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 Title
 NUMERICAL COMPUTATIONS FOR PDE MODELS OF ROCKET EXHAUST FLOW IN SOIL.
 Creator

Brennan, Brian, Moore, Brian, University of Central Florida
 Abstract / Description

We study numerical methods for solving the nonlinear porous medium and NavierLame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the CrankNicolson time stepping method with a spectral discretization in space. Since the NavierLame equation is a boundary value problem, it is solved using a finite element method...
Show moreWe study numerical methods for solving the nonlinear porous medium and NavierLame problems. When coupled together, these equations model the flow of exhaust through a porous medium, soil, and the effects that the pressure has on the soil in terms of spatial displacement. For the porous medium equation we use the CrankNicolson time stepping method with a spectral discretization in space. Since the NavierLame equation is a boundary value problem, it is solved using a finite element method where the spatial domain is represented by a triangulation of discrete points. The two problems are coupled by using approximations of solutions to the porous medium equation to define the forcing term in the NavierLame equation. The spatial displacement solutions can be used to approximate the strain and stress imposed on the soil. An analysis of these physical properties shows whether or not the material ceases to act as an elastic material and instead behaves like a plastic which will tell us if the soil has failed and a crater has formed. Analytical as well as experimental tests are used to find a good balance for solving the porous medium and NavierLame equations both accurately and efficiently.
Show less  Date Issued
 2010
 Identifier
 CFE0003217, ucf:48565
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003217
 Title
 STANDING WAVES OF SPATIALLY DISCRETE FITZHUGHNAGUMO EQUATIONS.
 Creator

Segal, Joseph, Moore, Brian, University of Central Florida
 Abstract / Description

We study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for...
Show moreWe study a system of spatially discrete FitzHughNagumo equations, which are nonlinear differentialdifference equations on an infinite onedimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.
Show less  Date Issued
 2009
 Identifier
 CFE0002892, ucf:48021
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002892
 Title
 PERCEPTIONS OF TEACHERS AND ADMINISTRATORS OF THE ORGANIZATIONAL SUPPORTS FOR INCLUSION PROGRAMS IN SOUTHWEST FLORIDA ELEMENTARY SCHOOLS.
 Creator

Moore, Brian, House, Jess, University of Central Florida
 Abstract / Description

The success of exceptional student education, although dependent upon the teachers involved, is largely made possible both by the role the school principal performs and the organizational support provided by the school district. The primary purpose of this study was to identify the sources and components of organizational support required to implement the inclusion of students with disabilities into general education classrooms. The provision of resources by administrators, particularly the...
Show moreThe success of exceptional student education, although dependent upon the teachers involved, is largely made possible both by the role the school principal performs and the organizational support provided by the school district. The primary purpose of this study was to identify the sources and components of organizational support required to implement the inclusion of students with disabilities into general education classrooms. The provision of resources by administrators, particularly the building principal, is an example of an organizational support that helps students with disabilities learn successfully in this setting. These resources include funding, special curricula, adaptive technology, organizational resources such as time for training, and hiring of additional personnel to assist these students. The role of educational leader in inclusive education has evolved beginning with changes in federal and state legislation that were initiated in the early 1970s. Administrators are legally responsible for the education of students with special needs in the least restrictive environment. This study identifies organizational supports as well as attitudes toward inclusion reported by teachers and principals in a medium sized southwest Florida school district.
Show less  Date Issued
 2005
 Identifier
 CFE0000615, ucf:46544
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000615
 Title
 Analytical and Numerical Investigations of the Kudryashov Generalized KdV Equation.
 Creator

Hilton, William, Schober, Constance, Moore, Brian, Choudhury, Sudipto, University of Central Florida
 Abstract / Description

This thesis concerns an analytical and numerical study of the Kudryashov Generalized Kortewegde Vries (KG KdV) equation. Using a refined perturbation expansion of the FermiPastaUlam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV...
Show moreThis thesis concerns an analytical and numerical study of the Kudryashov Generalized Kortewegde Vries (KG KdV) equation. Using a refined perturbation expansion of the FermiPastaUlam (FPU) equations of motion, the KG KdV equation, which arises at sixth order, and general higher order KdV equations are derived. Special solutions of the KG KdV equation are derived using the tanh method. A pseudospectral integrator, which can handle stiff equations, is developed for the higher order KdV equations. The numerical experiments indicate that although the higher order equations exhibit complex dynamics, they fail to reach energy equipartition on the time scale considered.
Show less  Date Issued
 2018
 Identifier
 CFE0007754, ucf:52395
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007754
 Title
 Iteratively Reweighted Least Squares Minimization with Prior Information: A New Approach.
 Creator

