Applied Mathematics Commons^™

Investigation Of Fundamental Principles Of Rigid Body Impact Mechanics, Khalid Alluhydan

Mechanical Engineering Research Theses and Dissertations

In impact mechanics, the collision between two or more bodies is a common, yet a very challenging problem. Producing analytical solutions that can predict the post-collision motion of the colliding bodies require consistent modeling of the dynamics of the colliding bodies. This dissertation presents a new method for solving the two and multibody impact problems that can be used to predict the post-collision motion of the colliding bodies. Also, we solve the rigid body collision problem of planar kinematic chains with multiple contacts with external surfaces.

In the first part of this dissertation, we study planar collisions of Balls and …

Meshless Modeling Of Flow Dispersion And Progressive Piping In Poroelastic Levees, Anthony Khoury, Eduardo Divo, Alain J. Kassab, Sai Kakuturu, Lakshmi Reddi

Publications

Performance data on earth dams and levees continue to indicate that piping is one of the major causes of failure. Current criteria for prevention of piping in earth dams and levees have remained largely empirical. This paper aims at developing a mechanistic understanding of the conditions necessary to prevent piping and to enhance the likelihood of self-healing of cracks in levees subjected to hydrodynamic loading from astronomical and meteorological (including hurricane storm surge-induced) forces. Systematic experimental investigations are performed to evaluate erosion in finite-length cracks as a result of transient hydrodynamic loading. Here, a novel application of the localized collocation …

Analysis Of An Eco-Epidemiological Model Under Optimal Control Measures For Infected Prey, Alfred Hugo, Emanuel Simanjilo

Applications and Applied Mathematics: An International Journal (AAM)

This paper examines the analysis of an eco-epidemiological model with optimal control strategies for infected prey. A model is proposed and analyzed qualitatively using the stability theory of the differential equations. A local and global study of the model is performed around the disease-free equilibrium and the endemic equilibrium to analyze the global stability using the Lyapunov function. The time-dependent control is introduced into the system to determine the best strategy for controlling the disease. The results obtained suggested the separation of the infected population plays a vital role in disease elimination.

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 …

Two Dimensional Mathematical Study Of Flow Dynamics Through Emphysemic Lung, Jyoti Kori, Pratibha _

Applications and Applied Mathematics: An International Journal (AAM)

There are various lung diseases, such as chronic obstructive pulmonary disease, asthma, fibrosis, emphysema etc., occurred due to deposition of different shape and size particles. Among them we focused on flow dynamics of viscous air through an emphysemic lung. We considered lung as a porous medium and porosity is a function of tidal volume. Two dimensional generalized equation of momentum is used to study the flow of air and equation of motion is used to study the flow of nanoparticles of elongated shape. Darcy term for flow in porous media and shape factor for nonspherical nanoparticles are used in mathematical …

Solitary And Periodic Exact Solutions Of The Viscosity-Capillarity Van Der Waals Gas Equations, Emad A. Az-Zo’Bi

Applications and Applied Mathematics: An International Journal (AAM)

Periodic and soliton solutions are derived for the (1+1)-dimensional van der Waals gas system in the viscosity-capillarity regularization form. The system is handled via the e-^φ(ξ) -expansion method. The obtained solutions have been articulated by the hyperbolic, trigonometric, exponential and rational functions with arbitrary constants. Mathematical analysis and numerical graphs are provided for some solitons, periodic and kink solitary wave solutions to visualize the dynamics of equations. Obtained results reveal that the method is very influential and effective tool for solving nonlinear partial differential equations in applied mathematics.

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 …

Transient Thermal Stresses Due To Axisymmetric Heat Supply In A Semi-Infinite Thick Circular Plate, S. D. Warbhe, K. C. Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the determination of thermal stresses in a semi-infinite thick circular plate of a finite length and infinite extent subjected to an axisymmetric heat supply. A thick circular plate is considered having constant initial temperature and arbitrary heat flux is applied on the upper and lower face. The governing heat conduction equation has been solved by using integral transform technique. The results are obtained in terms of Bessel’s function. The thermoelastic behavior has been computed numerically and illustrated graphically for a steel plate.

