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Full-Text Articles in Physical Sciences and Mathematics
An Investigation Into Lagrangian Coherent Structure Detection For Low Reynolds Number Flows, Kyle Fitzsimmons
An Investigation Into Lagrangian Coherent Structure Detection For Low Reynolds Number Flows, Kyle Fitzsimmons
Theses, Dissertations and Culminating Projects
In order to better understand and make use of complex fluid systems, regions of similar behavior can be categorized, thus reducing the problem to one of identifying the important structures within the fluid system, and examining their interaction. An important category of fluid structures are those known as Lagrangian Coherent Structures. An experimental setup has been constructed in order to study methods for improving the detection of Lagrangian Coherent Structures, and experimental data has been analyzed in order to verify the experimental setup. Several modifications to the basic gyre flow have been analyzed in order to provide direction, and a …
Adjusted Empirical Likelihood Method For Comparison Of Treatment Effects In Linear Model Setting, Xi Kang
Adjusted Empirical Likelihood Method For Comparison Of Treatment Effects In Linear Model Setting, Xi Kang
Theses, Dissertations and Culminating Projects
Empirical likelihood is a nonparametric method of statistical inference which was introduced by Owen. It allows the data analyst to use it without making distribution assumptions. Empirical likelihood method has been widely used not only for nonparametric models but also for semi-parametric models, with the effectiveness of the likelihood approach and good power properties. However, when the sample size is small or the dimension is high, the method is poorly calibrated, producing tests that generally have a higher type I error. In addition, it suffers from a limiting convex hull constraint. Many statisticians have proposed methods to address the performance. …
On God's Number(S) And The Rubik's Slide Extension, James F. Johnston Iii
On God's Number(S) And The Rubik's Slide Extension, James F. Johnston Iii
Theses, Dissertations and Culminating Projects
In a recent article, Jones, Shelton and Weaverdyck and Aim, Gramelspacher, and Rice provided two analyses of the Rubik’s Slide game on a board of dimensions 3x3. This paper extends the work of Jones, Shelton, and Weaverdyck to a board of dimensions 4x4. Concepts from abstract algebra and graph theory are used to calculate the God’s number of many classes of puzzles, which is the least number of moves necessary to reach any end configuration from any starting configuration of game play. It turns out that God’s number is equivalent to the diameter of a graph of the group formed …
Application Of Nonequilibrium Thermodynamics To Pattern Selection In Fluid Solid Interaction, Blas J. Ortega
Application Of Nonequilibrium Thermodynamics To Pattern Selection In Fluid Solid Interaction, Blas J. Ortega
Theses, Dissertations and Culminating Projects
The terminal orientation of a rigid body is a classic example of a system out of thermodynamic equilibrium and a perfect testing ground for the validity of the maximum entropy production principle(MEPP). A freely falling body in a quiescent fluid generates fluid flow around the body resulting in dissipative losses. Thus far, dynamical equations have been employed in deriving the equilibrium states of such falling bodies, but they are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In …
How Do Manipulatives Help Students Communicate Their Understanding Of Double-Digit Subtraction?, Rabab Abi-Hanna
How Do Manipulatives Help Students Communicate Their Understanding Of Double-Digit Subtraction?, Rabab Abi-Hanna
Theses, Dissertations and Culminating Projects
Multi-digit subtraction is difficult for students to learn. The purpose of this study is to explore how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives/tools. This qualitative study reports on six case studies of second-grade students where clinical interviews were the main source of data. Findings suggest that manipulatives/tools helped reveal cognitive constructs and difficulties that the handwritten algorithms were not conveying. For example, students who exhibited an understanding of the subtraction process had not yet developed an understanding of ten and 10 ones interchangeability. These results highlight the potential role of manipulatives/tools as communication …
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver
Computing The Optimal Path In Stochastic Dynamical Systems, Martha Bauver
Theses, Dissertations and Culminating Projects
In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. The optimal path is of great importance, since it represents the most likely path of a rare switching or escape event. For instance, the optimal path for an infectious disease model represents a switching from an infectious state to the extinction of the disease within …
Numerical Detection Of Wave Breaking In The Short-Pulse Equation, Jeffrey Slepoi
Numerical Detection Of Wave Breaking In The Short-Pulse Equation, Jeffrey Slepoi
Theses, Dissertations and Culminating Projects
Numerical analysis is a powerful resource in all mathematical sciences especially in the study of partial differential equations (PDEs). It allows evaluating and demonstrating derived solutions for PDEs and whenever the solution can’t be derived analytically it provides us with ability to calculate the solution function numerically and predict its behavior over time. This work presents a numerical method to evaluate an analytically known solution, demonstrates the needed parameters to achieve the desired accuracy, extends the methodology into the sphere of the mathematical unknown to be able to predict the results by using the same numerical methodology. The equation in …
Detection Of Coherent Structures In Flows, Klodiana Shkembi
Detection Of Coherent Structures In Flows, Klodiana Shkembi
Theses, Dissertations and Culminating Projects
In this work, we have developed an experimental flow tank that can produce realistic ocean-like flows, including multi-gyre flows. By generating controllable ocean-like flow fields, we can study the flows to gain a better understanding of ocean dynamics. In particular, we use particle image velocimetry and finite-time Lyapunov exponents to determine the location of the Lagrangian Coherent Structures that determine transport in complex fluid flows. This understanding is useful for designing control algorithms and for optimizing the use of autonomous vehicles operating in the stochastic and time-dependent ocean environment.