Popov, Dmitriy, Li, Xin, Moore, Brian, Mikusinski, Piotr, University of Central Florida
 Abstract / Description

Iteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to...
Show moreIteratively reweighted least squares (IRLS) algorithms provide an alternative to the more standard L1minimization approach in compressive sensing. Daubechies et al. introduced a particularly stable version of an IRLS algorithm and rigorously proved its convergence in 2010. They did not, however, consider the case in which prior information on the support of the sparse domain of the solution is available. In 2009, Miosso et al. proposed an IRLS algorithm that makes use of this information to further reduce the number of measurements required to recover the solution with specified accuracy. Although Miosso et al. obtained a number of simulation results strongly confirming the utility of their approach, they did not rigorously establish the convergence properties of their algorithm. In this paper, we introduce prior information on the support of the sparse domain of the solution into the algorithm of Daubechies et al. We then provide a rigorous proof of the convergence of the resulting algorithm.
Show less  Date Issued
 2011
 Identifier
 CFE0004154, ucf:49082
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004154
 Title
 Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic.
 Creator

Lydon, Elizabeth, Moore, Brian, Choudhury, Sudipto, Kaup, David, University of Central Florida
 Abstract / Description

Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle rosis. We construct steadystate, single front solutions by employing a piecewise linear reaction term. Using a combination of JacobiOperator theory and the ShermanMorrison formula we de rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain...
Show moreSpatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle rosis. We construct steadystate, single front solutions by employing a piecewise linear reaction term. Using a combination of JacobiOperator theory and the ShermanMorrison formula we de rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent a very specific solution to the spatially discrete Nagumo equation. For example, we only consider inhomogeneous media with one defect present. We created an original script in MATLAB which algorithmically solves more general cases of the equation, including the case for multiple defects. The algorithmic solutions are then compared to known exact solutions to determine their validity.
Show less  Date Issued
 2015
 Identifier
 CFE0005831, ucf:50903
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005831
 Title
 Modeling rogue waves in deep water.
 Creator

Strawn, Maria, Schober, Constance, Moore, Brian, Choudhury, Sudipto, Calini, Annalisa, University of Central Florida
 Abstract / Description

The evolution of surface waves in deep water is governed by the nonlinear Schrodinger (NLS) equation. Spatially periodic breathers (SPBs) and rational solutions of the NLS equation are used as typical models for rogue waves since they exhibit many features of rogue waves. A major component of the dissertation is the stability of solutions of the NLS equation.We address the stability of the rational solutions of the NLS equation used to model rogue waves using squared eigenfunctions of the...
Show moreThe evolution of surface waves in deep water is governed by the nonlinear Schrodinger (NLS) equation. Spatially periodic breathers (SPBs) and rational solutions of the NLS equation are used as typical models for rogue waves since they exhibit many features of rogue waves. A major component of the dissertation is the stability of solutions of the NLS equation.We address the stability of the rational solutions of the NLS equation used to model rogue waves using squared eigenfunctions of the associated Lax Pair. This allows us to contrast to the existing results for SPBs. The stability of the constant amplitude solution of the higher order NLS (HONLS) equation with additional novel perturbations, relevant toour subsequent study on downshifting, is considered next. In addition to the higher order perturbations, we include linear effects and nonlinear damping of the mean flow to the HONLS equation.In addition to stability, we discuss rogue waves and downshifting. Permanent downshifting occurs when energy if permanently transferred from the initially dominant mode to lower modes and is observed in physical experiments and field studies of deep water waves. Although these experimental observations are well documented, neither NLS nor HONLS equations describe this behavior. Nonlinear damping of the mean flow, included in our studies, is shown to model permanent downshifting. We examine the interaction of rogue waves and downshifting in a sea state with both nonlinear and linear effects. We show that there are no rogue waves after permanent downshifting. Analytical and numerical analysis are provided to support the findings.
Show less  Date Issued
 2016
 Identifier
 CFE0006402, ucf:51476
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006402
 Title
 Comparing the Variational Approximation and Exact Solutions of the Straight Unstaggered and Twisted Staggered Discrete Solitons.
 Creator

Marulanda, Daniel, Kaup, David, Moore, Brian, Vajravelu, Kuppalapalle, University of Central Florida
 Abstract / Description

