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SOLITARY WAVE FAMILIES IN TWO NON-INTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY
Title
SOLITARY WAVE FAMILIES IN TWO NON-INTEGRABLE MODELS USING REVERSIBLE SYSTEMS THEORY.
Creator
Leto, Jonathan, Choudhury, S. Roy, University of Central Florida
Abstract / Description
In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned...
Show moreIn this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned.
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Date Issued
2008
Identifier
CFE0002151, ucf:47930
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002151
MODELING SCENES AND HUMAN ACTIVITIES IN VIDEOS
Title
MODELING SCENES AND HUMAN ACTIVITIES IN VIDEOS.
Creator
Basharat, Arslan, Shah, Mubarak, University of Central Florida
Abstract / Description
In this dissertation, we address the problem of understanding human activities in videos by developing a two-pronged approach: coarse level modeling of scene activities and fine level modeling of individual activities. At the coarse level, where the resolution of the video is low, we rely on person tracks. At the fine level, richer features are available to identify different parts of the human body, therefore we rely on the body joint tracks. There are three main goals of this dissertation: ...
Show moreIn this dissertation, we address the problem of understanding human activities in videos by developing a two-pronged approach: coarse level modeling of scene activities and fine level modeling of individual activities. At the coarse level, where the resolution of the video is low, we rely on person tracks. At the fine level, richer features are available to identify different parts of the human body, therefore we rely on the body joint tracks. There are three main goals of this dissertation: (1) identify unusual activities at the coarse level, (2) recognize different activities at the fine level, and (3) predict the behavior for synthesizing and tracking activities at the fine level. The first goal is addressed by modeling activities at the coarse level through two novel and complementing approaches. The first approach learns the behavior of individuals by capturing the patterns of motion and size of objects in a compact model. Probability density function (pdf) at each pixel is modeled as a multivariate Gaussian Mixture Model (GMM), which is learnt using unsupervised expectation maximization (EM). In contrast, the second approach learns the interaction of object pairs concurrently present in the scene. This can be useful in detecting more complex activities than those modeled by the first approach. We use a 14-dimensional Kernel Density Estimation (KDE) that captures motion and size of concurrently tracked objects. The proposed models have been successfully used to automatically detect activities like unusual person drop-off and pickup, jaywalking, etc. The second and third goals of modeling human activities at the fine level are addressed by employing concepts from theory of chaos and non-linear dynamical systems. We show that the proposed model is useful for recognition and prediction of the underlying dynamics of human activities. We treat the trajectories of human body joints as the observed time series generated from an underlying dynamical system. The observed data is used to reconstruct a phase (or state) space of appropriate dimension by employing the delay-embedding technique. This transformation is performed without assuming an exact model of the underlying dynamics and provides a characteristic representation that will prove to be vital for recognition and prediction tasks. For recognition, properties of phase space are captured in terms of dynamical and metric invariants, which include the Lyapunov exponent, correlation integral, and correlation dimension. A composite feature vector containing these invariants represents the action and will be used for classification. For prediction, kernel regression is used in the phase space to compute predictions with a specified initial condition. This approach has the advantage of modeling dynamics without making any assumptions about the exact form (polynomial, radial basis, etc.) of the mapping function. We demonstrate the utility of these predictions for human activity synthesis and tracking.
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Date Issued
2009
Identifier
CFE0002897, ucf:48042
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002897
A Comparative Evaluation of FDSA,GA, and SA Non-Linear Programming Algorithms and Development of System-Optimal Dynamic Congestion Pricing Methodology on I-95 Express
Title
A Comparative Evaluation of FDSA,GA, and SA Non-Linear Programming Algorithms and Development of System-Optimal Dynamic Congestion Pricing Methodology on I-95 Express.
Creator
Graham, Don, Radwan, Ahmed, Abdel-Aty, Mohamed, Al-Deek, Haitham, Uddin, Nizam, University of Central Florida
Abstract / Description
As urban population across the globe increases, the demand for adequatetransportation grows. Several strategies have been suggested as a solution to the congestion which results from this high demand outpacing the existing supply of transportation facilities.High (-)Occupancy Toll (HOT) lanes have become increasingly more popular as a feature on today's highway system. The I-95 Express HOT lane in Miami Florida, which is currently being expanded from a single Phase (Phase I) into two Phases,...
Show moreAs urban population across the globe increases, the demand for adequatetransportation grows. Several strategies have been suggested as a solution to the congestion which results from this high demand outpacing the existing supply of transportation facilities.High (-)Occupancy Toll (HOT) lanes have become increasingly more popular as a feature on today's highway system. The I-95 Express HOT lane in Miami Florida, which is currently being expanded from a single Phase (Phase I) into two Phases, is one such HOT facility. With the growing abundance of such facilities comes the need for in- depth study of demand patterns and development of an appropriate pricing scheme which reduces congestion.This research develops a method for dynamic pricing on the I-95 HOT facility such as to minimize total travel time and reduce congestion. We apply non-linear programming (NLP) techniques and the finite difference stochastic approximation (FDSA), genetic algorithm (GA) and simulated annealing (SA) stochastic algorithms to formulate and solve the problem within a cell transmission framework. The solution produced is the optimal flow and optimal toll required to minimize total travel time and thus is the system-optimal solution.We perform a comparative evaluation of FDSA, GA and SA non-linear programmingalgorithms used to solve the NLP and the ANOVA results show that there are differences in the performance of the NLP algorithms in solving this problem and reducing travel time. We then conclude by demonstrating that econometric forecasting methods utilizing vector autoregressive (VAR) techniques can be applied to successfully forecast demand for Phase 2 of the 95 Express which is planned for 2014.
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Date Issued
2013
Identifier
CFE0005000, ucf:50019
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005000