Mathematics Commons^™

A Dual-Porosity-Stokes Model And Finite Element Method For Coupling Dual-Porosity Flow And Free Flow, Jiangyong Hou, Meilan Qiu, Xiaoming He, Chaohua Guo, Mingzhen Wei, Baojun Bai

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and microfractures, is described by a dual-porosity model. And the flow in the macrofractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macrofractures/conduits, which play a key role in a physically …

Generation And Validation Of Optimal Topologies For Solid Freeform Fabrication, Purnajyoti Bhaumik

Masters Theses

"The study of fabricating topologically optimized parts is presented hereafter. The mapping of topology optimization results for Standard Tessellation Language (STL) writing would enable the solid freeform fabrication of lightweight mechanisms. Aerospace leaders such as NASA, Boeing, Airbus, European Aeronautic Defense And Space Company (EADS), and GE Aero invest in topology optimization research for the production of lightweight materials. Certain concepts such as microstructural homogenization, discretization, and mapping are reviewed and presented in the context of topology optimization. Future biomedical applications of solid freeform fabrication such as organ printing stand to save millions of lives through the robust development of …

A Domain Decomposition Method For The Steady-State Navier-Stokes-Darcy Model With Beavers-Joseph Interface Condition, Xiaoming He, Jian Li, Yanping Lin, Ju Ming

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes and analyzes a Robin-type multiphysics domain decomposition method (DDM) for the steady-state Navier-Stokes-Darcy model with three interface conditions. In addition to the two regular interface conditions for the mass conservation and the force balance, the Beavers-Joseph condition is used as the interface condition in the tangential direction. The major mathematical difficulty in adopting the Beavers-Joseph condition is that it creates an indefinite leading order contribution to the total energy budget of the system [Y. Cao et al., Comm. Math. Sci., 8 (2010), pp. 1-25; Y. Cao et al., SIAM J. Numer. Anal., 47 (2010), pp. 4239-4256]. In …

New Pod Error Expressions, Error Bounds, And Asymptotic Results For Reduced Order Model Of Parabolic Pdes, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The derivations of existing error bounds for reduced order models of time varying partialdi erential equations (PDEs) constructed using proper orthogonal decomposition (POD) haverelied on bounding the error between the POD data and various POD projections of that data.Furthermore, the asymptotic behavior of the model reduction error bounds depends on theasymptotic behavior of the POD data approximation error bounds. We consider time varyingdata taking values in two di erent Hilbert spacesHandV, withVH, and prove exactexpressions for the POD data approximation errors considering four di erent POD projectionsand the two di erent Hilbert space error norms. Furthermore, the exact error expressions …

2nd Annual Undergraduate Research Conference Abstract Book, University Of Missouri--Rolla

Undergraduate Research Conference at Missouri S&T

No abstract provided.

Ensuring The Satisfaction Of A Temporal Specification At Run-Time, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Mathematics and Statistics Faculty Research & Creative Works

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences can occur if the run-time behavior does not conform to the expected behavior or specifications. In this paper, we present a formal approach to ensure satisfaction of the specifications in the operational environment as follows. First we specify behavior of the systems using Interval Temporal Logic (ITL). Next we give algorithms for trace checking of programs in such systems. Finally, we present a fully distributed run-time evaluation system which causally orders the events of the system during its execution and checks …

A Run-Time Decision Procedure For Responsive Computing Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A responsive computing system is a hybrid of real-time, distributed and fault-tolerant systems. In such a system, severe consequences will occur if the logical and physical specifications of the system are not met. In this paper, we present a logic, Interval Temporal Logic (ITL), to specify responsive systems and give decision procedures to verify properties of the system at run-time as follows. First, we collect, during execution, events occurring in the system to represent a distributed computation. Next, we specify properties of the system using ITL formulas. Finally, we apply the decision procedures to determine satisfaction of the formulas. Thus, …

Constructing An Interval Temporal Logic For Real-Time Systems, Grace Tsai, Matt Insall, Bruce M. Mcmillin

Computer Science Technical Reports

A real-time system is one that involves control of one or more physical devices with essential timing requirements. Examples of these systems are command and control systems, process control systems, flight control systems, and the space shuttle avionics systems. The characteristics of these systems are that severe consequences will occur if the logical and physical timing specifications of the systems are not met.

Formal specification and verification are among the techniques to achieve reliable software for real-time systems, in which testing may be impossible or too dangerous to perform. This paper presents a modal logic, Interval Temporal , built upon …

Dynamic Id3: A Symbolic Learning Algorithm For Many-Valued Attribute Domains, Roger Gallion, Chaman Sabharwal, Daniel C. St. Clair, William E. Bond

Computer Science Faculty Research & Creative Works

Quinlan's ID3 machine learning algorithm induces classification trees (rules) from a set of training examples. The algorithm is extremely effective when training examples are composed of attributes whose values are taken from small discrete domains. The classification accuracy of ID3-produced trees on domains whose attributes are many-valued tends to be marginal due to the large number of possible values which may be associated with each attribute. Attempts to solve this problem by a priori grouping of attribute values into distinct subsets has met with limited success. The dynamic ID3 algorithm improves the performance of ID3 on this type of problem …

Formation Of Clusters And Resolution Of Ordinal Attributes In Id3 Classification Trees, Chaman Sabharwal, Keith R. Hacke, Daniel C. St. Clair

Computer Science Faculty Research & Creative Works

Many learning systems have been designed to construct classification trees from a set of training examples. One of the most widely used approaches for constructing decision trees is the ID3 algorithm [Quinlan 1986]. Decision trees are ill-suited to handle attributes with ordinal values. Problems arise when a node representing an ordinal attribute has a branch for each value of the ordinal attribute in the training set. This is generally infeasible when the set of ordinal values is very large. Past approaches have sought to cluster large sets of ordinal values before the classification tree is constructed [Quinlan 1986; Lebowitz 1985; …

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs. © 1987, ACM. All Rights Reserved.

A Logic Programming Model Of The Game Of Sprouts, Ralph M. Butler, Selden Y. Trimble, Ralph W. Wilkerson

Computer Science Faculty Research & Creative Works

The Game of Sprouts Has Intrigued Mathematicians for Nearly Twenty Years. This Paper Describes a Representation Scheme Which Simplifies Much of the Geometry of the Game. using This Representation, We Develop a Prolog Program Which Will Play Sprouts. It is Hoped that the Program Will Prove to Be a Useful Research Tool in Finding the Key to a Winning Strategy for Sprouts and that the Representation Will Serve as a Useful Model for Studying Planar Graphs.