Discrete nonlinear Schr(&)#246;dinger equations (DNSL) have been used to provide models of a variety of physical settings. An application of DNSL equations is provided by BoseEinstein condensates which are trapped in deep opticallattice potentials. These potentials effectively splits the condensate into a set of droplets held in local potential wells, which are linearly coupled across the potential barriers between them [3]. In previous works, DNLS systems have also been used for symmetric...
Show moreDiscrete nonlinear Schr(&)#246;dinger equations (DNSL) have been used to provide models of a variety of physical settings. An application of DNSL equations is provided by BoseEinstein condensates which are trapped in deep opticallattice potentials. These potentials effectively splits the condensate into a set of droplets held in local potential wells, which are linearly coupled across the potential barriers between them [3]. In previous works, DNLS systems have also been used for symmetric onsitecentered solitons [11]. A few works have constructed different discrete solitons via the variational approximation (VA) and have explored their regions for their solutions [11, 12]. Exact solutions for straight unstaggeredtwisted staggered (SUTS) discrete solitons have been found using the shooting method [12].In this work, we will use Newton's method, which converges to the exact solutions of SUTS discrete solitons. The VA has been used to create starting points. There are two distinct types of solutions for the soliton's waveform: SUTS discrete solitons and straight unstaggered discrete solitons, where the twisted component is zero in the latter soliton. We determine the range of parameters for which each type of solution exists. We also compare the regions for the VA solutions and the exact solutions in certain selected cases. Then, we graphically and numerically compare examples of the VA solutions with their corresponding exact solutions. We also find that the VA provides reasonable approximations to the exact solutions.
Show less  Date Issued
 2016
 Identifier
 CFE0006350, ucf:51570
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006350
 Title
 Buidling Lax Integrable VariableCoefficient Generalizations to Integrable PDEs and Exact Solutions to Nonlinear PDEs.
 Creator

Russo, Matthew, Choudhury, Sudipto, Moore, Brian, Schober, Constance, Christodoulides, Demetrios, University of Central Florida
 Abstract / Description

This dissertation is composed of two parts. In Part I a technique based on extended Lax Pairs isfirst considered to derive variablecoefficient generalizations of various Laxintegrable NLPDE hierarchies recently introduced in the literature. It is demonstrated that the technique yields Lax or Sintegrable nonlinear partial differential equations (PDEs) with both time and spacedependent coefficients which are thus more general than almost all cases considered earlier via other methods such...
Show moreThis dissertation is composed of two parts. In Part I a technique based on extended Lax Pairs isfirst considered to derive variablecoefficient generalizations of various Laxintegrable NLPDE hierarchies recently introduced in the literature. It is demonstrated that the technique yields Lax or Sintegrable nonlinear partial differential equations (PDEs) with both time and spacedependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve Test, Bell Polynomials, and various similarity methods. However, this technique, although operationally effective, has the significant disadvantage that, for any integrable system with spatiotemporally varying coefficients, one must 'guess' a generalization of the structure of the known Lax Pair for the corresponding system with constant coefficients. Motivated by the somewhat arbitrary nature of the above procedure, we present a generalization to the well known EstabrookWahlquist prolongation technique which provides a systematic procedure for the derivation of the Lax representation. In order to obtain a nontrivial Lax representation we must impose differential constraints on the variable coefficients present in the nlpde. The resulting constraints determine a class of equations which represent generalizations to a previously known integrable constant coefficient nlpde. We demonstrate the effectiveness of this technique by deriving variablecoefficient generalizations to the nonlinear Schrodinger (NLS) equation, derivative NLS equation, PTsymmetric NLS, fifthorder KdV, and three equations in the MKdV hierarchy. In Part II of this dissertation, we introduce three types of singular manifold methods which have been successfully used in the literature to derive exact solutions to many nonlinear PDEs extending over a wide range of applications. The singular manifold methods considered are: truncated Painleve analysis, Invariant Painleve analysis, and a generalized Hirota expansion method. We then consider the KdV and KPII equations as instructive examples before using each method to derive nontrivial solutions to a microstructure PDE and two generalized PochhammerChree equations.
Show less  Date Issued
 2016
 Identifier
 CFE0006173, ucf:51144
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006173
 Title
 Comparison of Second Order Conformal Symplectic Schemes with Linear Stability Analysis.
 Creator

Floyd, Dwayne, Moore, Brian, Schober, Constance, Mohapatra, Ram, University of Central Florida
 Abstract / Description

Numerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the wellknown St(&)#246;rmerVerlet and implicit midpoint methods. The structure preservation properties of each method are shown analytically and numerically. Each method is shown to preserve a symplectic form up to a constantand are therefore conformal symplectic integrators, with each method shown to accurately preserve the rate of momentum...
Show moreNumerical methods for solving linearly damped Hamiltonian ordinary differential equations are analyzed and compared. The methods are constructed from the wellknown St(&)#246;rmerVerlet and implicit midpoint methods. The structure preservation properties of each method are shown analytically and numerically. Each method is shown to preserve a symplectic form up to a constantand are therefore conformal symplectic integrators, with each method shown to accurately preserve the rate of momentum dissipation. An analytical linear stability analysis is completed for each method, establishing thresholds between the value of the damping coefficient and the stepsize that ensure stability. The methods are all second order and the preservation of the rate of energy dissipation is compared to that of a third order RungeKutta method that does not preserve conformal properties. Numerical experiments will include the damped harmonic oscillator and the damped nonlinear pendulum.
Show less  Date Issued
 2014
 Identifier
 CFE0005793, ucf:50051
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005793
 Title
 Numerical Simulations for the Flow of Rocket Exhaust Through a Granular Medium.
 Creator

Kraakmo, Kristina, Moore, Brian, Brennan, Joseph, Rollins, David, University of Central Florida
 Abstract / Description

Physical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and efficiently model the changes in pressure as gas flows through a porous medium. A twodimensional model in...
Show morePhysical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and efficiently model the changes in pressure as gas flows through a porous medium. A twodimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy's law is used. An AlternatingDirection Implicit (ADI) temporal scheme is presented and implemented which reduces our multidimensional problem into a series of onedimensional problems. We take advantage of explicit approximations for the nonlinear terms using extrapolation formulas derived from Taylorseries, which increases efficiency when compared to other common methods. We couple our ADI temporal scheme with different spatial discretizations including a secondorder Finite Difference (FD) method, a fourthorder Orthogonal Spline Collocation (OSC) method, and an Nthorder Chebyshev Spectral method. Accuracy and runtime are compared among the three methods for comparison in a linear analogue of our problem. We see the best results for accuracy when using an ADISpectral method in the linear case, but discuss possibilities for increased efficiency using an ADIOSC scheme. Nonlinear results are presented using the ADISpectral method and the ADIFD method.
Show less  Date Issued
 2013
 Identifier
 CFE0005017, ucf:49998
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005017
 Title
 ACTION RECOGNITION USING PARTICLE FLOW FIELDS.
 Creator

Reddy, Kishore, Shah, Mubarak, Sukthankar, Gita, Wei, Lei, Moore, Brian, University of Central Florida
 Abstract / Description

In recent years, research in human action recognition has advanced on multiple fronts to address various types of actions including simple, isolated actions in staged data (e.g., KTH dataset), complex actions (e.g., Hollywood dataset), and naturally occurring actions in surveillance videos (e.g, VIRAT dataset). Several techniques including those based on gradient, flow, and interestpoints, have been developed for their recognition. Most perform very well in standard action recognition...
Show moreIn recent years, research in human action recognition has advanced on multiple fronts to address various types of actions including simple, isolated actions in staged data (e.g., KTH dataset), complex actions (e.g., Hollywood dataset), and naturally occurring actions in surveillance videos (e.g, VIRAT dataset). Several techniques including those based on gradient, flow, and interestpoints, have been developed for their recognition. Most perform very well in standard action recognition datasets, but fail to produce similar results in more complex, largescale datasets. Action recognition on large categories of unconstrained videos taken from the web is a very challenging problem compared to datasets like KTH (six actions), IXMAS (thirteen actions), and Weizmann (ten actions). Challenges such as camera motion, different viewpoints, huge interclass variations, cluttered background, occlusions, bad illumination conditions, and poor quality of web videos cause the majority of the stateoftheart action recognition approaches to fail. An increasing number of categories and the inclusion of actions with high confusion also increase the difficulty of the problem. The approach taken to solve this action recognition problem depends primarily on the dataset and the possibility of detecting and tracking the object of interest. In this dissertation, a new method for video representation is proposed and three new approaches to perform action recognition in different scenarios using varying prerequisites are presented. The prerequisites have decreasing levels of difficulty to obtain: 1) Scenario requires human detection and tracking to perform action recognition; 2) Scenario requires background and foreground separation to perform action recognition; and 3) No preprocessing is required for action recognition.First, we propose a new video representation using optical flow and particle advection. The proposed ``Particle Flow Field'' (PFF) representation has been used to generate motion descriptors and tested in a Bag of Video Words (BoVW) framework on the KTH dataset. We show that particle flow fields has better performance than other lowlevel video representations, such as 2DGradients, 3DGradients and optical flow. Second, we analyze the performance of the stateoftheart technique based on the histogram of oriented 3DGradients in spatio temporal volumes, where human detection and tracking are required. We use the proposed particle flow field and show superior results compared to the histogram of oriented 3DGradients in spatio temporal volumes. The proposed method, when used for human action recognition, just needs human detection and does not necessarily require human tracking and figure centric bounding boxes. It has been tested on KTH (six actions), Weizmann (ten actions), and IXMAS (thirteen actions, 4 different views) action recognition datasets.Third, we propose using the scene context information obtained from moving and stationary pixels in the key frames, in conjunction with motion descriptors obtained using Bag of Words framework, to solve the action recognition problem on a large (50 actions) dataset with videos from the web. We perform a combination of early and late fusion on multiple features to handle the huge number of categories. We demonstrate that scene context is a very important feature for performing action recognition on huge datasets.The proposed method needs separation of moving and stationary pixels, and does not require any kind of video stabilization, person detection, or tracking and pruning of features. Our approach obtains good performance on a huge number of action categories. It has been tested on the UCF50 dataset with 50 action categories, which is an extension of the UCF YouTube Action (UCF11) Dataset containing 11 action categories. We also tested our approach on the KTH and HMDB51 datasets for comparison.Finally, we focus on solving practice problems in representing actions by bag of spatio temporal features (i.e. cuboids), which has proven valuable for action recognition in recent literature. We observed that the visual vocabulary based (bag of video words) method suffers from many drawbacks in practice, such as: (i) It requires an intensive training stage to obtain good performance; (ii) it is sensitive to the vocabulary size; (iii) it is unable to cope with incremental recognition problems; (iv) it is unable to recognize simultaneous multiple actions; (v) it is unable to perform recognition frame by frame. In order to overcome these drawbacks, we propose a framework to index large scale motion features using Sphere/Rectangletree (SRtree) for incremental action detection and recognition. The recognition comprises of the following two steps: 1) recognizing the local features by nonparametric nearest neighbor (NN), and 2) using a simple voting strategy to label the action. It can also provide localization of the action. Since it does not require feature quantization it can efficiently grow the featuretree by adding features from new training actions or categories. Our method provides an effective way for practical incremental action recognition. Furthermore, it can handle large scale datasets because the SRtree is a diskbased data structure. We tested our approach on two publicly available datasets, the KTH dataset and the IXMAS multiview dataset, and achieved promising results.
Show less  Date Issued
 2012
 Identifier
 CFE0004626, ucf:49923
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004626
 Title
 Curvelets and the Radon Transform.
 Creator

