Mathematics Commons^™

Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …

Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Hypoelliptic Multiscale Langevin Diffusions: Large Deviations, Invariant Measures And Small Mass Asymptotics, Wenqing Hu, Konstantinos Spiliopoulosï

Mathematics and Statistics Faculty Research & Creative Works

We consider a general class of hypoelliptic Langevin diffusions and study two related questions. The first question is large deviations for hypoelliptic multiscale diffusions as the noise and the scale separation parameter go to zero. The second question is small mass asymptotics of (a) the invariant measure corresponding to the hypoelliptic Langevin operator and of (b) related hypoelliptic Poisson equations. The invariant measure corresponding to the hypoelliptic problem and appropriate hypoelliptic Poisson equations enter the large deviations rate function due to the multiscale effects. Based on the small mass asymptotics we derive that the large deviations behavior of the multiscale …

Oscillation Criteria For Third-Order Nonlinear Functional Difference Equations With Damping, Martin Bohner, C. Dharuman, R. Srinivasan, Ethiraju Thandapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

Stationary Acceleration Of Frenet Curves, Nemat Abazari, Martin Bohner, Ilgin Sager, Yusuf Yayli

Mathematics and Statistics Faculty Research & Creative Works

In this paper, the stationary acceleration of the spherical general helix in a 3-dimensional Lie group is studied by using a bi-invariant metric. The relationship between the Frenet elements of the stationary acceleration curve in 4-dimensional Euclidean space and the intrinsic Frenet elements of the Lie group is outlined. As a consequence, the corresponding curvature and torsion of these curves are computed. In Minkowski space, for the curves on a timelike surface to have a stationary acceleration, a necessary and sufficient condition is refined.

Itô'S Formula, The Stochastic Exponential, And Change Of Measure On General Time Scales, Wenqing Hu

Mathematics and Statistics Faculty Research & Creative Works

We provide an Itô formula for stochastic dynamical equation on general time scales. Based on this Itô's formula we give a closed-form expression for stochastic exponential on general time scales. We then demonstrate Girsanov's change of measure formula in the case of general time scales. Our result is being applied to a Brownian motion on the quantum time scale (𝑞-time scale).

Founders, Feminists, And A Fascist -- Some Notable Women In The Missouri Section Of The Maa, Leon M. Hall

Mathematics and Statistics Faculty Research & Creative Works

In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them, both …

Zero-Dimensional Spaces And Their Inverse Limits, Sahika Sahan

Doctoral Dissertations

"In this dissertation we investigate zero-dimensional compact metric spaces and their inverse limits. We construct an uncountable family of zero-dimensional compact metric spaces homeomorphic to their Cartesian squares. It is known that the inverse limit on [0,1] with an upper semi-continuous function with a connected graph has either one or infinitely many points. We show that this result cannot be generalized to the inverse limits on simple triods or simple closed curves. In addition to that, we introduce a class of zero-dimensional spaces that can be obtained as the inverse limits of arcs. We complete by answering a problem by …

Numerical Investigation On Nonlocal Problems With The Fractional Laplacian, Siwei Duo

Doctoral Dissertations

"Nonlocal models have recently become a powerful tool for studying complex systems with long-range interactions or memory effects, which cannot be described properly by the traditional differential equations. So far, different nonlocal (or fractional differential) models have been proposed, among which models with the fractional Laplacian have been well applied. The fractional Laplacian (-Δ)^α/2 represents the infinitesimal generator of a symmetric α-stable Lévy process. It has been used to describe anomalous diffusion, turbulent flows, stochastic dynamics, finance, and many other phenomena. However, the nonlocality of the fractional Laplacian introduces considerable challenges in its mathematical modeling, numerical simulations, and mathematical …

Programming Problems On Time Scales: Theory And Computation, Rasheed Basheer Al-Salih

Doctoral Dissertations

"In this dissertation, novel formulations for several classes of programming problems are derived and proved using the time scales technique. The new formulations unify the discrete and continuous programming models and extend them to other cases "in between." Moreover, the new formulations yield the exact optimal solution for the programming problems on arbitrary isolated time scales, which solve an important open problem. Throughout this dissertation, six distinct classes of programming problems are presented as follows. First, the primal as well as the dual time scales linear programming models on arbitrary time scales are formulated. Second, separated linear programming primal and …

A Harmonic M-Factorial Function And Applications, Reginald Alfred Brigham Ii

Doctoral Dissertations

"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.

Balanced Truncation Model Reduction Of Nonlinear Cable-Mass Pde System, Madhuka Hareena Lochana Weerasinghe

Doctoral Dissertations

We consider model order reduction of a cable-mass system modeled by a one dimensional wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at the left boundary of the cable. A mass-spring model at the right end of the cable includes a nonlinear stiffening force. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the right boundary. We believe the nonlinear cable-mass …

Bootstrap-Based Confidence Intervals In Partially Accelerated Life Testing, Ahmed Mohamed Eshebli

Doctoral Dissertations

"Accelerated life testing (ALT) is utilized to estimate the underlying failure distribution and related parameters of interest in situations where the components under study are designed for long life and therefore will not yield failure data within a reasonable test period. In ALT, life testing is carried out under two or more higher than normal stress levels, with the resulting acceleration of the failure process yielding a sufficient amount of un-censored life-span data within a practical test duration. Usually one (or more) parameters of the life distribution is linked to the stress level through a suitably selected model based on …

Local Holomorphic Extension Of Cauchy Riemann Functions, Brijitta Antony

Doctoral Dissertations

"The purpose of this dissertation is to give an analytic disc approach to the CR extension problem. Analytic discs give a very convenient tool for holomorphic extension of CR functions. The type function is introduced and showed how these type functions have direct application to important questions about CR extension. In this dissertation the CR extension theorem is proved for a rigid hypersurface M in C² given by y = (Re ω)^m(Im ω)ⁿ where m and n are non-negative integers. If the type function is identically zero at the origin, then there is no CR extension. …

T-Closed Sets, Multivalued Inverse Limits, And Hereditarily Irreducible Maps, Hussam Abobaker

Doctoral Dissertations

"This dissertation consists of three subjects: T-closed sets, inverse limits with multivalued functions, and hereditarily irreducible maps.

For a subset A of a continuum X define T(A) = X \ {x ∈ X : there exists a subcontinuum K of X such that x ∈ int_xX(K) ⊂ K ⊂ X \ A}. This function was defined by F. Burton Jones and extensively investigated in the book [20] by Sergio Macias. A subset A of a continuum X is called T-closed set if T(A) = A. A characterization of T-closed set is given using generalized …