Numerical Solution Of 3rd Order Ode Using Fdm: On A Moving Surface In Mhd Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

A Similarity group theoretical technique is used to transform the governing nonlinear partial differential equations of two dimensional MHD boundary layer flow of Sisko fluid into nonlinear ordinary differential equations. Then the resulting third order nonlinear ordinary differential equation with corresponding boundary conditions is linearised by Quasi linearization method. Numerical solution of the linearised third order ODE is obtained using Finite Difference method (FDM). Graphical presentation of the solution is given.

Comparative Analysis On Angular Flow And Mass Transfer In Haemodialysis, J. K. Misra, Pradeep K. Singh, Naseem Ahmad, Pankaj Sharma

Applications and Applied Mathematics: An International Journal (AAM)

Healthy kidney cleans blood and removes unwanted materials in the form of urine. When the kidney does not work properly, dialysis is one of the best solutions. Dialysis required if unhealthy kidney does not remove enough wastes and fluid from the blood. This usually happens when only 10 - 15 % of kidney’s function left. A dialyzer is used to clean blood. In an attempt to address clinical and experimental discrepancies, compartmental theoretical models have been used. Noda et al. (1979) were among the first to introduce a theoretical model on mass transfer using countercurrent flows. Their proposed model assumes …

Rare Event Sampling In Applied Stochastic Dynamical Systems, Yiming Yu

Dissertations

Predicting rare events is a challenging problem in many complex systems arising in physics, chemistry, biology, and materials science. Simulating rare events is often prohibitive in such systems due to their high dimensionality and the numerical cost of their simulation, yet analytical expressions for rare event probabilities are usually not available. This dissertation tackles the problem of approximation of the probability of rare catastrophic events in optical communication systems and spin-torque magnetic nanodevices. With the application of the geometric minimum action method, the probability of pulse position shifts or other parameter changes in a model of an actively mode-locked laser …

Exact Feedback Linearization Of Systems With State-Space Modulation And Demodulation, Nikolaos I. Xiros Deng

LSU New Orleans Theses and Dissertations

The control theory of nonlinear systems has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. In several key areas, such as aerospace, chemical and petrochemical industries, bioengineering, and robotics, a new practical application for this tool appears every day. System nonlinearity is characterized when at least one component or subsystem is nonlinear. Classical methods used in the study of linear systems, particularly superposition, are not usually applied to the nonlinear systems. It is necessary to use other methods to study the control of these systems. …

Quantifying Complex Systems Via Computational Fly Swarms, Troy Taylor

Senior Theses

Complexity is prevalent both in natural and in human-made systems, yet is not well understood quantitatively. Qualitatively, complexity describes a phenomena in which a system composed of individual pieces, each having simple interactions with one another, results in interesting bulk properties that would otherwise not exist. One example of a complex biological system is the bird flock, in particular, a starling murmuration. Starlings are known to move in the direction of their neighbors and avoid collisions with fellow starlings, but as a result of these simple movement choices, the flock as a whole tends to exhibit fluid-like movements and form …

Realization Of Tensor Product And Of Tensor Factorization Of Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

We study the state space realization of a tensor product of a pair of rational functions. At the expense of “inflating” the dimensions, we recover the classical expressions for realization of a regular product of rational functions. Under an additional assumption that the limit at infinity of a given rational function exists and is equal to identity, we introduce an explicit formula for a tensor factorization of this function.

Analytical Wave Solutions Of The Space Time Fractional Modified Regularized Long Wave Equation Involving The Conformable Fractional Derivative, M. Hafiz Uddin, Md. Ashrafuzzaman Khan, M. Ali Akbar, Md. Abdul Haque

Karbala International Journal of Modern Science

The space time fractional modified regularized long wave equation is a model equation to the gravitational water waves in the long-wave occupancy, shallow waters waves in coastal seas, the hydro-magnetic waves in cold plasma, the phonetic waves in dissident quartz and phonetic gravitational waves in contractible liquids. In nonlinear science and engineering, the mentioned equation is applied to analyze the one way tract of long waves in seas and harbors. In this study, the closed form traveling wave solutions to the above equation are evaluated due to conformable fractional derivatives through double (G'⁄G,1⁄G)-expansion method and the Exp-function method. The existence …

Optimal Homotopy Asymptotic Solution For Thermal Radiation And Chemical Reaction Effects On Electrical Mhd Jeffrey Fluid Flow Over A Stretching Sheet Through Porous Media With Heat Source, Gossaye Aliy, Naikoti Kishan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed.