Dickerson, Jill, Katsevich, Alexander, Tamasan, Alexandru, Moore, Brian, University of Central Florida
 Abstract / Description

Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data...
Show moreComputed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial or truncated Radon data problems. As a result, using a curvelet representation to invert radon data allows the chance of higher quality images to be produced. This paper examines this method of reconstruction for computed tomography (CT). A brief history of CT, an introduction to the theory behind the method, and implementation details will be provided.
Show less  Date Issued
 2013
 Identifier
 CFE0004674, ucf:49852
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004674
 Title
 Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems.
 Creator

Groves, Curtis, Kassab, Alain, Das, Tuhin, Kauffman, Jeffrey, Moore, Brian, University of Central Florida
 Abstract / Description

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data...
Show moreSpacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulationbased product. The method could provide an alternative to traditional (")validation by test only(") mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, nonproprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly threedimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in (")Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations("). This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the reattachment length of a backward facing step. For the flow regime being analyzed (turbulent, threedimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.
Show less  Date Issued
 2014
 Identifier
 CFE0005174, ucf:50662
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005174
 Title
 Analysis of Behaviors in Crowd Videos.
 Creator

Mehran, Ramin, Shah, Mubarak, Sukthankar, Gita, Behal, Aman, Tappen, Marshall, Moore, Brian, University of Central Florida
 Abstract / Description

