Applied Mathematics Commons^™

(R2078) Analyzing The Effects Of Fifth And Seventh Order Terms In A Generalized Henon-Heiles Potential, Nandana Madhukara

Applications and Applied Mathematics: An International Journal (AAM)

The Hénon-Heiles system is a 2-dimensional axisymmetric Hamiltonian system that was first formed to determine the third integral of motion in galactic dynamics. After its inception, it has become a paradigm in dynamical systems due to its apparent simplicity but extremely complicated dynamical behavior. In this paper, we perform a series expansion up to the seventh order of a general potential with axial and reflection symmetries. After some transformations, this becomes a generalized Hénon-Heiles (GHH) system where we separate the fifth and seventh-order terms. We qualitatively analyze this system for energies near the threshold between bounded and unbounded motion with …

(R2086) Circular Restricted Three-Body Interaction Problem With Various Perturbations, Shiv K. Sahdev, Abdullah .

Applications and Applied Mathematics: An International Journal (AAM)

The motion properties of the infinitesimal body is studied under the forces due to kerr-like oblate heterogeneous primary, continuation fractional potential for secondary, solar sail, three-body interactions, Coriolis and centrifugal forces in the circular restricted three-body problem. The equations of motion of infinitesimal body are evaluated under the above-said perturbations. Using these equations of motion, we illustrate the locations of equilibrium points, their stability, the periodic orbits and Poincaré surfaces of section. This study will applicable on the motion of the artificial satellite.

(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …

(R2085) Heat And Mass Transport Characteristics In Williamson Fluid Flow Over A Permeable Stretching Cylinder, Amala Olkha, Mukesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The intention of this research endeavor is to examine heat and mass transport in Williamson fluid flow induced by a permeable stretching cylinder in a porous medium. Various physical factors (like viscous dissipation, chemical reaction, etc.) affecting the relevant fields (flow, temperature and concentration) are incorporated in the investigation. The governing PDEs are turned into nondimensional ODEs using adequate similarity transformation relations, and then tackled numerically using MATLAB based Bvp4c technique along with shooting method. The impacts of various parameters arising in the problem are exhibited on fluid flow, temperature and concentration distribution by drawing portraits and discussed. Moreover, impressions …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Advances In Computational And Statistical Inverse Problems, Dylan Green

Dartmouth College Ph.D Dissertations

Inverse problems are prevalent in many fields of science and engineering, such as signal processing and medical imaging. In such problems, indirect data are used to recover information regarding some unknown parameters of interest. When these problems fail to be well-posed, the original problems must be modified to include additional constraints or optimization terms, giving rise to so-called regularization techniques. Classical methods for solving inverse problems are often deterministic and focus on finding point estimates for the unknowns. Some newer methods approach the solving of inverse problems by instead casting them in a statistical framework, allowing for novel point estimate …

Comparison Of Methods For Creating Populations Of Models By Solving Stochastic Inverse Problems, Elizabeth Epstein

Theses

Given a parametric family of models and observational data, a researcher may be faced with an inverse problem: what distribution of parameters best creates a set of models that produce the observed data? Traditionally, Markov Chain Monte Carlo (MCMC) has commonly been used as a method to solve these stochastic inverse problems. In recent years, however, Generative Adversarial Networks (GANs) have been employed. The effectiveness of Markov Chain Monte Carlo methods as compared to a conditional generative adversarial network (cGAN) when applied to a family of models produced by a system of ordinary differential equations that model viral load over …

Mathematical Modeling And Simulation Of The Photopolymerization Process In Different Industrial Applications, Maged Shaban

Doctoral

Photopolymerization is a complex physicochemical process that uses a specific wavelength of light to convert a liquid monomer resin to a solid polymer. This study investigates the evolution of photopolymerization kinetics through mathematical modeling and simulation in different industrial applications, such as stereolithography, ceramics additive manufacturing, and photonic crystal fabrication. In stereolithography, existing photopolymerization models do not fully capture the complexity of the curing process. Therefore, we develop a novel model for photopolymerization kinetics in a realistic stereolithography setting, which attempts to advance the understanding of the impact of several material properties and parameters on this process. This model significantly …

Existence And Uniqueness Results For Deformable Fractional Differential Equations, Sreedharan R

Theses and Dissertations

Fractional calculus and fractional differential equations are considered to be the valuable tools in modeling many phenomena in various fields of science and engineering. In the literature, many definitions for fractional order derivatives, such as Riemann-Liouville, Caputo, Jumarie, Hadamard, Weyl, and more, were developed to study the fractional differential equations that govern various phenomena in science and engineering. But these definitions have their own limitations, such as derivatives of constants, product of two functions, quotient of two functions, assertion laws, and limiting values of the derivatives at zero and negative numbers.

To overcome the deficiencies, researchers have recently introduced some …

Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey

Biology and Medicine Through Mathematics Conference

No abstract provided.

