Applied Mathematics Commons^™

Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general …

Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad

Applications and Applied Mathematics: An International Journal (AAM)

The present study deals with the applications of the planar Newtonian four-body problem to
the different central configurations. The basic concept of central configuration is that the
vector force must be in the direction of the position vector so that the origin may be taken at
the centre of mass of the four bodies and the force towards the position vector multiplied by
corresponding inverse mass is directly proportional to the position vector relative to the
centre of mass. For applying the Newtonian four body problem to the central configuration,
the equations of motion of four bodies have been established …

Rogue Rotary - Modular Robotic Rotary Joint Design, Sean Wesley Murphy, Tyler David Riessen, Jacob Mark Triplett

Mechanical Engineering

This paper describes the design process from ideation to test validation for a singular robotic joint to be configured into a myriad of system level of robots.

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

LSU Doctoral Dissertations

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical …

A Critical Firing Rate In Synchronous Transitions Of Coupled Neurons, Annabelle Shaffer, Epaminondas Rosa, Rosangela Follmann

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Evolution Of Superoscillations For Schrödinger Equation In A Uniform Magnetic Field, Fabrizio Colombo, Jonathan Gantner, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

Aharonov-Berry superoscillations are band-limited functions that oscillate faster than their fastest Fourier component. Superoscillations appear in several fields of science and technology, such as Aharonov’s weak measurement in quantum mechanics, in optics, and in signal processing. An important issue is the study of the evolution of superoscillations using the Schrödinger equation when the initial datum is a weak value. Some superoscillatory functions are not square integrable, but they are real analytic functions that can be extended to entire holomorphic functions. This fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of …

Nonlinear Waves, Instabilities And Singularities In Plasma And Hydrodynamics, Denis Albertovich Silantyev

Mathematics & Statistics ETDs

This work concentrates on Langmuir wave filamentation instability in the kinetic regime of plasma and computation of Stokes wave with high precision using conformal maps.

Nonlinear effects are present in almost every area of science as soon as one tries to go beyond the first order approximation. In particular, nonlinear waves emerge in such areas as hydrodynamics, nonlinear optics, plasma physics, quantum physics, etc. The results of this work are related to nonlinear waves in two areas, plasma physics and hydrodynamics, united by concepts of instability, singularity and advanced numerical methods used for their investigation.

The first part of this …

Interplay Of Quantum Size Effect, Anisotropy And Surface Stress Shapes The Instability Of Thin Metal Films, Mikhail Khenner

Mathematics Faculty Publications

Morphological instability of a planar surface ([111], [011], or [001]) of an ultra-thin metal film is studied in a parameter space formed by three major effects (the quantum size effect, the surface energy anisotropy and the surface stress) that influence a film dewetting. The analysis is based on the extended Mullins equation, where the effects are cast as functions of the film thickness. The formulation of the quantum size effect (Z. Zhang et al., PRL 80, 5381 (1998)) includes the oscillation of the surface energy with thickness caused by electrons confinement. By systematically comparing the effects, their contributions into the …

On The Ramberg-Osgood Stress-Strain Model And Large Deformations Of Cantilever Beams, Ronald J. Giardina Jr

LSU New Orleans Theses and Dissertations

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are …

Solution Of Pdes For First-Order Photobleaching Kinetics Using Krylov Subspace Spectral Methods, Somayyeh Sheikholeslami

Dissertations

We solve the first order reaction-diffusion equations which describe binding-diffusion kinetics using a photobleaching scanning profile of a confocal laser scanning microscope approximated by a Gaussian laser profile. We show how to solve these equations with prebleach steady-state initial conditions using a time-domain method known as a Krylov Subspace Spectral (KSS) method. KSS methods are explicit methods for solving time- dependent variable-coefficient partial differential equations (PDEs). KSS methods are advantageous compared to other methods because of their stability and their superior scalability. These advantages are obtained by applying Gaussian quadrature rules in the spectral domain developed by Golub and Meurant. …

Evaluation And Enhancement Of Clean Energy Systems: Analytical, Computational And Experimental Study Of Solar And Nuclear Cycles, Nima Fathi

Mechanical Engineering ETDs

Clean (and specifically renewable) energy is steadily improving its global share. However, finite availability of fossil fuels and the growing effects of climate change make it an urgent priority to convince the industry and governments to incentivize investment in the renewable energy field and to make it more attractive by decreasing the capital cost. Until recently, uncertainties in funding limited renewable energy development, especially in the US. That limitation has been one of the barriers to progress. Another limitation of many renewable energy systems is the variability in their output, which makes them unsuitable for baseline power production. Therefore, fossil …