In this dissertation, we address the problem of discovery and representation of group activity of humans and objects in a variety of scenarios, commonly encountered in vision applications. The overarching goal is to devise a discriminative representation of human motion in social settings, which captures a wide variety of human activities observable in video sequences. Such motion emerges from the collective behavior of individuals and their interactions and is a significant source of...
Show moreIn this dissertation, we address the problem of discovery and representation of group activity of humans and objects in a variety of scenarios, commonly encountered in vision applications. The overarching goal is to devise a discriminative representation of human motion in social settings, which captures a wide variety of human activities observable in video sequences. Such motion emerges from the collective behavior of individuals and their interactions and is a significant source of information typically employed for applications such as event detection, behavior recognition, and activity recognition. We present new representations of human group motion for static cameras, and propose algorithms for their application to variety of problems.We first propose a method to model and learn the scene activity of a crowd using Social Force Model for the first time in the computer vision community. We present a method to densely estimate the interaction forces between people in a crowd, observed by a static camera. Latent Dirichlet Allocation (LDA) is used to learn the model of the normal activities over extended periods of time. Randomly selected spatiotemporal volumes of interaction forces are used to learn the model of normal behavior of the scene. The model encodes the latent topics of social interaction forces in the scene for normal behaviors. We classify a short video sequence of $n$ frames as normal or abnormal by using the learnt model. Once a sequence of frames is classified as an abnormal, the regions of anomalies in the abnormal frames are localized using the magnitude of interaction forces.The representation and estimation framework proposed above, however, has a few limitations. This algorithm proposes to use a global estimation of the interaction forces within the crowd. It, therefore, is incapable of identifying different groups of objects based on motion or behavior in the scene. Although the algorithm is capable of learning the normal behavior and detects the abnormality, but it is incapable of capturing the dynamics of different behaviors.To overcome these limitations, we then propose a method based on the Lagrangian framework for fluid dynamics, by introducing a streakline representation of flow. Streaklines are traced in a fluid flow by injecting color material, such as smoke or dye, which is transported with the flow and used for visualization. In the context of computer vision, streaklines may be used in a similar way to transport information about a scene, and they are obtained by repeatedly initializing a fixed grid of particles at each frame, then moving both current and past particles using optical flow. Streaklines are the locus of points that connect particles which originated from the same initial position.This approach is advantageous over the previous representations in two aspects: first, its rich representation captures the dynamics of the crowd and changes in space and time in the scene where the optical flow representation is not enough, and second, this model is capable of discovering groups of similar behavior within a crowd scene by performing motion segmentation. We propose a method to distinguish different group behaviors such as divergent/convergent motion and lanes using this framework. Finally, we introduce flow potentials as a discriminative feature to recognize crowd behaviors in a scene. Results of extensive experiments are presented for multiple real life crowd sequences involving pedestrian and vehicular traffic.The proposed method exploits optical flow as the low level feature and performs integration and clustering to obtain coherent group motion patterns. However, we observe that in crowd video sequences, as well as a variety of other vision applications, the cooccurrence and interrelation of motion patterns are the main characteristics of group behaviors. In other words, the group behavior of objects is a mixture of individual actions or behaviors in specific geometrical layout and temporal order.We, therefore, propose a new representation for group behaviors of humans using the interrelation of motion patterns in a scene. The representation is based on bag of visual phrases of spatiotemporal visual words. We present a method to match the highorder spatial layout of visual words that preserve the geometry of the visual words under similarity transformations. To perform the experiments we collected a dataset of group choreography performances from the YouTube website. The dataset currently contains four categories of group dances.
Show less  Date Issued
 2011
 Identifier
 CFE0004482, ucf:49317
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004482
 Title
 Structurepreserving finite difference methods for linearly damped differential equations.
 Creator

Bhatt, Ashish, Moore, Brian, Choudhury, Sudipto, Gurel, Basak, Kauffman, Jeffrey L., University of Central Florida
 Abstract / Description

Differential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical...
Show moreDifferential equations (DEs) model a variety of physical phenomena in science and engineering. Many physical phenomena involve conservative or dissipative forces, which manifest themselves as qualitative properties of DEs that govern these phenomena. Since only a few and simplistic models are known to have exact solutions, approximate solution techniques, such as numerical integration, are used to reveal important insights about solution behavior and properties of these models. Numerical integrators generally result in undesirable quantitative and qualitative errors . Standard numerical integrators aim to reduce quantitative errors, whereas geometric (numerical) integrators aim to reduce or eliminate qualitative errors, as well, in order to improve the accuracy of numerical solutions. It is now widely recognized that geometric (or structurepreserving) integrators are advantageous compared to nongeometric integrators for DEs, especially for long time integration.Geometric integrators for conservative DEs have been proposed, analyzed, and investigated extensively in the literature. The motif of this thesis is to extend the idea of structure preservation to linearly damped DEs. More specifically, we develop, analyze, and implement geometric integrators for linearly damped ordinary and partial differential equations (ODEs and PDEs) that possess conformal invariants, which are qualitative properties that decay exponentially along any solution of the DE as the system evolves over time. In particular, we derive restrictions on the coefficient functions of exponential RungeKutta (ERK) numerical methods for preservation of certain conformal invariants of linearly damped ODEs. An important class of these methods is shown to preserve the damping rate of solutions of damped linear ODEs. Linearly stability and order of accuracy for some specific cases of ERK methods are investigated. Geometric integrators for PDEs are designed using structurepreserving ERK methods in space, time, or both. These integrators for PDEs are also shown to preserve additional structure in certain special cases. Numerical experiments illustrate higher order accuracy and structure preservation properties of various ERK based methods, demonstrating clear advantages over nonstructurepreserving methods, as well as usefulness for solving a wide range of DEs.
Show less  Date Issued
 2016
 Identifier
 CFE0006832, ucf:51763
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006832
 Title
 Dynamical Formation of Protoplanetesimals.
 Creator

