Applied Mathematics Commons^™

(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino

Applications and Applied Mathematics: An International Journal (AAM)

The study discusses the numerical solution for a time fractional Burgers’ equation using explicit (scheme 1) and implicit scheme (scheme 2), respectively. The approximation of the differential equation is discretized using the finite difference method (FDM). A non-linear term present in the Burgers’ equation is approximated using the time-averaged values. The Von-Neumann analysis shows that the Scheme 1 is conditionally stable and Scheme 2 is unconditionally stable. The numerical solutions are compared with the exact solutions and are good in agreement. Also, the error is estimated between exact and numerical solutions.

(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript investigates a broad class of second-order stochastic differential inclusions consisting of infinite delay and non-instantaneous impulses in a Hilbert space setting. We first formulate a new collection of sufficient conditions that ensure the approximate controllability of the considered system. Next, to investigate our main findings, we utilize stochastic analysis, the fundamental solution, resolvent condition, and Dhage’s fixed point theorem for multi-valued maps. Finally, an application is presented to demonstrate the effectiveness of the obtained results.

(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The …

(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav

Applications and Applied Mathematics: An International Journal (AAM)

Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …

(Si10-123) Comparison Between The Homotopy Perturbation Method And Variational Iteration Method For Fuzzy Differential Equations, P. Chandru, B. Radhakrishnan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the authors discusses the numerical simulations of higher-order differential equations under a fuzzy environment by using Homotopy Perturbation Method and Variational Iteration Method. The fuzzy parameter and variables are represented by triangular fuzzy convex normalized sets. Comparison of the results are obtained by the homotopy perturbation method with those obtained by the variational iteration method. Examples are provided to demonstrate the theory.

Bounds On Cohomological Support Varieties, Benjamin Briggs, Eloisa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

Over a local ring R, the theory of cohomological support varieties attaches to any bounded complex M of finitely generated R-modules an algebraic variety VR(M) that encodes homological properties of M. We give lower bounds for the dimension of VR(M) in terms of classical invariants of R. In particular, when R is Cohen-Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M has finite projective dimension, we also give an upper bound for dimVR(M) in terms of the dimension of the radical of the homotopy …

(Si10-077) A Novel Collocation Method For Solving Second-Order Volterra Integro-Differential Equations, Nimai Sarkar, Mausumi Sen, Pratiksha Jadli, Dipankar Saha

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we present an efficient numerical methodology to solve second-order linear Volterra integro-differential equations. Further, the modified Chebyshev collocation method is used at the Gauss-Lobatto collocation points. In that context, some theoretical investigation related to error analysis is suggested through residual function. Numerical examples are also encountered to study the applicability of the present method. In order to get a vivid illustration of the efficiency, we present a comparative survey with three existing collocation methods.

(Si10-062) Comprehensive Study On Methodology Of Orthogonal Interleavers, Priyanka Agarwal, Shivani Dixit, M. Shukla, Gaurish Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Interleaving permutes the data bits by employing a user defined sequence to reduce burst error which at times exceeds the minimum hamming distance. It serves as the sole medium to distinguish user data in the overlapping channel and is the heart of Interleave Division Multiple Access (IDMA) scheme. Versatility of interleavers relies on various design parameters such as orthogonality, correlation, latency and performance parameters like bit error rate (BER), memory occupancy and computation complexity. In this paper, a comprehensive study of interleaving phenomenon and discussion on numerous interleavers is presented. Also, the BER performance of interleavers using IDMA scheme is …

Approximation By Basis Pursuit: Background And Application To The Construction Of Efficient Spline Approximations, Babita Timalsina

Graduate Student Scholarship

Basis Pursuit was developed primarily as a tool in the field of signal processing, beginning in the mid 1990’s. The idea is to model the behavior of discrete signals using a wide range of functional behaviors and scales and to obtain an accurate and efficient representation of the signal using a minimal number of functions from a large “dictionary” of possible behaviors. The key observation is by formulating the representation as an ℓ1 optimization, the problem can be posed as a linear program so that the optimal solution uses no more than the number of constraints - it must be …

A Data Driven Modeling Approach For Store Distributed Load And Trajectory Prediction, Nicholas Peters

Doctoral Dissertations and Master's Theses

The task of achieving successful store separation from aircraft and spacecraft has historically been and continues to be, a critical issue for the aerospace industry. Whether it be from store-on-store wake interactions, store-parent body interactions or free stream turbulence, a failed case of store separation poses a serious risk to aircraft operators. Cases of failed store separation do not simply imply missing an intended target, but also bring the risk of collision with, and destruction of, the parent body vehicle. Given this risk, numerous well-tested procedures have been developed to help analyze store separation within the safe confines of wind …

A Mode-Sum Prescription For The Renormalized Stress Energy Tensor On Black Hole Spacetimes, Peter Taylor, Cormac Breen, Adrian Ottewill

Articles

In this paper, we describe an extremely efficient method for computing the renormalized stress-energy tensor of a quantum scalar field in spherically symmetric black hole spacetimes. The method applies to a scalar field with arbitrary field parameters. We demonstrate the utility of the method by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime, applying our results to discuss the null energy condition and the semiclassical backreaction.

