping time. The most of the material is based on the semigroup theory, infinitesimal generators and resolvents. …

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

Open Educational Resources

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

Global Stability Of Generalized Within-Host Chikungunya Virus Dynamics Models, Taofeek O. Alade, Afeez Abidemi, Cemil Tunç, Shafeek A. Ghaleb

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes two models of a general nonlinear within-host Chikungunya virus (CHIKV) dynamics. The production, incidence, proliferation and removal rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The second model takes into consideration two forms of infected host cells: (i) latently infected cells which do not produce the CHIKV, (ii) actively infected cells which generate the CHIKV particles. We show that all the solutions of the models are nonnegative and bounded. The global stability of the steady states of the models is proven by applying Lyapunov method and LaSalle’s invariance …

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 …

Axisymmetric Thermoelastic Response In A Semi-Elliptic Plate With Kassir’S Nonhomogeneity In The Thickness Direction, Sonal Bhoyar, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of the …

Anti-Synchronization Scheme For The Stability Analysis Of A Newly Designed Hamiltonian Chaotic System Based On Hénon-Heiles Model Using Adaptive Control Method, Ayub Khan, Anu Jain, Santosh Kaushik, Manoj Kumar, Harindri Chaudhary

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a systematic approach to investigate the anti-synchronization among identical Hamiltonian chaotic systems has been proposed by using adaptive control method (ACM). Initially an adaptive controller and parameter update law are described to achieve asymptotical stability of state variables of given system with uncertain parameters using Lyapunov stability theory (LST). In addition, numerical simulations using MATLAB software are performed to validate the efficacy and effectiveness of the designed technique. Moreover, the proposed technique has numerous applications in encryption and secure communication.

Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal

Applications and Applied Mathematics: An International Journal (AAM)

A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the …

A Stochastic Knapsack Game: Revenue Management In Competitions, Yingdong Lu

Applications and Applied Mathematics: An International Journal (AAM)

We study a mathematical model for revenue management under competitions with multiple sellers. The model combines the stochastic knapsack problem, a classic revenue management model, with a non-coorperative game model that characterizes the sellers’ rational behavior. We are able to establish a dynamic recursive procedure that incorporate the value function with the utility function of the games. The formalization of the dynamic recursion allows us to establish some fundamental structural properties.

Maximum Difference Extreme Difference Method For Finding The Initial Basic Feasible Solution Of Transportation Problems, Ridwan Raheem Lekan, Lord Clifford Kavi, Nancy Ann Neudauer

Applications and Applied Mathematics: An International Journal (AAM)

A Transportation Problem can be modeled using Linear Programming to determine the best transportation schedule that will minimize the transportation cost. Solving a transportation problem requires finding the Initial Basic Feasible Solution (IBFS) before obtaining the optimal solution. We propose a new method for finding the IBFS called the Maximum Difference Extreme Difference Method (MDEDM) which yields an optimal or close to the optimal solution. We also investigate the computational time complexity of MDEDM, and show that it is O(mn).