Whizin, Akbar, Colwell, Joshua, Fernandez, Yan, Klemm, Richard, Lewis, Mark, Moore, Brian, University of Central Florida
 Abstract / Description

The seeds of planetesimals that formed in the gaseous protoplanetary disk (PPD) have many barriers to overcome in their growth from millimeter to metersized and larger bodies. Centimetersized aggregates are weakly bound and selfgravity is almost nonexistent so surface forces play a critical role in holding small looselybound rubblepiles together. Their orbital motions and effects form disk processes impart relative velocities leading to collisions so understanding the macroscopic disk...
Show moreThe seeds of planetesimals that formed in the gaseous protoplanetary disk (PPD) have many barriers to overcome in their growth from millimeter to metersized and larger bodies. Centimetersized aggregates are weakly bound and selfgravity is almost nonexistent so surface forces play a critical role in holding small looselybound rubblepiles together. Their orbital motions and effects form disk processes impart relative velocities leading to collisions so understanding the macroscopic disk environment is also necessary. To this end we analyze the dynamics of particles in Saturn's F ring as an analogue to understanding the orbital evolution of protoplanetesimals embedded in a PPD. We also study how the mechanical, material, and collisional properties affect the dynamical accretion of cmsized bodies. The collisional outcomes can be determined by a set of definable collision parameters, and experimental constraints on these parameters will improve formation models for planetesimals. We have carried out a series of microgravity laboratory collision experiments of small aggregates to determine under what conditions collisional growth can occur for protoplanetary aggregates. We measure coefficients of restitution, sticking and fragmentation thresholds, compressive strengths, and sticking probabilities for collision velocities of 1  200 cm/s, then compare the results of our experiments with results from a collisional Nbody code that includes adhesion between particles. We find that cmsized aggregates are very weakly bound and require high internal cohesion to avoid fragmentation in agreement with simulations. The threshold for sticking is found to be under 10 cm/s and the fragmentation threshold near 1 m/s. Quiescent regions in the midplane of the disk may cultivate abnormally low relative velocities permitting sticking to occur (~1 cm/s), however, without a welldefined path to formation it is difficult to determine whether collisional accretion as a mechanism can overcome low thresholds for sticking and fragmentation. We discuss this research's implications to both the meterbarrier and planetesimal formation.
Show less  Date Issued
 2016
 Identifier
 CFE0006196, ucf:51103
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006196
 Title
 Recognition of Complex Events in Opensource Webscale Videos: Features, Intermediate Representations and their Temporal Interactions.
 Creator

Bhattacharya, Subhabrata, Shah, Mubarak, Guha, Ratan, Laviola II, Joseph, Sukthankar, Rahul, Moore, Brian, University of Central Florida
 Abstract / Description

Recognition of complex events in consumer uploaded Internet videos, captured under realworld settings, has emerged as a challenging area of research across both computer vision and multimedia community. In this dissertation, we present a systematic decomposition of complex events into hierarchical components and make an indepth analysis of how existing research are being used to cater to various levels of this hierarchy and identify three key stages where we make novel contributions,...
Show moreRecognition of complex events in consumer uploaded Internet videos, captured under realworld settings, has emerged as a challenging area of research across both computer vision and multimedia community. In this dissertation, we present a systematic decomposition of complex events into hierarchical components and make an indepth analysis of how existing research are being used to cater to various levels of this hierarchy and identify three key stages where we make novel contributions, keeping complex events in focus. These are listed as follows: (a) Extraction of novel semiglobal features  firstly, we introduce a Liealgebra based representation of dominant camera motion present while capturing videos and show how this can be used as a complementary feature for video analysis. Secondly, we propose compact clip level descriptors of a video based on covariance of appearance and motion features which we further use in a sparse coding framework to recognize realistic actions and gestures. (b) Construction of intermediate representations  We propose an efficient probabilistic representation from lowlevel features computed from videos, basedon Maximum Likelihood Estimates which demonstrates state of the art performancein large scale visual concept detection, and finally, (c) Modeling temporal interactions between intermediate concepts  Using block Hankel matrices and harmonic analysis of slowly evolving Linear Dynamical Systems, we propose two new discriminative feature spaces for complex event recognition and demonstratesignificantly improved recognition rates over previously proposed approaches.
Show less  Date Issued
 2013
 Identifier
 CFE0004817, ucf:49724
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004817
 Title
 Holistic Representations for Activities and Crowd Behaviors.
 Creator