Classification Of Pixel Tracks To Improve Track Reconstruction From Proton-Proton Collisions, Kebur Fantahun, Jobin Joseph, Halle Purdom, Nibhrat Lohia

SMU Data Science Review

In this paper, machine learning techniques are used to reconstruct particle collision pathways. CERN (Conseil européen pour la recherche nucléaire) uses a massive underground particle collider, called the Large Hadron Collider or LHC, to produce particle collisions at extremely high speeds. There are several layers of detectors in the collider that track the pathways of particles as they collide. The data produced from collisions contains an extraneous amount of background noise, i.e., decays from known particle collisions produce fake signal. Particularly, in the first layer of the detector, the pixel tracker, there is an overwhelming amount of background noise that …

Morton-Ordered Gpu Lattice Boltzmann Cfd Simulations With Application To Blood Flow, Gerald Gallagher, Fergal J. Boyle

Conference Papers

Computational fluid dynamics (CFD) is routinely used for numerically predicting cardiovascular-system medical device fluid flows. Most CFD simulations ignore the suspended cellular phases of blood due to computational constraints, which negatively affects simulation accuracy. A graphics processing unit (GPU) lattice Boltzmann-immersed boundary (LB-IB) CFD software package capable of accurately modelling blood flow is in development by the authors, focusing on the behaviour of plasma and stomatocyte, discocyte and echinocyte red blood cells during flow. Optimised memory ordering and layout schemes yield significant efficiency improvements for LB GPU simulations. In this work, comparisons of row-major-ordered Structure of Arrays (SoA) and Collected …

The Effect Of Habitat Fragmentation On Plant Communities In A Spatially-Implicit Grassland Model, Mika T. Cooney, Benjamin R. Hafner, Shelby E. Johnson, Sean Lee

Rose-Hulman Undergraduate Mathematics Journal

The spatially implicit Tilman-Levins ODE model helps to explain why so many plant species can coexist in grassland communities. This now-classic modeling framework assumes a trade-off between colonization and competition traits and predicts that habitat destruction can lead to long transient declines called ``extinction debts.'' Despite its strengths, the Tilman-Levins model does not explicitly account for landscape scale or the spatial configuration of viable habitat, two factors that may be decisive for population viability. We propose modifications to the model that explicitly capture habitat geometry and the spatial pattern of seed dispersal. The modified model retains implicit space and is …

Permitted Sets And Convex Coding In Nonthreshold Linear Networks, Steven Collazos, Duane Nykamp

Mathematics Publications

Hebbian theory proposes that ensembles of neurons form a basis for neural processing. It is possible to gain insight into the activity patterns of these neural ensembles through a binary analysis, regarding neurons as either active or inactive. The framework of permitted and forbidden sets, introduced by Hahnloser, Seung, and Slotine (2003), is a mathematical model of such a binary analysis: groups of coactive neurons can be permitted or forbidden depending on the network's structure.

In order to widen the applicability of the framework of permitted sets, we extend the permitted set analysis from the original threshold-linear regime. …

Abiogenesis: The Carter Argument Reconsidered, Daniel P. Whitmire

Mathematical Sciences Faculty Publications and Presentations

The observation of life on Earth is commonly believed to be uninformative regarding the probability of abiogenesis on other Earth-like planets. This belief is based on the selection effect of our existence. We necessarily had to find ourselves on a planet where abiogenesis occurred, thus nothing can be inferred about the probability of abiogenesis from this observation alone. This argument was first formalized in a Bayesian framework by Brandon Carter. Though we definitely had to find ourselves on a planet where abiogenesis occurred, I argue here that (1) the Carter conclusion is based on what is known as the ‘Old …

Leveraging Subject Matter Expertise To Optimize Machine Learning Techniques For Air And Space Applications, Philip Y. Cho

Theses and Dissertations

We develop new machine learning and statistical methods that are tailored for Air and Space applications through the incorporation of subject matter expertise. In particular, we focus on three separate research thrusts that each represents a different type of subject matter knowledge, modeling approach, and application. In our first thrust, we incorporate knowledge of natural phenomena to design a neural network algorithm for localizing point defects in transmission electron microscopy (TEM) images of crystalline materials. In our second research thrust, we use Bayesian feature selection and regression to analyze the relationship between fighter pilot attributes and flight mishap rates. We …

Entropy Analysis Of Sutterby Nanofluid Flow Over A Riga Sheet With Gyrotactic Microorganisms And Cattaneo–Christov Double Diffusion, M. Faizan, F. Ali, K. Loganathan, A. Zaib, C. A. Reddy, Sara I. Abdelsalam

Basic Science Engineering

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. …

Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu

Dissertations

Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …

Computing Rational Powers Of Monomial Ideals, Pratik Dongre, Benjamin Drabkin, Josiah Lim, Ethan Partida, Ethan Roy, Dylan Ruff, Alexandra Seceleanu, Tingting Tang

Department of Mathematics: Faculty Publications

This paper concerns fractional powers of monomial ideals. Rational powers of a monomial ideal generalize the integral closure operation as well as recover the family of symbolic powers. They also highlight many interesting connections to the theory of convex polytopes. We provide multiple algorithms for computing the rational powers of a monomial ideal. We also introduce a mild generalization allowing real powers of monomial ideals. An important result is that given any monomial ideal I, the function taking a real number to the corresponding real power of I is a step function which is left continuous and has rational …