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Articles 211 - 240 of 434
Full-Text Articles in Statistics and Probability
Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno
Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno
Mathematics and Statistics Faculty Research & Creative Works
This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …
Model Reduction Of Linear Pde Systems: A Continuous Time Eigensystem Realization Algorithm, John R. Singler
Model Reduction Of Linear Pde Systems: A Continuous Time Eigensystem Realization Algorithm, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
The Eigensystem Realization Algorithm (ERA) is a well known system identification and model reduction algorithm for discrete time systems. Recently, Ma, Ahuja, and Rowley (Theoret. Comput. Fluid Dyn. 25(1) : 233-247, 2011) showed that ERA is theoretically equivalent to the balanced POD algorithm for model reduction of discrete time systems. We propose an ERA for model reduction of continuous time linear partial differential equation systems. The algorithm differs from other existing approaches as it is based on a direct approximation of the Hankel integral operator of the system. We show that the algorithm produces accurate balanced reduced order models for …
Mathematical Modeling And Simulation Of Biologically Inspired Hair Receptor Arrays In Laminar Unsteady Flow Separation, John R. Singler, Belinda A. Batten, Benjamin T. Dickinson
Mathematical Modeling And Simulation Of Biologically Inspired Hair Receptor Arrays In Laminar Unsteady Flow Separation, John R. Singler, Belinda A. Batten, Benjamin T. Dickinson
Mathematics and Statistics Faculty Research & Creative Works
Bats possess arrays of distributed flow-sensitive hair-like mechanoreceptors on their dorsal and ventral wing surfaces. Bat wing hair receptors are known to play a significant role in flight maneuverability and are directionally most sensitive to reversed flow over the wing. in this work, we consider the mechanics of flexible hair-like structures for the time accurate detection and visualization of hydrodynamic images associated with unsteady near surface flow phenomena. a nonlinear viscoelastic model of a hair-like structure coupled to an unsteady nonuniform flow is proposed. Writing the hair model in nondimensional form, we identify five dimensionless groups that govern hair behavior. …
A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise
A Linear Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Sidafa Conde, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
We present a linear numerical scheme for a model of epitaxial thin film growth without slope selection. the PDE, which is a nonlinear, fourth-order parabolic equation, is the L2 gradient flow of the energy ∫Ω(-1/2 ln(1 + |ø|2) + ε2 2 |Ø(x)|2) dx. the idea of convex-concave decomposition of the energy functional is applied, which results in a numerical scheme that is unconditionally energy stable, i.e., energy dissipative. the particular decomposition used here places the nonlinear term in the concave part of the energy, in contrast to a previous convexity splitting scheme. as a result, the numerical scheme is fully …
Productivity Formulae Of An Infinite-Conductivity Hydraulically Fractured Well Producing At Constant Wellbore Pressure Based On Numerical Solutions Of A Weakly Singular Integral Equation Of The First Kind, Chaolang Hu, Jing Lu, Xiaoming He
Productivity Formulae Of An Infinite-Conductivity Hydraulically Fractured Well Producing At Constant Wellbore Pressure Based On Numerical Solutions Of A Weakly Singular Integral Equation Of The First Kind, Chaolang Hu, Jing Lu, Xiaoming He
Mathematics and Statistics Faculty Research & Creative Works
In order to increase productivity, it is important to study the performance of a hydraulically fractured well producing at constant wellbore pressure. This paper constructs a new productivity formula, which is obtained by solving a weakly singular integral equation of the first kind, for an infinite-conductivity hydraulically fractured well producing at constant pressure. And the two key components of this paper are a weakly singular integral equation of the first kind and a steady-state productivity formula. A new midrectangle algorithm and a Galerkin method are presented in order to solve the weakly singular integral equation. The numerical results of these …
Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence
Almost Oscillatory Three Dimensional Dynamic Systems, Elvan Akin, Zuzana Dosla, Bonita Lawrence
Mathematics and Statistics Faculty Research & Creative Works
In this article, we investigate oscillation and asymptotic properties for 3D systems of dynamic equations. We show the role of nonlinearities and we apply our results to the adjoint dynamic systems.
Absolute Differentiation In Metric Spaces, W. J. Charatonik, Matt Insall
Absolute Differentiation In Metric Spaces, W. J. Charatonik, Matt Insall
Mathematics and Statistics Faculty Research & Creative Works
In this article, we introduce a new notion of (strong) absolute derivative, for functions derived between metric spaces, and we investigate various properties and uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure.
Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan
Equivalent Circuit Model Of Coaxial Probes For Patch Antennas, Y. S. Hu, Yanzhi Zhang, Jun Fan
Mathematics and Statistics Faculty Research & Creative Works
An equivalent circuit model of coaxial probes is derived directly from the intrinsic via circuit model. as all the higher-order evanescent modes have been included analytically in the parasitic circuit elements, only the propagating mode needs to be considered by the simplest uniform-current model of a coaxial probe in numerical solvers such as -nite element method (FEM) or -nite divergence time domain (FDTD). This avoids dense meshes or sub-gridding techniques and greatly reduces the computational efforts for accurate calculation of the probe input impedance. the derived equivalent circuit model and the new feeding technique have been validated by both analytical …
Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Integral Inequalities On Time Scales Via The Theory Of Isotonic Linear Functionals, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić
Mathematics and Statistics Faculty Research & Creative Works
We apply the theory of isotonic linear functionals to derive a series of known inequalities, extensions of known inequalities, and new inequalities in the theory of dynamic equations on time scales. © 2011 Matloob Anwar et al.
Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang
Analysis And Finite Element Approximation Of A Coupled, Continuum Pipe-Flow/Darcy Model For Flow In Porous Media With Embedded Conduits, Yanzhao Cao, Max Gunzburger, Fei Hua, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider the continuum Darcy/pipe flow model for flows in a porous matrix containing embedded conduits; such coupled flows are present in, e.g., karst aquifers. the mathematical well-posedness of the coupled problem as well as convergence rates of finite element approximation are established in the two-dimensional case. Computational results are also provided. © 2010 Wiley Periodicals, Inc.
A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang
A Parallel Robin-Robin Domain Decomposition Method For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Fei Hua, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We propose a new parallel Robin-Robin domain decomposition method for the coupled Stokes-Darcy system with Beavers-Joseph-Saffman-Jones interface boundary condition. in particular, we prove that, with an appropriate choice of parameters, the scheme converges geometrically independent of the mesh size. © 2011 Society for Industrial and Applied Mathematics.
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le
A Range And Existence Theorem For Pseudomonotone Perturbations Of Maximal Monotone Operators, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we prove a range and existence theorem for multivalued pseudomonotone perturbations of maximal monotone operators. We assume a general coercivity condition on the sum of a maximal monotone and a pseudomonotone operator instead of a condition on the pseudomonotone operator only. An illustrative example of a variational inequality in a Sobolev space with variable exponent is given.
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler
Balanced Pod For Model Reduction Of Linear Pde Systems: Convergence Theory, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider convergence analysis for a model reduction algorithm for a class of linear infinite dimensional systems. The algorithm computes an approximate balanced truncation of the system using solution snapshots of specific linear infinite dimensional differential equations. The algorithm is related to the proper orthogonal decomposition, and it was first proposed for systems of ordinary differential equations by Rowley (Int. J. Bifurc. Chaos Appl. Sci. Eng. 15(3), 997-1013, 2005). For the convergence analysis, we consider the algorithm in terms of the Hankel operator of the system, rather than the product of the system Gramians as originally proposed by Rowley. For …
Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten
Balanced Pod For Linear Pde Robust Control Computations, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale nite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented …
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten
A Model Based Feedback Controller For Wing-Twist Via Piezoceramic Actuation, John R. Singler, Belinda A. Batten
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a rubber plate with piezoceramic actuators to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute a linear quadratic based tracking control for piezoelectric actuators placed along both leading and trailing edges. Using these piezoceramic devices, we demonstrate the effectiveness of model based feedback control in achieving a desired wing tip position; this modified shape is analogous to aircraft roll moment generation via wing twist.
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler
Convergent Snapshot Algorithms For Infinite-Dimensional Lyapunov Equations, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We consider two algorithms to approximate the solution Z of a class of stable operator Lyapunov equations of the form AZ + ZA* + BB* = 0. The algorithms utilize time snapshots of solutions of certain linear infinite-dimensional differential equations to construct the approximations. Matrix approximations of the operators a and B are not required and the algorithms are applicable as long as the rank of B is relatively small. The first algorithm produces an optimal low-rank approximate solution using proper orthogonal decomposition. The second algorithm approximates the product of the solution with a few vectors and can be implemented …
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le
Sub-Supersolution Method In Variational Inequalities With Multivalued Operators Given By Integrals, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal
Global Stability Of Complex-Valued Neural Networks On Time Scales, Martin Bohner, V. Sree Hari Rao, Suman Sanyal
Mathematics and Statistics Faculty Research & Creative Works
In this paper, activation dynamics of complex-valued neural networks are studied on general time scales. Besides presenting conditions guaranteeing the existence of a unique equilibrium pattern, its global exponential stability is discussed. Some numerical examples for different time scales are given in order to highlight the results. © 2011 Foundation for Scientific Research and Technological Innovation.