Mathematical Description And Mechanistic Reasoning: A Pathway Toward Stem Integration, Paul J. Weinberg

Journal of Pre-College Engineering Education Research (J-PEER)

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith’s (2007) characterization of mathematical description of scientific phenomena as ‘‘bootstrapping,’’ where negotiating the relationship between target phenomena and represented relations is fundamental to learning. In addition, the development of mathematical representation presents a viable pathway towards STEM integration. In this study, participants responded to an assessment of mechanistic reasoning while cognitive interviews …

Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker

Mahurin Honors College Capstone Experience/Thesis Projects

Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in …

Asymptotic Behavior Of Waves In A Nonuniform Medium, Nezam Iraniparast, Lan Nguyen, Mikhail Khenner

Applications and Applied Mathematics: An International Journal (AAM)

An incoming wave on an infinite string, that has uniform density except for one or two jump discontinuities, splits into transmitted and reflected waves. These waves can explicitly be described in terms of the incoming wave with changes in the amplitude and speed. But when a string or membrane has continuous inhomogeneity in a finite region the waves can only be approximated or described asymptotically. Here, we study the cases of monochromatic waves along a nonuniform density string and plane waves along a membrane with nonuniform density. In both cases the speed of the physical system is assumed to tend …

Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …

Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …

Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma

Applications and Applied Mathematics: An International Journal (AAM)

The vibrations of circular plate in modified couple stress thermoelastic medium using Kirchhoff- Love plate theory has been presented. The basic equations of motion and heat conduction equation for Lord Shulman (L-S, 1967) theory are written with the help of Kirchhoff-Love plate theory. The thermoelastic damping of micro beam resonators is studied by applying normal mode analysis method. The solutions for the free vibrations of plates under clamped, simply supported and free boundary conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized couple stress thermoelastic and coupled thermoelastic plates. Numerical results …

Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma

Applications and Applied Mathematics: An International Journal (AAM)

This communication addresses the influence of nonlinear thermal radiation on magneto hydrodynamic Maxwell fluid flow past a linearly stretching surface with heat and mass transfer. The effects of heat generation/absorption and chemical reaction are taken into account. At first, we converted the governing partial differential equations into nonlinear ordinary differential equations with the help of suitable similarity transformations and solved by using Runge-Kutta based shooting technique. Further, the effects of various physical parameters on velocity, temperature and concentration fields were discussed thoroughly with the help of graphs obtained by using bvp5c MATLAB package. In view of many engineering applications we …

Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin

Applications and Applied Mathematics: An International Journal (AAM)

In this present paper, damped vibrations of an orthotropic rectangular plate resting on elastic foundation with thermal gradient is modeled, considering variable thickness of plate. Following Le`vy approach, the governed equation of motion is solved numerically using quintic spline technique with clamped and simply supported edges. The effect of damping parameter and thermal gradient together with taper constant, density parameter and elastic foundation parameter on the natural frequencies of vibration for the first three modes of vibration are depicted through Tables and Figures, and mode shapes have been computed for fixed value of plate parameter. It has been observed that …

New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper new fractional derivative and direct algebraic method are used to construct exact solutions of the nonlinear time fractional Sharma-Tasso-Olver equation. As a result, three families of exact analytical solutions are obtained. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.

Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali

Applications and Applied Mathematics: An International Journal (AAM)

In the present study, the classical fourth-order Runge-Kutta method with seventh-order automatic step-size control has been carried out to examine the stability of triangular libration points in the Sun-Jupiter system. The Sun is a highly luminous body and Jupiter is a highly spinning body, so radiation pressure of the Sun and oblateness of the Jupiter cannot be neglected. These factors must have some effects on the motion of the infinitesimal mass (spacecraft) and consequent effects on the stability of the triangular libration points. It is to be noted that in our problem, infinitesimal mass exerts no influence of attraction on …

Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.

