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Mathematics

Mathematics and Statistics Faculty Research & Creative Works

2023

Articles 1 - 18 of 18

Full-Text Articles in Physical Sciences and Mathematics

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions, David Lund, Xiaoming He, Daoru Frank Han Jul 2023

Kinetic Particle Simulations Of Plasma Charging At Lunar Craters Under Severe Conditions, David Lund, Xiaoming He, Daoru Frank Han

Mathematics and Statistics Faculty Research & Creative Works

This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the regolith layer thickness and permittivity as well as the lunar lander module in the simulation domain, resolving a nontrivial surface terrain or lunar lander configuration. Simulations were carried out to study the lunar surface and lunar lander module charging near craters at the lunar terminator region under mean and severe plasma environments. …

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Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya Jun 2023

Uniqueness For An Inverse Quantum-Dirac Problem With Given Weyl Function, Martin Bohner, Ayça Çetinkaya

Mathematics and Statistics Faculty Research & Creative Works

In this work, we consider a boundary value problem for a q-Dirac equation. We prove orthogonality of the eigenfunctions, realness of the eigenvalues, and we study asymptotic formulas of the eigenfunctions. We show that the eigenfunctions form a complete system, we obtain the expansion formula with respect to the eigenfunctions, and we derive Parseval's equality. We construct the Weyl solution and the Weyl function. We prove a uniqueness theorem for the solution of the inverse problem with respect to the Weyl function.

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Vallée-Poussin Theorem For Equations With Caputo Fractional Derivative, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava Jun 2023

Vallée-Poussin Theorem For Equations With Caputo Fractional Derivative, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the functional differential equation (CDaα+x)(t) + mΣi=0 (Tix(i))(t) = f(t); t 2 [a; b]; with Caputo fractional derivative CDaα+ is studied. The operators Ti act from the space of continuous to the space of essentially bounded functions. They can be operators with deviations (delayed and advanced), integral operators and their various linear combinations and superpositions. Such equations could appear in various applications and in the study of systems of, for example, two fractional differential equations, when one of the components can be …

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Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata Jun 2023

Asymptotic Stability Of Solitary Waves For The 1d Nls With An Attractive Delta Potential, Satoshi Masaki, Jason Murphy, Jun Ichi Segata

Mathematics and Statistics Faculty Research & Creative Works

We Consider the One-Dimensional Nonlinear Schrödinger Equation with an Attractive Delta Potential and Mass-Supercritical Nonlinearity. This Equation Admits a One-Parameter Family of Solitary Wave Solutions in Both the Focusing and Defocusing Cases. We Establish Asymptotic Stability for All Solitary Waves Satisfying a Suitable Spectral Condition, Namely, that the Linearized Operator Around the Solitary Wave Has a Two-Dimensional Generalized Kernel and No Other Eigenvalues or Resonances. in Particular, We Extend Our Previous Result [35] Beyond the Regime of Small Solitary Waves and Extend the Results of [19, 29] from Orbital to Asymptotic Stability for a Suitable Family of Solitary Waves.

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Modeling And A Domain Decomposition Method With Finite Element Discretization For Coupled Dual-Porosity Flow And Navier–Stokes Flow, Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He Jun 2023

Modeling And A Domain Decomposition Method With Finite Element Discretization For Coupled Dual-Porosity Flow And Navier–Stokes Flow, Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We First Propose and Analyze a Steady State Dual-Porosity-Navier–Stokes Model, Which Describes Both Dual-Porosity Flow and Free Flow (Governed by Navier–Stokes Equation) Coupled through Four Interface Conditions, Including the Beavers–Joseph Interface Condition. Then We Propose a Domain Decomposition Method for Efficiently Solving Such a Large Complex System. Robin Boundary Conditions Are Used to Decouple the Dual-Porosity Equations from the Navier–Stokes Equations in the Coupled System. based on the Two Decoupled Sub-Problems, a Parallel Robin-Robin Domain Decomposition Method is Constructed and Then Discretized by Finite Elements. We Analyze the Convergence of the Domain Decomposition Method with the Finite …

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Fractal Newton Methods, Ali Akgül, David E. Grow May 2023

Fractal Newton Methods, Ali Akgül, David E. Grow

Mathematics and Statistics Faculty Research & Creative Works

We introduce fractal Newton methods for solving (Formula presented.) that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

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An Integer Garch Model For A Poisson Process With Time-Varying Zero-Inflation, Isuru Panduka Ratnayake, V. A. Samaranayake May 2023

An Integer Garch Model For A Poisson Process With Time-Varying Zero-Inflation, Isuru Panduka Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

A serially dependent Poisson process with time-varying zero-inflation is proposed. Such formulations have the potential to model count data time series arising from phenomena such as infectious diseases that ebb and flow over time. The model assumes that the intensity of the Poisson process evolves according to a generalized autoregressive conditional heteroscedastic (GARCH) formulation and allows the zero-inflation parameter to vary over time and be governed by a deterministic function or by an exogenous variable. Both the expectation maximization (EM) and the maximum likelihood estimation (MLE) approaches are presented as possible estimation methods. A simulation study shows that both parameter …

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Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin May 2023

Fully Decoupled Energy-Stable Numerical Schemes For Two-Phase Coupled Porous Media And Free Flow With Different Densities And Viscosities, Yali Gao, Xiaoming He, Tao Lin, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in matrix, a Cahn-illiard-Navier-Stokes system with different densities/viscosities describing the free fluid in conduit, and seven interface conditions coupling the flows in the matrix and the conduit. Based on the separate Cahn-Hilliard equations in the porous media region and the free flow region, a weak formulation is proposed to incorporate the …

