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Physical Sciences and Mathematics Commons™

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Mathematics

Missouri University of Science and Technology

2007

Articles 1 - 14 of 14

Full-Text Articles in Physical Sciences and Mathematics

Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang Sep 2007

Asymptotic Behavior Of The Global Attractors To The Boussinesq System For Rayleigh-Bénard Convection At Large Prandtl Number, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number. in particular, we show that the global attractors to the Boussinesq system for Rayleigh-Bénard convection converge to that of the infinite-Prandtl- number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite-Prandtl-number model for convection as a valid simplified model for convection at large Prandtl number even in the long-time regime. © 2006 Wiley Periodicals, Inc.

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Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jul 2007

Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation.

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Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang Jun 2007

Discrete Kato-Type Theorem On Inviscid Limit Of Navier-Stokes Flows, Wenfang Cheng, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

The inviscid limit of wall bounded viscous flows is one of the unanswered central questions in theoretical fluid dynamics. Here we present a somewhat surprising result related to numerical approximation of the problem. More precisely, we show that numerical solutions of the incompressible Navier-Stokes equations converge to the exact solution of the Euler equations at vanishing viscosity and vanishing mesh size provided that small scales of the order of U in the directions tangential to the boundary are not resolved in the scheme. Here is the kinematic viscosity of the fluid and U is the typical velocity taken to be …

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Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang Jun 2007

Note On The Emergence Of Large Scale Coherent Structure Under Small Scale Random Bombardments: The Discrete Case, Andrew Majda, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We continue our study on mathematical justification of the emergence of large-scale coherent structure in a two-dimensional fluid system under small scale random bombardments. We treat the case of small-scale random bombardments at discrete times which is different from our earlier work [Commun. Pure Appl. Math. 59, 467 (2006)], where we approximated the small-scale random kicks by a continuous in time random process. in the absence of geophysical effects, the large-scale structure emerging out of the small-scale random forcing is the same as the case of continuous in time forcing that we studied before. © 2007 American Institute of Physics.

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Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten Jun 2007

Balanced Proper Orthogonal Decomposition For Model Reduction Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we extend a method for reduced order model derivation for finite dimensional systems developed by Rowley to infinite dimensional systems. The method is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method is also applicable to nonlinear systems. The method is applied to a convection diffusion equation.

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Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner Mar 2007

Periodic Solutions Of Functional Dynamic Equations With Infinite Delay, Li Bi, Meng Fan, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this paper, sufficient criteria are established for the existence of periodic solutions of some functional dynamic equations with infinite delays on time scales, which generalize and incorporate as special cases many known results for differential equations and for difference equations when the time scale is the set of the real numbers or the integers, respectively. The approach is mainly based on the Krasnosel'skilatin small letter i with breve fixed point theorem, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in studying dynamic equations on time scales. This study shows …

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The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner Jan 2007

The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …

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Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner Jan 2007

Trench's Perturbation Theorem For Dynamic Equations, Stevo Stevic, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

We consider a nonoscillatory second-order linear dynamic equation on a time scale together with a linear perturbation of this equation and give conditions on the perturbation that guarantee that the perturbed equation is also nonoscillatory and has solutions that behave asymptotically like a recessive and dominant solutions of the unperturbed equation. As the theory of time scales unifies continuous and discrete analysis, our results contain as special cases results for corresponding differential and difference equations by William F. Trench.

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Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler Jan 2007

Differentiability With Respect To Parameters Of Weak Solutions Of Linear Parabolic Equations, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We consider the differentiability of weak solutions of linear parabolic equations with respect to parameters and initial data. under natural assumptions, it is shown that solutions possess as much differentiability with respect to the data as do the terms appearing in the equation. The derivatives are shown to satisfy the appropriate sensitivity equations. The theoretical results are illustrated with an example.

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Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner Jan 2007

Oscillation And Nonoscillation Of Forced Second Order Dynamic Equations, Christopher C. Tisdell, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

Oscillation and nonoscillation properties of second order Sturm-Liouville dynamic equations on time scales — for example, second order self-adjoint differential equations and second order Sturm-Liouville difference equations — have attracted much interest. Here we consider a given homogeneous equation and a corresponding equation with forcing term. We give new conditions implying that the latter equation inherits the oscillatory behavior of the homogeneous equation. We also give new conditions that introduce oscillation of the inhomogeneous equation while the homogeneous equation is nonoscillatory. Finally, we explain a gap in a result given in the literature for the continuous and the discrete case. …

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Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner Jan 2007

Oscillation Criteria For A Certain Class Of Second Order Emden-Fowler Dynamic Equations, Elvan Akin, S. H. Saker, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

By means of Riccati transformation techniques we establish some oscillation criteria for the second order Emden-Fowler dynamic equation on a time scale. Such equations contain the classical Emden-Fowler equation as well as their discrete counterparts. The classical oscillation results of Atkinson (in the superlinear case) and Belohorec (in the sublinear case) are extended in this paper to Emden-Fowler dynamic equations on any time scale.

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The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du Jan 2007

The Dynamics And Interaction Of Quantized Vortices In The Ginzburg-Landau-Schrödinger Equation, Yanzhi Zhang, Weizhu Bao, Qiang Du

Mathematics and Statistics Faculty Research & Creative Works

The dynamic laws of quantized vortex interactions in the Ginzburg-Landau-Schrödinger equation (GLSE) are analytically and numerically studied. A review of the reduced dynamic laws governing the motion of vortex centers in the GLSE is provided. The reduced dynamic laws are solved analytically for some special initial data. By directly simulating the GLSE with an efficient and accurate numerical method proposed recently in [Y. Zhang, W. Bao, and Q. Du, Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation, European J. Appl. Math., to appear], we can qualitatively and quantitatively compare quantized vortex interaction patterns of the GLSE with those from the …

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On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le Jan 2007

On A Sub-Supersolution Method For The Prescribed Mean Curvature Problem, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational inequality and propose appropriate concepts of sub- and supersolutions for such inequality. Existence and enclosure results for solutions and extremal solutions between sub- and supersolutions are established.

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Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain Jan 2007

Effective Use Of Process Capability Indices For Supplier Management, Elizabeth A. Cudney, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Process capability indices were originally invented to enable an organization to make economically sound decisions for process management. Process capability is a comparison of the voice of the process with the voice of the customer. Current practice is to use Cp and Cpk regardless of the validity of the underlying assumptions necessary for their use. Even if all necessary assumptions are satisfied, important problems can be missed if these indices are the sole process evaluation examined. Customer-supplier axioms are introduced to motivate more useful process evaluations and foster long-term harmonious relationships. This paper explores the alternative capability indices Cpm, Cpmk, …

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