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Articles 1 - 23 of 23
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Predicting Convection Configurations In Coupled Fluid-Porous Systems, Matthew Mccurdy, Nicholas J. Moore, Xiaoming Wang
Predicting Convection Configurations In Coupled Fluid-Porous Systems, Matthew Mccurdy, Nicholas J. Moore, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
A ubiquitous arrangement in nature is a free-flowing fluid coupled to a porous medium, for example a river or lake lying above a porous bed. Depending on the environmental conditions, thermal convection can occur and may be confined to the clear fluid region, forming shallow convection cells, or it can penetrate into the porous medium, forming deep cells. Here, we combine three complementary approaches - linear stability analysis, fully nonlinear numerical simulations and a coarse-grained model - to determine the circumstances that lead to each configuration. the coarse-grained model yields an explicit formula for the transition between deep and shallow …
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang
Conservative Unconditionally Stable Decoupled Numerical Schemes For The Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq System, Wenbin Chen, Daozhi Han, Xiaoming Wang, Yichao Zhang
Mathematics and Statistics Faculty Research & Creative Works
We propose two mass and heat energy conservative, unconditionally stable, decoupled numerical algorithms for solving the Cahn–Hilliard–Navier–Stokes–Darcy–Boussinesq system that models thermal convection of two-phase flows in superposed free flow and porous media. The schemes totally decouple the computation of the Cahn–Hilliard equation, the Darcy equations, the heat equation, the Navier–Stokes equations at each time step, and thus significantly reducing the computational cost. We rigorously show that the schemes are conservative and energy-law preserving. Numerical results are presented to demonstrate the accuracy and stability of the algorithms.
Second-Order, Fully Decoupled, Linearized, And Unconditionally Stable Scalar Auxiliary Variable Schemes For Cahn–Hilliard–Darcy System, Yali Gao, Xiaoming He, Yufeng Nie
Second-Order, Fully Decoupled, Linearized, And Unconditionally Stable Scalar Auxiliary Variable Schemes For Cahn–Hilliard–Darcy System, Yali Gao, Xiaoming He, Yufeng Nie
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods have the features of second order accuracy, totally decoupling, linearization, and unconditional energy stability. The unconditionally stability of the two proposed decoupled numerical schemes are rigorously proved. Abundant numerical results are reported to verify the accuracy and effectiveness of proposed numerical methods.
Pattern Selection In The Schnakenberg Equations: From Normal To Anomalous Diffusion, Hatim K. Khudhair, Yanzhi Zhang, Nobuyuki Fukawa
Pattern Selection In The Schnakenberg Equations: From Normal To Anomalous Diffusion, Hatim K. Khudhair, Yanzhi Zhang, Nobuyuki Fukawa
Mathematics and Statistics Faculty Research & Creative Works
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the same diffusion power, the Turing instability space depends only on the ratio of diffusion coefficients (Formula presented.). However, smaller diffusive powers might introduce larger unstable wave numbers with wider band, implying that the patterns may be more chaotic in the fractional cases. We then apply a weakly nonlinear analysis to predict the parameter regimes for spot, stripe, and mixed patterns in the Turing space. Our numerical …
Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang
Numerical Analysis Of A Second Order Ensemble Method For Evolutionary Magnetohydrodynamics Equations At Small Magnetic Reynolds Number, John Carter, Nan Jiang
Mathematics and Statistics Faculty Research & Creative Works
We study a second order ensemble method for fast computation of an ensemble of magnetohydrodynamics flows at small magnetic Reynolds number. Computing an ensemble of flow equations with different input parameters is a common procedure for uncertainty quantification in many engineering applications, for which the computational cost can be prohibitively expensive for nonlinear complex systems. We propose an ensemble algorithm that requires only solving one linear system with multiple right-hands instead of solving multiple different linear systems, which significantly reduces the computational cost and simulation time. Comprehensive stability and error analyses are presented proving conditional stability and second order in …
A Positivity Preserving, Energy Stable Finite Difference Scheme For The Flory-Huggins-Cahn-Hilliard-Navier-Stokes System, Wenbin Chen, Jianyu Jing, Cheng Wang, Xiaoming Wang
A Positivity Preserving, Energy Stable Finite Difference Scheme For The Flory-Huggins-Cahn-Hilliard-Navier-Stokes System, Wenbin Chen, Jianyu Jing, Cheng Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we propose and analyze a finite difference numerical scheme for the Cahn-Hilliard-Navier-Stokes system, with logarithmic Flory-Huggins energy potential. in the numerical approximation to the singular chemical potential, the logarithmic term and the surface diffusion term are implicitly updated, while an explicit computation is applied to the concave expansive term. Moreover, the convective term in the phase field evolutionary equation is approximated in a semi-implicit manner. Similarly, the fluid momentum equation is computed by a semi-implicit algorithm: implicit treatment for the kinematic diffusion term, explicit update for the pressure gradient, combined with semi-implicit approximations to the fluid convection …
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Delay Dynamic Equations On Isolated Time Scales And The Relevance Of One-Periodic Coefficients, Martin Bohner, Tom Cuchta, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
