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- Autoregressive Integrated Moving Average (ARIMA) (1)
- Beavers-Joseph Boundary (1)
- Bootstrap (Statistics)<br />Prediction (Logic)<br />Time-series analysis (1)
- Canonical correlation (Statistics)<br />Difference equations<br />Functions, Abelian (1)
- Collocation (1)
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- Conduit and Matrix Domains (1)
- Convex-Concave Decomposition (1)
- Convexity Splitting (1)
- Derivative (1)
- Ehrlich-Schwoebel Type Energy (1)
- Energy Stability (1)
- Epitaxial Growth (1)
- Epitaxial Thin Film Growth (1)
- Fourier Collocation Spectral (1)
- Fractional Auto-Regressive Integrated Moving Average (FARIMA) (1)
- Global Attractor (1)
- Hausdorff Besicovitch dimension (1)
- Hausdorff measure (1)
- Invariant Measures (1)
- Karst Aquifer (1)
- Mass Exchange Rate (1)
- Metric (1)
- Metric phase (1)
- Metric-preserving functions (1)
- Oscillation (1)
- Pipe Flow Model (1)
- Second Order Scheme (1)
- Semi-Implicit Schemes (1)
- Slope Selection (1)
- Spectral (1)
- Publication
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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme …
Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao
Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao
Mathematics and Statistics Faculty Research & Creative Works
In our previous study, we developed the Stokes-Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers-Joseph (BJ) condition was used to describe the matrix-conduit interface. We also studied the mathematical well-posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. in this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further …
Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise
Mathematics and Statistics Faculty Research & Creative Works
We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …
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.
Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert
Abel Dynamic Equations Of The First And Second Kind, Sabrina Heike Streipert
Masters Theses
"In this work, we study Abel dynamic equations of the first and the second kind. After a brief introduction to time scales, we introduce the Abel differential equations of the first and the second kind, as well as the canonical Abel form in the continuous case. Using the existing information, we derive novel results for time scales. We provide formulas for the Abel dynamic equations of the second kind and present a solution method. We furthermore achieve a special class of Abel equations of the first kind and discuss the canonical Abel equation. We get relations between common dynamic equations …
Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe
Sieve Bootstrap Based Prediction Intervals And Unit Root Tests For Time Series, Maduka Rupasinghe
Doctoral Dissertations
"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for …