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A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler Apr 2023

A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

In a Recent Work (Koc Et Al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the Authors Showed that Including Difference Quotients (DQs) is Necessary in Order to Prove Optimal Pointwise in Time Error Bounds for Proper Orthogonal Decomposition (POD) Reduced Order Models of the Heat Equation. in This Work, We Introduce a New Approach to Including DQs in the POD Procedure. Instead of Computing the POD Modes using All of the Snapshot Data and DQs, We Only Use the First Snapshot Along with All of the DQs and Special POD Weights. We Show that This Approach Retains All of the …

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Rank-Based Inference For Survey Sampling Data, Akim Adekpedjou, Huybrechts F. Bindele Apr 2023

Rank-Based Inference For Survey Sampling Data, Akim Adekpedjou, Huybrechts F. Bindele

Mathematics and Statistics Faculty Research & Creative Works

For regression models where data are obtained from sampling surveies, the statistical analysis is often based on approaches that are either non-robust or inefficient. The handling of survey data requires more appropriate techniques, as the classical methods usually result in biased and inefficient estimates of the underlying model parameters. This article is concerned with the development of a new approach of obtaining robust and efficient estimates of regression model parameters when dealing with survey sampling data. Asymptotic properties of such estimators are established under mild regularity conditions. To demonstrate the performance of the proposed method, Monte Carlo simulation experiments are …

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Dynamic Equations, Control Problems On Time Scales, And Chaotic Systems, Martin Bohner Mar 2023

Dynamic Equations, Control Problems On Time Scales, And Chaotic Systems, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The unification of integral and differential calculus with the calculus of finite differences has been rendered possible by providing a formal structure to study hybrid discrete-continuous dynamical systems besides offering applications in diverse fields that require simultaneous modeling of discrete and continuous data concerning dynamic equations on time scales. Therefore, the theory of time scales provides a unification between the calculus of the theory of difference equations with the theory of differential equations. In addition, it has become possible to examine diverse application problems more precisely by the use of dynamical systems on time scales whose calculus is made up …

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Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara Feb 2023

Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara

Mathematics and Statistics Faculty Research & Creative Works

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.

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Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani Jan 2023

Three Solutions For Discrete Anisotropic Kirchhoff-Type Problems, Martin Bohner, Giuseppe Caristi, Ahmad Ghobadi, Shapour Heidarkhani

Mathematics and Statistics Faculty Research & Creative Works

In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.

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Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong Jan 2023

Inequalities For Interval-Valued Riemann Diamond-Alpha Integrals, Martin Bohner, Linh Nguyen, Baruch Schneider, Tri Truong

Mathematics and Statistics Faculty Research & Creative Works

We propose the concept of Riemann diamond-alpha integrals for time scales interval-valued functions. We first give the definition and some properties of the interval Riemann diamond-alpha integral that are naturally investigated as an extension of interval Riemann nabla and delta integrals. With the help of the interval Riemann diamond-alpha integral, we present interval variants of Jensen inequalities for convex and concave interval-valued functions on an arbitrary time scale. Moreover, diamond alpha Hölder's and Minkowski's interval inequalities are proved. Also, several numerical examples are provided in order to illustrate our main results.

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Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská Jan 2023

Oscillation Of Second-Order Half-Linear Neutral Noncanonical Dynamic Equations, Martin Bohner, Hassan El-Morshedy, Said Grace, Irena Jadlovská

Mathematics and Statistics Faculty Research & Creative Works

In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations.

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Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He Jan 2023

Trilinear Immersed-Finite-Element Method For Three-Dimensional Anisotropic Interface Problems In Plasma Thrusters, Yajie Han, Guangqing Xia, Chang Lu, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. …

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The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao Jan 2023

The Generalized Lyapunov Function As Ao’S Potential Function: Existence In Dimensions 1 And 2, Haoyu Wang, Wenqing Hu, Xiaoliang Gan, Ping Ao

Mathematics and Statistics Faculty Research & Creative Works

By using Ao's decomposition for stochastic dynamical systems, a new notion of potential function has been introduced by Ao and his collabora-tors recently. We show that this potential function agrees with the generalized Lyapunov function of the deterministic part of the stochastic dynamical sys-tem. We further prove the existence of Ao's potential function in dimensions 1 and 2 via the solution theory of first-order partial differential equations. Our framework reveals the equivalence between Ao's potential function and Lyapunov function, the latter being one of the most significant central notions in dynamical systems. Using this equivalence, our existence proof can also …

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Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang Jan 2023

Second Order, Unconditionally Stable, Linear Ensemble Algorithms For The Magnetohydrodynamics Equations, John Carter, Daozhi Han, Nan Jiang

Mathematics and Statistics Faculty Research & Creative Works

We Propose Two Unconditionally Stable, Linear Ensemble Algorithms with Pre-Computable Shared Coefficient Matrices Across Different Realizations for the Magnetohydrodynamics Equations. the Viscous Terms Are Treated by a Standard Perturbative Discretization. the Nonlinear Terms Are Discretized Fully Explicitly within the Framework of the Generalized Positive Auxiliary Variable Approach (GPAV). Artificial Viscosity Stabilization that Modifies the Kinetic Energy is Introduced to Improve Accuracy of the GPAV Ensemble Methods. Numerical Results Are Presented to Demonstrate the Accuracy and Robustness of the Ensemble Algorithms.

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