We are motivated by the idea that certain properties of delay differential and difference equations with constant coefficients arise as a consequence of their one-periodic nature. We apply the recently introduced definition of periodicity for arbitrary isolated time scales to linear delay dynamic equations and a class of nonlinear delay dynamic equations. Utilizing a derived identity of higher order delta derivatives and delay terms, we rewrite the considered linear and nonlinear delayed dynamic equations with one-periodic coefficients as a linear autonomous dynamic system with constant matrix. As the simplification of a constant matrix is only obtained for one-periodic coefficients, dynamic …
Derivation And Analysis Of A Discrete Predator–Prey Model, Sabrina H. Streipert, Gail S.K. Wolkowicz, Martin Bohner
Derivation And Analysis Of A Discrete Predator–Prey Model, Sabrina H. Streipert, Gail S.K. Wolkowicz, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We derive a discrete predator–prey model from first principles, assuming that the prey population grows to carrying capacity in the absence of predators and that the predator population requires prey in order to grow. The proposed derivation method exploits a technique known from economics that describes the relationship between continuous and discrete compounding of bonds. We extend standard phase plane analysis by introducing the next iterate root-curve associated with the nontrivial prey nullcline. Using this curve in combination with the nullclines and direction field, we show that the prey-only equilibrium is globally asymptotic stability if the prey consumption-energy rate of …
Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang
Error Estimate Of A Decoupled Numerical Scheme For The Cahn-Hilliard-Stokes-Darcy System, Wenbin Chen, Shufen Wang, Yichao Zhang, Daozhi Han, Cheng Wang, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between the Cahn-Hilliard equation and the fluid motion, we make use of the operator-splitting in the numerical scheme, so that these two solvers are decoupled, which in turn would greatly improve the computational efficiency. The unique solvability and the energy stability have been proved in Chen et al. (2017, Uniquely solvable and energy stable decoupled numerical schemes for the Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry. …
Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç
Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç
Mathematics and Statistics Faculty Research & Creative Works
This paper deals with the asymptotic behavior of the nonoscillatory solutions of a certain forced fractional differential equations with positive and negative terms, involving the Caputo fractional derivative. The results obtained are new and generalize some known results appearing in the literature. Two examples are also provided to illustrate the results.
Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou
Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou
Mathematics and Statistics Faculty Research & Creative Works
We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event's level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and …
Joint Control Of Manufacturing And Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms, Jiaojiao Yang, Zeyi Sun, Wenqing Hu, Louis Steinmeister
Joint Control Of Manufacturing And Onsite Microgrid System Via Novel Neural-Network Integrated Reinforcement Learning Algorithms, Jiaojiao Yang, Zeyi Sun, Wenqing Hu, Louis Steinmeister
Mathematics and Statistics Faculty Research & Creative Works
Microgrid is a promising technology of distributed energy supply system, which consists of storage devices, generation capacities including renewable sources, and controllable loads. It has been widely investigated and applied for residential and commercial end-use customers as well as critical facilities. In this paper, we propose a joint state-based dynamic control model on microgrids and manufacturing systems where optimal controls for both sides are implemented to coordinate the energy demand and supply so that the overall production cost can be minimized considering the constraint of production target. Markov Decision Process (MDP) is used to formulate the decision-making procedure. The main …
Combining Cardiac Monitoring With Actigraphy Aids Nocturnal Arousal Detection During Ambulatory Sleep Assessment In Insomnia, Lara Rösler, Glenn Van Der Lande, Jeanne Leerssen, Austin G. Vandegriffe, Oti Lakbila-Kamal, Jessica C. Foster-Dingley, Anne C.W. Albers, Eus J.W. Van Someren
Combining Cardiac Monitoring With Actigraphy Aids Nocturnal Arousal Detection During Ambulatory Sleep Assessment In Insomnia, Lara Rösler, Glenn Van Der Lande, Jeanne Leerssen, Austin G. Vandegriffe, Oti Lakbila-Kamal, Jessica C. Foster-Dingley, Anne C.W. Albers, Eus J.W. Van Someren
Mathematics and Statistics Faculty Research & Creative Works
Study Objectives: The objective assessment of insomnia has remained difficult. Multisensory devices collecting heart rate (HR) and motion are regarded as the future of ambulatory sleep monitoring. Unfortunately, reports on altered average HR or heart rate variability (HRV) during sleep in insomnia are equivocal. Here, we evaluated whether the objective quantification of insomnia improves by assessing state-related changes in cardiac measures. Methods: We recorded electrocardiography, posture, and actigraphy in 33 people without sleep complaints and 158 patients with mild to severe insomnia over 4 d in their home environment. At the microscale, we investigated whether HR changed with proximity to …
Stability For Generalized Caputo Proportional Fractional Delay Integro-Differential Equations, Martin Bohner, Snezhana Hristova
Stability For Generalized Caputo Proportional Fractional Delay Integro-Differential Equations, Martin Bohner, Snezhana Hristova
Mathematics and Statistics Faculty Research & Creative Works
A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included.