Mhd Boundary Layer Flow Of Darcy-Forchheimer Mixed Convection In A Nanofluid Saturated Porous Media With Viscous Dissipation, S. Jagadha, P. Amrutha

Applications and Applied Mathematics: An International Journal (AAM)

The steady laminar viscous incompressible nanofluid flow of mixed convection and mass transfer about an isothermal vertical flat plate embedded in Darcy porous medium in the presence of magnetic field and viscous dissipation is analyzed. The governing partial differential equations are converted into ordinary differential equations by similarity transformations. The coupled nonlinear ordinary differential equations are linearized by Quasi-linearization technique. The linear ordinary differential equations are solved by using implicit finite difference scheme with the help of C-programming. Numerical calculations are carried out for different values of dimensionless parameter such as magnetic field, mixed convection parameter, inertia parameter, buoyancy ratio …

Spacetime Groups, Ian M. Anderson, Charles G. Torre

Publications

A spacetime group is a connected 4-dimensional Lie group G endowed with a left invariant Lorentz metric h and such that the connected component of the isometry group of h is G itself. The Newman-Penrose formalism is used to give an algebraic classification of spacetime groups, that is, we determine a complete list of inequivalent spacetime Lie algebras, which are pairs (g,η), with g being a 4-dimensional Lie algebra and η being a Lorentzian inner product on g. A full analysis of the equivalence problem for spacetime Lie algebras is given which leads to a completely algorithmic solution to the …

A New Model For Lifting Condensation Levels Estimation, Nihad E. Daidzic

Aviation Department Publications

Knowledge of and the ability to predict lifting condensation levels (LCL) is important ingredient in weather predictions, cloud formation, planetary albedo and Earth’s energy balance. It is also essential topic in aviation safety and flight operations. In this article, we derive a new model of LCL and compare it to some older commonly-used models. This includes also the recently published Romps’ (2017) model. The new model presented here includes dependence, however weak, of the surface atmospheric pressure and the specific humidity on the LCL height and temperature. Such is not the case with widely used models and expressions by Espy …

Surface Waves Over Currents And Uneven Bottom, Alan Compelli, Rossen Ivanov, Calin I. Martin, Michail D. Todorov

Articles

The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution …

Practical Chaos: Using Dynamical Systems To Encrypt Audio And Visual Data, Julia Ruiter

Scripps Senior Theses

Although dynamical systems have a multitude of classical uses in physics and applied mathematics, new research in theoretical computer science shows that dynamical systems can also be used as a highly secure method of encrypting data. Properties of Lorenz and similar systems of equations yield chaotic outputs that are good at masking the underlying data both physically and mathematically. This paper aims to show how Lorenz systems may be used to encrypt text and image data, as well as provide a framework for how physical mechanisms may be built using these properties to transmit encrypted wave signals.

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 …

A Detection And Data Acquisition System For Precision Beta Decay Spectroscopy, Aaron P. Jezghani

Theses and Dissertations--Physics and Astronomy

Free neutron and nuclear beta decay spectroscopy serves as a robust laboratory for investigations of the Standard Model of Particle Physics. Observables such as decay product angular correlations and energy spectra overconstrain the Standard Model and serve as a sensitive probe for Beyond the Standard Model physics. Improved measurement of these quantities is necessary to complement the TeV scale physics being conducted at the Large Hadron Collider. The UCNB, ⁴⁵Ca, and Nab experiments aim to improve upon existing measurements of free neutron decay angular correlations and set new limits in the search for exotic couplings in beta decay. To …

