Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, 2022 Nova Southeastern University
Spatial Patterning Of Predator-Prey Distributions Arising From Prey Defense, Evan C. Haskell, Jonathan Bell
Biology and Medicine Through Mathematics Conference
No abstract provided.
Genetically Explicit Model May Explain Multigenerational Control Of Emergent Turing Patterns In Hybrid Mimulus, 2022 William & Mary
Genetically Explicit Model May Explain Multigenerational Control Of Emergent Turing Patterns In Hybrid Mimulus, Emily Simmons
Biology and Medicine Through Mathematics Conference
No abstract provided.
Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, 2022 University of California, Merced
Mathematical Modeling Of Brain Cancer Growth Using A Level-Set Method, Gbocho M. Terasaki
Biology and Medicine Through Mathematics Conference
No abstract provided.
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, 2022 Clemson University
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, Evan Butterworth
All Theses
An energy-conserving numerical scheme is developed for the multilayer shallow water equations (SWE’s). The scheme is derived through the Hamiltonian formulation of the inviscid shallow water flows related to the vorticity-divergence variables. Through the employment of the skew-symmetric Poisson bracket, the continuous system for the multilayer SWE’s is shown to preserve an infinite number of quantities, most notably the energy and enstrophy. An energy-preserving numerical scheme is then developed through the careful discretization of the Hamiltonian and the Poisson bracket, ensuring the skew-symmetry of the latter. This serves as the groundwork for developing additional schemes that preserve other conservation properties …
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, 2022 University of Arkansas, Fayetteville
Finite Dimensional Approximation And Pin(2)-Equivariant Property For Rarita-Schwinger-Seiberg-Witten Equations, Minh Lam Nguyen
Graduate Theses and Dissertations
The Rarita-Schwinger operator Q was initially proposed in the 1941 paper by Rarita and Schwinger to study wave functions of particles of spin 3/2, and there is a vast amount of physics literature on its properties. Roughly speaking, 3/2−spinors are spinor-valued 1-forms that also happen to be in the kernel of the Clifford multiplication. Let X be a simply connected Riemannian spin 4−manifold. Associated to a fixed spin structure on X, we define a Seiberg-Witten-like system of non-linear PDEs using Q and the Hodge-Dirac operator d∗ + d+ after suitable gauge-fixing. The moduli space of solutions M contains (3/2-spinors, purely …
Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, 2022 University of Tennessee, Knoxville
Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo
Doctoral Dissertations
This dissertation consists of three main parts with each part focusing on numerical approximations of the stochastic Stokes and Navier-Stokes equations.
Part One concerns the mixed finite element methods and Chorin projection methods for solving the stochastic Stokes equations with general multiplicative noise. We propose a modified mixed finite element method for solving the Stokes equations and show that the numerical solutions converge optimally to the PDE solutions. The convergence is under energy norms (strong convergence) for the velocity and in a time-averaged norm (weak convergence) for the pressure. In addition, after establishing the error estimates in second moment, high …
A Weak Fractional Calculus Theory And Numerical Methods For Fractional Differential Equations, 2022 University of Tennessee, Knoxville
A Weak Fractional Calculus Theory And Numerical Methods For Fractional Differential Equations, Mitchell D. Sutton
Doctoral Dissertations
This dissertation is comprised of four integral parts. The first part comprises a self-contained new theory of weak fractional differential calculus in one-dimension. The crux of this new theory is the introduction of a weak fractional derivative notion which is a natural generalization of integer order weak derivatives; it also helps to unify multiple existing fractional derivative definitions.
The second part of this work presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed notion of weak fractional derivatives, which are natural generalizations of the …
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., 2022 Ohio Northern University
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., Quinnlan Paul Aiken
ONU Student Research Colloquium
Approximation of the functions which are the solutions of complex or difficult problems is a worthwhile endeavor. This has resulted in many ways to effectively approximate the solution of the partial differential equations. One such way to approximate the solution of the partial differential equation is Oscillatory radial basis function method. This method can approximate the solution of the partial differential equation well however relies heavily on a “shape parameter” to achieve acceptable error. Choosing this parameter was traditionally done through a trial-and-error method. Selecting shape parameters in a more analytical way has been desired. One such method is the …
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, 2022 Augustana College
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
Rose-Hulman Undergraduate Mathematics Journal
While the well-researched Finite Difference Method (FDM) discretizes every independent variable into algebraic equations, Method of Lines discretizes all but one dimension, leaving an Ordinary Differential Equation (ODE) in the remaining dimension. That way, ODE's numerical methods can be applied to solve Partial Differential Equations (PDEs). In this project, Linear Multistep Methods and Method of Lines are used to numerically solve the heat equation. Specifically, the explicit Adams-Bashforth method and the implicit Backward Differentiation Formulas are implemented as Alternative Finite Difference Schemes. We also examine the consistency of these schemes.