Solmaz, Berkan, Shah, Mubarak, Da Vitoria Lobo, Niels, Jha, Sumit, Ilie, Marcel, Moore, Brian, University of Central Florida
 Abstract / Description

In this dissertation, we address the problem of analyzing the activities of people in a variety of scenarios, this is commonly encountered in vision applications. The overarching goal is to devise new representations for the activities, in settings where individuals or a number of people may take a part in specific activities. Different types of activities can be performed by either an individual at the fine level or by several people constituting a crowd at the coarse level. We take into...
Show moreIn this dissertation, we address the problem of analyzing the activities of people in a variety of scenarios, this is commonly encountered in vision applications. The overarching goal is to devise new representations for the activities, in settings where individuals or a number of people may take a part in specific activities. Different types of activities can be performed by either an individual at the fine level or by several people constituting a crowd at the coarse level. We take into account the domain specific information for modeling these activities. The summary of the proposed solutions is presented in the following.The holistic description of videos is appealing for visual detection and classification tasks for several reasons including capturing the spatial relations between the scene components, simplicity, and performance [1, 2, 3]. First, we present a holistic (global) frequency spectrum based descriptor for representing the atomic actions performed by individuals such as: bench pressing, diving, hand waving, boxing, playing guitar, mixing, jumping, horse riding, hula hooping etc. We model and learn these individual actions for classifying complex user uploaded videos. Our method bypasses the detection of interest points, the extraction of local video descriptors and the quantization of local descriptors into a code book; it represents each video sequence as a single feature vector. This holistic feature vector is computed by applying a bank of 3D spatiotemporal filters on the frequency spectrum of a video sequence; hence it integrates the information about the motion and scene structure. We tested our approach on two of the most challenging datasets, UCF50 [4] and HMDB51 [5], and obtained promising results which demonstrates the robustness and the discriminative power of our holistic video descriptor for classifying videos of various realistic actions.In the above approach, a holistic feature vector of a video clip is acquired by dividing the video into spatiotemporal blocks then concatenating the features of the individual blocks together. However, such a holistic representation blindly incorporates all the video regions regardless of their contribution in classification. Next, we present an approach which improves the performance of the holistic descriptors for activity recognition. In our novel method, we improve the holistic descriptors by discovering the discriminative video blocks. We measure the discriminativity of a block by examining its response to a prelearned support vector machine model. In particular, a block is considered discriminative if it responds positively for positive training samples, and negatively for negative training samples. We pose the problem of finding the optimal blocks as a problem of selecting a sparse set of blocks, which maximizes the total classifier discriminativity. Through a detailed set of experiments on benchmark datasets [6, 7, 8, 9, 5, 10], we show that our method discovers the useful regions in the videos and eliminates the ones which are confusing for classification, which results in significant performance improvement over the stateoftheart.In contrast to the scenes where an individual performs a primitive action, there may be scenes with several people, where crowd behaviors may take place. For these types of scenes the traditional approaches for recognition will not work due to severe occlusion and computational requirements. The number of videos is limited and the scenes are complicated, hence learning these behaviors is not feasible. For this problem, we present a novel approach, based on the optical flow in a video sequence, for identifying five specific and common crowd behaviors in visual scenes. In the algorithm, the scene is overlaid by a grid of particles, initializing a dynamical system which is derived from the optical flow. Numerical integration of the optical flow provides particle trajectories that represent the motion in the scene. Linearization of the dynamical system allows a simple and practical analysis and classification of the behavior through the Jacobian matrix. Essentially, the eigenvalues of this matrix are used to determine the dynamic stability of points in the flow and each type of stability corresponds to one of the five crowd behaviors. The identified crowd behaviors are (1) bottlenecks: where many pedestrians/vehicles from various points in the scene are entering through one narrow passage, (2) fountainheads: where many pedestrians/vehicles are emerging from a narrow passage only to separate in many directions, (3) lanes: where many pedestrians/vehicles are moving at the same speeds in the same direction, (4) arches or rings: where the collective motion is curved or circular, and (5) blocking: where there is a opposing motion and desired movement of groups of pedestrians is somehow prohibited. The implementation requires identifying a region of interest in the scene, and checking the eigenvalues of the Jacobian matrix in that region to determine the type of flow, that corresponds to various welldefined crowd behaviors. The eigenvalues are only considered in these regions of interest, consistent with the linear approximation and the implied behaviors. Since changes in eigenvalues can mean changes in stability, corresponding to changes in behavior, we can repeat the algorithm over clips of long video sequences to locate changes in behavior. This method was tested on over real videos representing crowd and traffic scenes.
Show less  Date Issued
 2013
 Identifier
 CFE0004941, ucf:49638
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004941