Measuring The Reflection Matrix Of A Rough Surface, Kenneth W. Burgi, Michael A. Marciniak, Mark E. Oxley, Stephen E. Nauyoks

Faculty Publications

Phase modulation methods for imaging around corners with reflectively scattered light required illumination of the occluded scene with a light source either in the scene or with direct line of sight to the scene. The RM (reflection matrix) allows control and refocusing of light after reflection, which could provide a means of illuminating an occluded scene without access or line of sight. Two optical arrangements, one focal-plane, the other an imaging system, were used to measure the RM of five different rough-surface reflectors. Intensity enhancement values of up to 24 were achieved. Surface roughness, correlation length, and slope were examined …

Building And Validating A Model For Investigating The Dynamics Of Isolated Water Molecules, Grant Cates

Senior Theses

Understanding how water molecules behave in isolation is vital to understand many fundamental processes in nature. To that end, scientists have begun studying crystals in which single water molecules become trapped in regularly occurring cavities in the crystal structure. As part of that investigation, numerical models used to investigate the dynamics of isolated water molecules are sought to help bolster our fundamental understanding of how these systems behave. To that end, the efficacy of three computational methods—the Euler Method, the Euler-Aspel Method and the Beeman Method—is compared using a newly defined parameter, called the predictive stability coefficient ρ. This …

Electrodynamical Modeling For Light Transport Simulation, Michael G. Saunders

Undergraduate Honors Theses

Modernity in the computer graphics community is characterized by a burgeoning interest in physically based rendering techniques. That is to say that mathematical reasoning from first principles is widely preferred to ad hoc, approximate reasoning in blind pursuit of photorealism. Thereby, the purpose of our research is to investigate the efficacy of explicit electrodynamical modeling by means of the generalized Jones vector given by Azzam [1] and the generalized Jones matrix given by Ortega-Quijano & Arce-Diego [2] in the context of stochastic light transport simulation for computer graphics. To augment the status quo path tracing framework with such a modeling …

An Rbf Interpolation Blending Scheme For Effective Shock-Capturing, M. Harris, Eduardo Divo, Alain J. Kassab

Publications

In recent years significant focus has been given to the study of Radial basis functions (RBF), especially in their use on solving partial differential equations (PDE). RBF have an impressive capability of inter- polating scattered data, even when this data presents localized discontinuities. However, for infinitely smooth RBF such as the Multiquadrics, inverse Multiquadrics, and Gaussian, the shape parameter must be chosen properly to obtain accurate approximations while avoiding ill-conditioning of the interpolating matrices. The optimum shape parameter can vary significantly depending on the field, particularly in locations of steep gradients, shocks, or discontinuities. Typically, the shape parameter is chosen …

A Coupled Localized Rbf Meshless/Drbem Formulation For Accurate Modeling Of Incompressible Fluid Flows, Leonardo Bueno, Eduardo Divo, Alain J. Kassab

Publications

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like equations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensure proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each level of an iteration process. Inaccurate solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at …

Code For "Noise-Enhanced Coding In Phasic Neuron Spike Trains", Cheng Ly, Brent D. Doiron

Statistical Sciences and Operations Research Data

This zip file contains Matlab scripts and ode (XPP) files to calculate the statistics of the models in "Noise-Enhanced Coding in Phasic Neuron Spike Trains". This article is published in PLoS ONE.

Fire, Ice, Water, And Dirt: A Simple Climate Model, John Kroll

Mathematics & Statistics Faculty Publications

A simple paleoclimate model was developed as a modeling exercise. The model is a lumped parameter system consisting of an ocean (water), land (dirt), glacier, and sea ice (ice) and driven by the sun (fire). In comparison with other such models, its uniqueness lies in its relative simplicity yet yielding good results. For nominal values of parameters, the system is very sensitive to small changes in the parameters, yielding equilibrium, steady oscillations, and catastrophes such as freezing or boiling oceans. However, stable solutions can be found, especially naturally oscillating solutions. For nominally realistic conditions, natural periods of order 100kyrs are …

Orbital Stability Results For Soliton Solutions To Nonlinear Schrödinger Equations With External Potentials, Joseph B. Lindgren

Theses and Dissertations--Mathematics

For certain nonlinear Schroedinger equations there exist solutions which are called solitary waves. Addition of a potential $V$ changes the dynamics, but for small enough $||V||_{L^\infty}$ we can still obtain stability (and approximately Newtonian motion of the solitary wave's center of mass) for soliton-like solutions up to a finite time that depends on the size and scale of the potential $V$. Our method is an adaptation of the well-known Lyapunov method.

For the sake of completeness, we also prove long-time stability of traveling solitons in the case $V=0$.