Feedback Control Of A Bioinspired Plate-Beam System, Cody W. Ray, Belinda A. Batten, John R. Singler
Feedback Control Of A Bioinspired Plate-Beam System, Cody W. Ray, Belinda A. Batten, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
In this paper we present a model for a plate-beam system to represent a bioinspired flexible wing. Using a Galerkin based finite element approximation to the system, we compute functional gains that can be used for sensor placement and show that a piezoceramic actuator on the beam can be used for camber control
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Analysis Of Nonlinear Spectral Eddy-Viscosity Models Of Turbulence, Max Gunzburger, Eunjung Lee, Yuki Saka, Catalin Trenchea, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parameter limits, to solutions of the Navier-Stokes equations. We also show, using the mathematical analyses, how effective choices for the parameters appearing in the models can be made. Finally, we consider temporal discretizations of the models and investigate their stability. © 2009 Springer …
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Partial And Spectral-Viscosity Models For Geophysical Flows, Qingshan Chen, Max Gunzburger, Xiaoming Wang
Partial And Spectral-Viscosity Models For Geophysical Flows, Qingshan Chen, Max Gunzburger, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
Two models based on the hydrostatic primitive equations are proposed. the first model is the primitive equations with partial viscosity only and is oriented towards large-scale wave structures in the ocean and atmosphere. the second model is the viscous primitive equations with spectral eddy viscosity and is oriented towards turbulent geophysical flows. for both models, the existence and uniqueness of global strong solutions are established. for the second model, the convergence of the solutions to the solutions of the classical primitive equations as eddy viscosity parameters tend to zero is also established. © 2010 Editorial Office of CAM (Fudan University) …
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by …
Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson
Structural Measurements For Enhanced Mav Flight, John R. Singler, Gregg Abate, Benjamin T. Dickinson
Mathematics and Statistics Faculty Research & Creative Works
Our sense of touch allows us to feel the forces in our limbs when we walk, swim, or hold our arms out the window of a moving car. We anticipate this sense is key in the locomotion of natural flyers. Inspired by the sense of touch, the overall goal of this research is to develop techniques for the estimation of aerodynamic loads from structural measurements for flight control applications. We submit a general algorithm for the direct estimation of distributed steady loads over bodies from embedded noisy deformation-based measurements. The estimation algorithm is applied to a linearly elastic membrane test …
Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang
Asymptotic Analysis Of The Differences Between The Stokes-Darcy System With Different Interface Conditions And The Stokes-Brinkman System, Nan Chen, Max Gunzburger, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider the coupling of the Stokes and Darcy systems with different choices for the interface conditions. We show that, comparing results with those for the Stokes-Brinkman equations, the solutions of Stokes-Darcy equations with the Beavers-Joseph interface condition in the one-dimensional and quasi-two-dimensional (periodic) cases are more accurate than are those obtained using the Beavers-Joseph-Saffman-Jones interface condition and that both of these are more accurate than solutions obtained using a zero tangential velocity interface condition. the zero tangential velocity interface condition is in turn more accurate than the free-slip interface boundary condition. We also prove that the summation of the …
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
No abstract provided.
Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang
Approximation Of Stationary Statistical Properties Of Dissipative Dynamical Systems: Time Discretization, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We consider temporal approximation of stationary statistical properties of dissipative infinite-dimensional dynamical systems. We demonstrate that stationary statistical properties of the time discrete approximations, i.e., numerical scheme, converge to those of the underlying continuous dissipative infinite-dimensional dynamical system under three very natural assumptions as the time step approaches zero. the three conditions that are sufficient for the convergence of the stationary statistical properties are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors for the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to …
Finite Element Approximations For Stokes-Darcy Flow With Beavers-Joseph Interface Conditions, Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, Weidong Zhao
Finite Element Approximations For Stokes-Darcy Flow With Beavers-Joseph Interface Conditions, Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, Weidong Zhao
Mathematics and Statistics Faculty Research & Creative Works
Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. the coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. on the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results. © 2010 Society for Industrial and Applied Mathematics.
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition, Benjamin T. Dickinson, John R. Singler
Nonlinear Model Reduction Using Group Proper Orthogonal Decomposition, Benjamin T. Dickinson, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
We propose a new method to reduce the cost of computing nonlinear terms in projec- tion based reduced order models with global basis functions. We develop this method by extending ideas from the group nite element (GFE) method to proper orthogonal decomposition (POD) and call it the group POD method. Here, a scalar two-dimensional Burgers' equation is used as a model problem for the group POD method. Numerical results show that group POD models of Burgers' equation are as accurate and are computationally more e cient than standard POD models of Burgers' equation.
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction, John R. Singler
Optimality Of Balanced Proper Orthogonal Decomposition For Data Reconstruction, John R. Singler
Mathematics and Statistics Faculty Research & Creative Works
Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. the theoretical result is illustrated with an example.