Benefit Of Medication Reconciliation Practices On Patient Health Outcomes In A Healthcare Setting, Helen Harris, David Petrulis, Lauren Trepp, Bryan Chong, Jillian Haas, David Chan, Laura Ellwein Fix

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model Of Oocyte Population Dynamics For Fish Oogenesis, Louis Fostier, Frédérique Clément, Romain Yvinec, Violette Thermes

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Fast Information And Slow(Er) Disease Spreading: A Geometric Analysis, Iulia Martina Bulai, Mattia Sensi, Sara Sottile

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling And Control Of Drug Resistance In Cancer Dynamics, James Greene

Biology and Medicine Through Mathematics Conference

No abstract provided.

Reaction-Diffusions System Simulated On Irregular Shapes And Surfaces Model Petal Spot Patterns In Monkeyflower Hybrids, Emily Simmons, Arielle M. Cooley, Joshua R. Puzey, Gregory D. Conradi Smith

Biology and Medicine Through Mathematics Conference

No abstract provided.

Exploring The Evolution Of Altruistic Punishment Using A Pde Model For Multilevel Selection, Daniel Cooney

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using Splines To Investigate The Effects Of Temperature On The Within-Mosquito Malaria Parasite Forms, Alexander J. Diefes, Miranda I. Teboh-Ewungkem

Biology and Medicine Through Mathematics Conference

No abstract provided.

Tracking Food Quality In Algae-Daphnia Ecosystems Through Stage Structured Models And Colimitation, Tomas Ascoli

Biology and Medicine Through Mathematics Conference

No abstract provided.

Identifiability For Pde Models Of Fluorescence Microscopy Experiments, Veronica Ciocanel

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multiscale Modeling Of Microtubule Polarity Mechanisms Following Neuronal Axotomy, Hannah Scanlon

Biology and Medicine Through Mathematics Conference

No abstract provided.

Statistical Mobility Of Aggregated Microswimmers, Yonatan Ashenafi

Biology and Medicine Through Mathematics Conference

No abstract provided.

Local Geometry Of Elementary Visual Computations, Peter Neri

MODVIS Workshop

Visual operators (e.g. edge detectors) are classically modelled using small circuits involving canonical computations, such as template-matching and gain control. Circuit models explain many aspects of the empirical descriptors that are used to characterize local visual operators, from sensitivity to classification images. Notwithstanding their utility, these models fail to provide a unified framework encompassing the variety of effects observed experimentally, such as the impact of contrast, SNR, and attention on the above descriptors. My goal is to start with a simple, plausible geometrical representation of the perceptual operation carried out by the observer, and to show that this representation is …

H1-Conforming Finite Elements On Nonstandard Meshes, Samuel Edward Reynolds

Dissertations and Theses

We present a finite element method for linear elliptic partial differential equations on bounded planar domains that are meshed with cells that are permitted to be curvilinear and multiply connected. We employ Poisson spaces, as used in virtual element methods, consisting of globally continuous functions that locally satisfy a Poisson problem with polynomial data. This dissertation presents four peer-reviewed articles concerning both the theory and computation of using such spaces in the context of finite elements. In the first paper, we propose a Dirichlet-to-Neumann map for harmonic functions by way of computing the trace of a harmonic conjugate by numerically …

Improved Rational Approximation Of Near-To-Far Propagation Kernels For The Wave Equation, Sampson Owusu

Mathematics & Statistics ETDs

The 3-space, 1-time dimensional scalar wave equation, or 3+1 wave equation, describes the propagation of scalar or acoustic waves. The unforced homogeneous equation admits a class of outgoing solutions relative to a chosen fixed center, so called “multipole” solutions. This thesis examines near-to-far signal propagation in the context of these multipole solutions. Given a time-series (history of values) for a multipole solution recorded at a radius r1, near- to-far signal propagation recovers the corresponding time-series at larger radius r2 ≫ r1. This propagation takes into account both the appropriate time delay r2 − r1 and corrections to the wave shape. …

Conjugations Of Unitary Operators, I, Javad Mashreghi, Mraek Ptak, William T. Ross

Department of Math & Statistics Faculty Publications

If U is a unitary operator on a separable complex Hilbert space H, an application of the spectral theorem says there is a conjugation C on H (an antilinear, involutive isometry on H) for which CUC= U*. In this paper, we fix a unitary operator U and describe all of the conjugations C which satisfy this property. As a consequence of our results, we show that a subspace is hyperinvariant for U if and only if it is invariant for any conjugation C for which CUC = U*.

Chemoattractant Distribution In The Drosophila Egg Chamber, Lara Scott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Sperm-Egg Interaction For Fertilization Success, Prajakta P. Bedekar

Biology and Medicine Through Mathematics Conference

No abstract provided.

Impacts Of Hematodinium Infection In A Seasonal Population Model Of The Chesapeake Bay Blue Crab, Gwendolyn R. Sargent, Romuald Lipcius, Leah Shaw, Junping Shi, Jeffrey D. Shields

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Comparative Analysis Of Source Identification Algorithms, Pablo A. Curiel

Biology and Medicine Through Mathematics Conference

No abstract provided.