Oscillation Of Noncanonical Second-Order Advanced Differential Equations Via Canonical Transform, Martin Bohner, Kumar S. Vidhyaa, Ethiraju Thandapani
Oscillation Of Noncanonical Second-Order Advanced Differential Equations Via Canonical Transform, Martin Bohner, Kumar S. Vidhyaa, Ethiraju Thandapani
Mathematics and Statistics Faculty Research & Creative Works
In this paper, we develop a new technique to deduce oscillation of a second-order noncanonical advanced differential equation by using established criteria for second-order canonical advanced differential equations. We illustrate our results by presenting two examples.
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Periodicity On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we formulate the definition of periodicity for functions defined on isolated time scales. The introduced definition is consistent with the known formulations in the discrete and quantum calculus settings. Using the definition of periodicity, we discuss the existence and uniqueness of periodic solutions to a family of linear dynamic equations on isolated time scales. Examples in quantum calculus and for mixed isolated time scales are presented.
A Multigrid Multilevel Monte Carlo Method For Stokes–Darcy Model With Random Hydraulic Conductivity And Beavers–Joseph Condition, Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
A Multigrid Multilevel Monte Carlo Method For Stokes–Darcy Model With Random Hydraulic Conductivity And Beavers–Joseph Condition, Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, Xiaoming He
Mathematics and Statistics Faculty Research & Creative Works
A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Three interface conditions with randomness are considered on the interface between Stokes and Darcy equations, especially the Beavers–Joesph interface condition with random hydraulic conductivity. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes–Darcy model to improve the fidelity. Under suitable assumptions on the random coefficient, we prove the existence and uniqueness of the weak solution of the variational form. To construct …
On Inclusions With Monotone-Type Mappings In Nonreflexive Banach Spaces, Vy Khoi Le
On Inclusions With Monotone-Type Mappings In Nonreflexive Banach Spaces, Vy Khoi Le
Mathematics and Statistics Faculty Research & Creative Works
We are concerned in this article with the existence of solutions to inclusions containing generalized pseudomonotone perturbations of maximal monotone mappings in general Banach spaces. Our approach is based on a truncation–regularization technique and an extension of the Moreau–Yosida–Brezis–Crandall–Pazy regularization for maximal monotone mappings in general Banach spaces. We also consider some applications to multivalued variational inequalities containing elliptic operators with rapidly growing coefficients in Orlicz–Sobolev spaces.
The Beverton-Hold Model On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
The Beverton-Hold Model On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert
Mathematics and Statistics Faculty Research & Creative Works
In this work, we formulate the Beverton-Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton-Holt equation. The first main theorem provides conditions for the existence of a unique !-periodic solution that is globally asymptotically stable, which addresses the first Cushing-Henson conjecture on isolated time scales. The second main theorem concerns the generalization of the second Cushing-Henson conjecture. It investigates the effects of …
Optimal Equivalence Testing In Exponential Families, Renren Zhao, Robert L. Paige
Optimal Equivalence Testing In Exponential Families, Renren Zhao, Robert L. Paige
Mathematics and Statistics Faculty Research & Creative Works
We develop uniformly most powerful unbiased (UMPU) two sample equivalence test for a difference of canonical parameters in exponential families. This development involves a non-unique reparameterization. We address this issue via a novel characterization of all possible reparameterizations of interest in terms of a matrix group. Furthermore, our procedure involves an intractable conditional distribution which we reproduce to a high degree of accuracy using saddle point approximations. The development of this saddle point-based procedure involves a non-unique reparameterization, but we show that our procedure is invariant under choice of reparameterization. Our real data example considers the mean-to-variance ratio for normally …
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská
Mathematics and Statistics Faculty Research & Creative Works
The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.
On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten
Mathematics and Statistics Faculty Research & Creative Works
Let Ω ⊂ Cn, n > 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of Cn \ Ω is Cn. It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in Cn for which the …
Fundamental Structure Of General Stochastic Dynamical Systems: High-Dimension Case, Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao
Fundamental Structure Of General Stochastic Dynamical Systems: High-Dimension Case, Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao
Mathematics and Statistics Faculty Research & Creative Works
No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.