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Articles 1 - 13 of 13
Full-Text Articles in Mathematics
A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang
A Uniformly Dissipative Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang (Wendy) Cheng, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
The purpose of this short communication is to announce that a class of numerical schemes, uniformly dissipative approximations, which uniformly preserve the dissipativity of the continuous infinite dimensional dissipative complex (chaotic) systems possess desirable properties in terms of approximating stationary statistics properties. in particular, the stationary statistical properties of these uniformly dissipative schemes converge to those of the continuous system at vanishing mesh size. the idea is illustrated on the infinite Prandtl number model for convection and semi-discretization in time, although the general strategy works for a broad class of dissipative complex systems and fully discretized approximations. as far as …
A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang
A Semi-Implicit Scheme For Stationary Statistical Properties Of The Infinite Prandtl Number Model, Wenfang Cheng, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We propose a semisecret in time semi-implicit numerical scheme for the infinite Prandtl model for convection. Besides the usual finite time convergence, this scheme enjoys the additional highly desirable feature that the stationary statistical properties of the scheme converge to those of the infinite Prandtl number model at vanishing time stop. One of the key characteristics of the scheme is that it preserves the dissipativity of the infinite Prandtl number model uniformly in terms of the time stop. So far as wo know, this is the first rigorous result on convergence of stationary statistical properties of numerical schemes for infinite …
Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik
Confluent Mappings And Arc Kelley Continua, W. J. Charatonik, Janusz R. Prajs, J. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
A Kelley continuum X, also called a continuum with the property of Kelley, such that, for each p X, each subcontinuum K containing p is approximated by arc-wise connected continua containing p, is called an arc Kelley continuum. A continuum homeomorphic to the inverse limit of locally connected continua with confluent bonding maps is said to be confluently LC-representable. The main subject of the paper is a study of deep connections between the arc Kelley continua and confluent mappings. It is shown that if a continuum X admits, for each ε > 0, a confluent ε-mapping onto a(n) (arc) Kelley continuum, …
The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten
The Detection Of Unsteady Flow Separation With Bioinspired Hair-Cell Sensors, Benjamin T. Dickinson, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
Biologists hypothesize that thousands of micro-scale hairs found on bat wings function as a network of air-flow sensors as part of a biological feedback flow control loop. In this work, we investigate hair-cell sensors as a means of detecting flow features in an unsteady separating flow over a cylinder. Individual hair-cell sensors were modeled using an Euler-Bernoulli beam equation forced by the fluid flow. When multiple sensor simulations are combined into an array of hair-cells, the response is shown to detect the onset and span of flow reversal, the upstream movement of the point of zero wall shear-stress, and the …
Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler
Approximate Low Rank Solutions Of Lyapunov Equations Via Proper Orthogonal Decomposition, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.
Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang
Stationary Statistical Properties Of Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number to infinity. We study asymptotic behavior of stationary statistical solutions, or in-variant measures, to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the invariant measures of the Boussinesq system for Rayleigh-Bénard convection converge …
Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik
Property Of Kelley For The Cartesian Products And Hyperspaces, W. J. Charatonik, J. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.
On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner
On The Asymptotic Integration Of Nonlinear Dynamic Equations, Elvan Akin, Smail Djebali, Toufik Moussaoui, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis I: A Motivating Problem, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new "mostly linear" theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity …
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler
Transition To Turbulence, Small Disturbances, And Sensitivity Analysis Ii: The Navier-Stokes Equations, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
Recent research has shown that small disturbances in the linearized Navier-Stokes equations cause large energy growth in solutions. Although many researchers believe that this interaction triggers transition to turbulence in flow systems, the role of the nonlinearity in this process has not been thoroughly investigated. This paper is the second of a two part work in which sensitivity analysis is used to study the effects of small disturbances on the transition process. In the first part, sensitivity analysis was used to predict the effects of a small disturbance on solutions of a motivating problem, a highly sensitive one dimensional Burgers' …
Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner
Iterated Oscillation Criteria For Delay Dynamic Equations Of First Order, B. Karpuz, O. Öcalan, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We obtain new sufficient conditions for the oscillation of all solutions of first-order delay dynamic equations on arbitrary time scales, hence combining and extending results for corresponding differential and difference equations. Examples, some of which coincide with well-known results on particular time scales, are provided to illustrate the applicability of our results.
Estimating Bounds For Nonidentifiale Parameters Using Potential Outcomes, Thidaporn Supapakorn
Estimating Bounds For Nonidentifiale Parameters Using Potential Outcomes, Thidaporn Supapakorn
Doctoral Dissertations
"Conclusions from studies vary regarding the association of weight loss among obese people and measures of health and/or mortality. Total weight loss for individuals in a population may be a combination of intentional weight loss (IWL) and unintentional weight loss (UWL). Among people who have no intention to lose weight, the total weight loss observed is UWL. Among people who have intention to lose weight, the total weight loss is assumed to be UWL and IWL. Note that total weight loss among subjects intending to lose weight is observable but IWL itself is not and, therefore, the latent variable that …
Inverse Limits Of Permutation Maps, Robbie A. Beane
Inverse Limits Of Permutation Maps, Robbie A. Beane
Doctoral Dissertations
"In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to …