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Partial Differential Equations Commons

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Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer 2019 Illinois State University

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose 2019 University of Mary Washington

Algorithms To Approximate Solutions Of Poisson's Equation In Three Dimensions, Ray Dambrose

Rose-Hulman Undergraduate Mathematics Journal

The focus of this research was to develop numerical algorithms to approximate solutions of Poisson's equation in three dimensional rectangular prism domains. Numerical analysis of partial differential equations is vital to understanding and modeling these complex problems. Poisson's equation can be approximated with a finite difference approximation. A system of equations can be formed that gives solutions at internal points of the domain. A computer program was developed to solve this system with inputs such as boundary conditions and a nonhomogenous source function. Approximate solutions are compared with exact solutions to prove their accuracy. The program is tested ...


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 2019 Jessore University of Science and Technology

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 ...


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski 2018 Wojciech Budzianowski Consulting Services

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore 2018 Western Kentucky University

Creating A Computational Tool To Simulate Vibration Control For Piezoelectric Devices, Ahmet Ozkan Ozer, Emma J. Moore

Posters-at-the-Capitol

Piezoelectric materials have the unique ability to convert electrical energy to mechanical vibrations and vice versa. This project takes a stab to develop a reliable computational tool to simulate the vibration control of a novel “partial differential equation” model for a piezoelectric device, which is designed by integrating electric conducting piezoelectric layers constraining a viscoelastic layer to provide an active and lightweight intelligent structure. Controlling unwanted vibrations on piezoelectric devices (or harvesting energy from ambient vibrations) through piezoelectric layers has been the major focus in cutting-edge engineering applications such as ultrasonic welders and inchworms. The corresponding mathematical models for piezoelectric ...


Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov 2018 University of New Mexico

Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov

Shared Knowledge Conference

Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the ...


Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu 2018 Illinois State University

Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling The Impact Of The Latent Period On The Spatial Spread Of Dengue Fever, Juan Melendez-Alvarez 2018 Illinois State University

Modeling The Impact Of The Latent Period On The Spatial Spread Of Dengue Fever, Juan Melendez-Alvarez

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Boundary Homogenization And Capture Time Distributions Of Semipermeable Membranes With Periodic Patterns Of Reactive Sites, Andrew J. Bernoff, Daniel Schmidt, Alan E. Lindsay 2018 Harvey Mudd College

Boundary Homogenization And Capture Time Distributions Of Semipermeable Membranes With Periodic Patterns Of Reactive Sites, Andrew J. Bernoff, Daniel Schmidt, Alan E. Lindsay

All HMC Faculty Publications and Research

We consider the capture dynamics of a particle undergoing a random walk in a half- space bounded by a plane with a periodic pattern of absorbing pores. In particular, we numerically measure and asymptotically characterize the distribution of capture times. Numerically we develop a kinetic Monte Carlo (KMC) method that exploits exact solutions to create an efficient particle- based simulation of the capture time that deals with the infinite half-space exactly and has a run time that is independent of how far from the pores one begins. Past researchers have proposed homogenizing the surface boundary conditions, replacing the reflecting (Neumann ...


Reduction Of Multivariate Mixtures And Its Applications, Xinshuo Yang 2018 University of Colorado, Boulder

Reduction Of Multivariate Mixtures And Its Applications, Xinshuo Yang

Applied Mathematics Graduate Theses & Dissertations

We consider a fast deterministic algorithm to identify the "best" linearly independent terms in multivariate mixtures and use them to compute an equivalent representation with fewer terms, up to user-selected accuracy. Our algorithm employs the well-known pivoted Cholesky decomposition of the Gram matrix constructed using terms of the mixture. Importantly, the multivariate mixtures do not have to be a separated representation of a function and complexity of the algorithm is independent of the number of variables (dimensions). The algorithm requires $\mathcal{O}\left(r^{2}N\right)$ operations, where $N$ is the initial number of terms in a multivariate mixture ...


On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson 2018 University of Nebraska - Lincoln

On The Well-Posedness And Global Boundary Controllability Of A Nonlinear Beam Model, Jessie Jamieson

Dissertations, Theses, and Student Research Papers in Mathematics

The theory of beams and plates has been long established due to works spanning many fields, and has been explored through many investigations of beam and plate mechanics, controls, stability, and the well-posedness of systems of equations governing the motions of plates and beams. Additionally, recent investigations of flutter phenomena by Dowell, Webster et al. have reignited interest into the mechanics and stability of nonlinear beams. In this thesis, we wish to revisit the seminal well-posedness results of Lagnese and Leugering for the one dimensional, nonlinear beam from their 1991 paper, "Uniform stabilization of a nonlinear beam by nonlinear boundary ...