The Gelfand Problem For The Infinity Laplacian, 2022 Wayne State University
The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang
Mathematics Faculty Research Publications
We study the asymptotic behavior as p → ∞ of the Gelfand problem
−Δpu = λeu in Ω ⊂ Rn, u = 0 on ∂Ω.
Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of
min{|∇u|−Λeu, −Δ∞u} = 0 in Ω, u = 0 on ∂Ω.
We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.
Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, 2022 University of Jyväskylä
Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi
Mathematics Faculty Research Publications
We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.
A Meshless Approach To Computational Pharmacokinetics, 2022 Embry-Riddle Aeronautical University
A Meshless Approach To Computational Pharmacokinetics, Anthony Matthew Khoury
Doctoral Dissertations and Master's Theses
The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless …
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, 2022 Old Dominion University
A Spatially And Temporally Second Order Method For Solving Parabolic Interface Problems, Kumudu Gamage, Yan Peng
College of Sciences Posters
Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.
Numerical Study Of Highly Efficient Centrifugal Cyclones, 2022 Ferghana Polytechnic Institute
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Scientific-technical journal
Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …
Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, 2022 University of Nebraska - Lincoln
Existence And Uniqueness Of Minimizers For A Nonlocal Variational Problem, Michael Pieper
Honors Theses
Nonlocal modeling is a rapidly growing field, with a vast array of applications and connections to questions in pure math. One goal of this work is to present an approachable introduction to the field and an invitation to the reader to explore it more deeply. In particular, we explore connections between nonlocal operators and classical problems in the calculus of variations. Using a well-known approach, known simply as The Direct Method, we establish well-posedness for a class of variational problems involving a nonlocal first-order differential operator. Some simple numerical experiments demonstrate the behavior of these problems for specific choices of …
Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, 2022 CUNY City College
Towards Simulation Of Complex Ocean Flows: Analysis And Algorithm For Computation Of Coupled Partial Differential Equations, Wenbin Dong
Dissertations and Theses
The hybrid CFD models which usually consist of 2 sub-models, develop our capability to simulate many emerging problems with multiphysics and multiscale flows, especially for the coastal ocean flows interacted with local phenomena of interest. For most cases, the sub-models are connected with direct interpolation which is easy and workable. It becomes urgently needed to investigate the inner mechanism of such model integration as this simple method does not work well if the two sub-models are different in governing equations, numerical methods, and computational grids. Also, it can not treat complex flow structures as well as the balance in mass …
Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, 2022 University of Kentucky
Inverse Boundary Value Problems For Polyharmonic Operators With Non-Smooth Coefficients, Landon Gauthier
Theses and Dissertations--Mathematics
We consider inverse boundary problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity required to establish uniqueness. The proof relies on an averaging technique introduced by Haberman and Tataru for the study of an inverse boundary value problem for a second order operator.
(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, 2021 Imam Khomeini International University
(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed …
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, 2021 Bangladesh University of Engineering and Technology
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs …
(R1494) Approximate Solutions Of The Telegraph Equation, 2021 Texas Southern University
(R1494) Approximate Solutions Of The Telegraph Equation, Ilija Jegdić
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the initial boundary value problems for the linear telegraph equation in one and two space dimensions are considered. To find approximate solutions, a recently proposed optimization-free approach that utilizes artificial neural networks with one hidden layer is used, in which the connecting weights from the input layer to the hidden layer are chosen randomly and the weights from the hidden layer to the output layer are found by solving a system of linear equations. One of the advantages of this method, in comparison to the usual discretization methods for the two-dimensional linear telegraph equation, is that this …