Equatorial Wave–Current Interactions, Adrian Constantin, Rossen Ivanov

Articles

We study the nonlinear equations of motion for equatorial wave–current interactions in the physically realistic setting of azimuthal two-dimensional inviscid flows with piecewise constant vorticity in a two-layer fluid with a flat bed and a free surface. We derive a Hamiltonian formulation for the nonlinear governing equations that is adequate for structure-preserving perturbations, at the linear and at the nonlinear level. Linear theory reveals some important features of the dynamics, highlighting differences between the short- and long-wave regimes. The fact that ocean energy is concentrated in the long-wave propagation modes motivates the pursuit of in-depth nonlinear analysis in the long-wave …

Solutions For Fermi Questions, November 2019: Question 1: Cell Phones Make Me Boil; Question 2: Charging The Phone, Larry Weinstein

Physics Faculty Publications

Answers to the Fermi questions:

How much water can you boil with the energy stored in a cell phone battery?

How much does the electrical energy for a cell phone cost each year?

Thermoelastic Stress Analysis Of A Functionally Graded Transversely Isotropic Hollow Cylinder In Elliptical Coordinates, Tara Dhakate, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the axisymmetric thermoelastic problem to investigate the influence of nonlinear heat conduction equation, displacement functions and thermal stresses of a functionally graded transversely isotropic hollow cylinder that is presented in the elliptical coordinate system. The method of integral transform technique is used to produce an exact solution of the heat conduction equation in which sources are generated according to a linear function of the temperature. An explicit exact solution of the governing thermoelastic equation is proposed when material properties are power-law functions with the exponential form of the radial coordinate. Numerical calculations are also carried …

Quasi-Linearization Method With Rational Legendre Collocation Method For Solving Mhd Flow Over A Stretching Sheet With Variable Thickness And Slip Velocity Which Embedded In A Porous Medium, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

The quasi-linearization method (QLM) and the rational Legendre functions are introduced here to present the numerical solution for the Newtonian fluid flow past an impermeable stretching sheet which embedded in a porous medium with a power-law surface velocity, variable thickness and slip velocity. Firstly, due to the high nonlinearity which yielded from the ordinary differential equation which describes the proposed physical problem, we construct a sequence of linear ODEs by using the QLM, hence the resulted equations become a system of linear algebraic equations. The comparison with the available results in the literature review proves that the obtained results via …

Similarity Analysis Of Three Dimensional Nanofluid Flow By Deductive Group Theoretic Method, Hemangini Shukla, Hema C. Surati, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to obtain similarity solution of three-dimensional nanofluid flow over flat surface stretched continuously in two lateral directions. Two independent variables from governing equations are reduced by applying deductive two parameter group theoretical method. Partial differential equations with boundary conditions are converted into ordinary differential equations with appropriate boundary conditions. Obtained equations are solved for temperature and velocity. The effect of nanoparticles volume fraction on temperature and velocity profile is investigated.

Numerical Studies For Mhd Flow And Gradient Heat Transport Past A Stretching Sheet With Radiation And Heat Production Via Dtm, Khadijah M. Abualnaja

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents a numerically study for the effect of the internal heat generation, magnetic field and thermal radiation effects on the flow and gradient heat transfer of a Newtonian fluid over a stretching sheet. By using a similarity transformation, the governing PDEs can be transformed into a coupled non-linear system of ODEs with variable coefficients. Numerical solutions for these equations subject to appropriate boundary conditions are obtained by using the differential transformation method (DTM). The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl …

The Basins Of Convergence In The Planar Restricted Four-Body Problem With Variable Mass, Amit Mittal, Monika Arora, Md S. Suraj, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have studied the existence, location and stability of the libration points in the model of restricted four-body problem (R4BP) with variable mass. It is assumed that three primaries, one dominant primary and the other two with equal masses, are always forming an equilateral triangle. We have determined the equations of motion of the above mentioned problem for the fourth body which is an infinitesimal mass. The libration points have been determined numerically for different values of the parameters considered. It is found that there are eight or ten libration points out of which six are non-collinear and two or …