Adaptive Meshfree Methods For Partial Differential Equations, Jaeyoun Oh 2018 The University of Southern Mississippi

Adaptive Meshfree Methods For Partial Differential Equations, Jaeyoun Oh

Dissertations

There are many types of adaptive methods that have been developed with different algorithm schemes and definitions for solving Partial Differential Equations (PDE). Adaptive methods have been developed in mesh-based methods, and in recent years, they have been extended by using meshfree methods, such as the Radial Basis Function (RBF) collocation method and the Method of Fundamental Solutions (MFS). The purpose of this dissertation is to introduce an adaptive algorithm with a residual type of error estimator which has not been found in the literature for the adaptive MFS. Some modifications have been made in developing the algorithm schemes depending ...


Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek 2018 Tallinn University of Technology

Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek

Publications

In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a one-dimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and ...


Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang 2018 Louisiana State University and Agricultural and Mechanical College

Spectra Of Quantum Trees And Orthogonal Polynomials, Zhaoxia Wang

LSU Doctoral Dissertations

We investigate the spectrum of regular quantum-graph trees, where the edges are endowed with a Schr\"odinger operator with self-adjoint Robin vertex conditions. It is known that, for large eigenvalues, the Robin spectrum approaches the Neumann spectrum. In this research, we compute the lower Robin spectrum. The spectrum can be obtained from the roots of a sequence of orthogonal polynomials involving two variables. As the length of the quantum tree increases, the spectrum approaches a band-gap structure. We find that the lowest band tends to minus infinity as the Robin parameter increases, whereas the rest of the bands remain positive ...


Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley 2018 National Institute of Standards and Technology

Transport Phenomena In Field Effect Transistors, Ryan M. Evans, Arvind Balijepalli, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.


Spatial Spread Of Defective Interfering Particles And Its Role In Suppressing Viral Load, Qasim Ali QA, Ruian Ke 2018 North Carolina State University at Raleigh

Spatial Spread Of Defective Interfering Particles And Its Role In Suppressing Viral Load, Qasim Ali Qa, Ruian Ke

Biology and Medicine Through Mathematics Conference

No abstract provided.


Dual-Norm Least-Squares Finite Element Methods For Hyperbolic Problems, Delyan Zhelev Kalchev 2018 University of Colorado, Boulder

Dual-Norm Least-Squares Finite Element Methods For Hyperbolic Problems, Delyan Zhelev Kalchev

Applied Mathematics Graduate Theses & Dissertations

Least-squares finite element discretizations of first-order hyperbolic partial differential equations (PDEs) are proposed and studied. Hyperbolic problems are notorious for possessing solutions with jump discontinuities, like contact discontinuities and shocks, and steep exponential layers. Furthermore, nonlinear equations can have rarefaction waves as solutions. All these contribute to the challenges in the numerical treatment of hyperbolic PDEs.

The approach here is to obtain appropriate least-squares formulations based on suitable minimization principles. Typically, such formulations can be reduced to one or more (e.g., by employing a Newton-type linearization procedure) quadratic minimization problems. Both theory and numerical results are presented.

A method ...


Properties And Convergence Of State-Based Laplacians, Kelsey Wells 2018 University of Nebraska - Lincoln

Properties And Convergence Of State-Based Laplacians, Kelsey Wells

Dissertations, Theses, and Student Research Papers in Mathematics

The classical Laplace operator is a vital tool in modeling many physical behaviors, such as elasticity, diffusion and fluid flow. Incorporated in the Laplace operator is the requirement of twice differentiability, which implies continuity that many physical processes lack. In this thesis we introduce a new nonlocal Laplace-type operator, that is capable of dealing with strong discontinuities. Motivated by the state-based peridynamic framework, this new nonlocal Laplacian exhibits double nonlocality through the use of iterated integral operators. The operator introduces additional degrees of flexibility that can allow better representation of physical phenomena at different scales and in materials with different ...


Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Montiforte 2018 The University of Southern Mississippi

Automatic Construction Of Scalable Time-Stepping Methods For Stiff Pdes, Vivian Montiforte

Master's Theses

Krylov Subspace Spectral (KSS) Methods have been demonstrated to be highly scalable time-stepping methods for stiff nonlinear PDEs. However, ensuring this scalability requires analytic computation of frequency-dependent quadrature nodes from the coefficients of the spatial differential operator. This thesis describes how this process can be automated for various classes of differential operators to facilitate public-domain software implementation.


Energy Calculations And Wave Equations, Ellen R. Hunter 2018 Missouri State University

Energy Calculations And Wave Equations, Ellen R. Hunter

MSU Graduate Theses

The focus of this thesis is to show how methods of Fourier analysis, in particular Parseval’s equality, can be used to provide explicit energy calculations for solutions of wave equations in one dimension. These calculations are discussed for simple examples and then extended to fit the general wave equation with Robin boundary conditions. Ideas from Sobolev space theory are used to provide justification of the method.


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