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MODELING INTER-PLANT INTERACTIONS
Title
MODELING INTER-PLANT INTERACTIONS.
Creator
Larson, Jessica, Kaup, David, University of Central Florida
Abstract / Description
The purpose of this paper is to examine the interactions between two plant species endemic to Florida and develop a model for the growth of one of the plant species. An equation for the growth of Hypericum cumulicola is developed through analyzing how the distance to and the height of the nearest Ceratiola ericoides (Florida rosemary) affects the growth of Hypericum cumulicola. The hypericums were separated into five separate regions according to the distance to the nearest rosemary plant....
Show moreThe purpose of this paper is to examine the interactions between two plant species endemic to Florida and develop a model for the growth of one of the plant species. An equation for the growth of Hypericum cumulicola is developed through analyzing how the distance to and the height of the nearest Ceratiola ericoides (Florida rosemary) affects the growth of Hypericum cumulicola. The hypericums were separated into five separate regions according to the distance to the nearest rosemary plant. The parameters for a basic growth equation were obtained in each of the five regions and compared to each other along with the average deviations in each of the five regions. Analysis of the five separate regions aided in the creation of different growth equations that each encompassed all of the regions together. Four different growth equations are developed and then compared and analyzed for their accuracy.
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Date Issued
2006
Identifier
CFE0001374, ucf:46998
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001374
SOLITON SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING VARIATIONAL APPROXIMATIONS AND INVERSE SCATTERING TECHNIQUES
Title
SOLITON SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING VARIATIONAL APPROXIMATIONS AND INVERSE SCATTERING TECHNIQUES.
Creator
Vogel, Thomas, Kaup, David, University of Central Florida
Abstract / Description
Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of...
Show moreThroughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the error of a variational approximation is established. Note that the material in chapter 2, "Quantitative Measurements of Variational Approximations" has recently been published. Variational problems have long been used to mathematically model physical systems. Their advantage has been the simplicity of the model as well as the ability to deduce information concerning the functional dependence of the system on various parameters embedded in the variational trial functions. However, the only method in use for estimating the error in a variational approximation has been to compare the variational result to the exact solution. In this work, it is demonstrated that one can computationally obtain estimates of the errors in a one-dimensional variational approximation, without any a priori knowledge of the exact solution. Additionally, this analysis can be done by using only linear techniques. The extension of this method to multidimensional problems is clearly possible, although one could expect that additional difficulties would arise. One condition for the existence of a localized soliton is that the propagation constant does not fall into the continuous spectrum of radiation modes. For a higher order dispersive systems, the linear dispersion relation exhibits a multiple branch structure. It could be the case that in a certain parameter region for which one of the components of the solution has oscillations (i.e., is in the continuous spectrum), there exists a discrete value of the propagation constant, k(ES), for which the oscillations have zero amplitude. The associated solution is referred to as an embedded soliton (ES). This work examines the ES solutions in a CHI(2):CHI(3), type II system. The method employed in searching for the ES solutions is a variational method recently developed by Kaup and Malomed [Phys. D 184, 153-61 (2003)] to locate ES solutions in a SHG system. The variational results are validated by numerical integration of the governing system. A model used for the 1-D longitudinal wave propagation in microstructured solids is a KdV-type equation with third and fifth order dispersions as well as first and third order nonlinearities. Recent work by Ilison and Salupere (2004) has identified certain types of soliton solutions in the aforementioned model. The present work expands the known family of soliton solutions in the model to include embedded solitons. The existence of embedded solitons with respect to the dispersion parameters is determined by a variational approximation. The variational results are validated with selected numerical solutions.
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Date Issued
2007
Identifier
CFE0001800, ucf:47379
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0001800
TOWARDS CALIBRATION OF OPTICAL FLOW OF CROWD VIDEOS USING OBSERVED TRAJECTORIES
Title
TOWARDS CALIBRATION OF OPTICAL FLOW OF CROWD VIDEOS USING OBSERVED TRAJECTORIES.
Creator
Elbadramany, Iman, Kaup, David, University of Central Florida
Abstract / Description
The need exists for finding a quantitative method for validating crowd simulations. One approach is to use optical flow of videos of real crowds to obtain velocities that can be used for comparison to simulations. Optical flow, in turn, needs to be calibrated to be useful. It is essential to show that optical flow velocities obtained from crowd videos can be mapped into the spatially averaged velocities of the observed trajectories of crowd members, and to quantify the extent of the...
Show moreThe need exists for finding a quantitative method for validating crowd simulations. One approach is to use optical flow of videos of real crowds to obtain velocities that can be used for comparison to simulations. Optical flow, in turn, needs to be calibrated to be useful. It is essential to show that optical flow velocities obtained from crowd videos can be mapped into the spatially averaged velocities of the observed trajectories of crowd members, and to quantify the extent of the correlation of the results. This research investigates methods to uncover the best conditions for a good correlation between optical flow and the average motion of individuals in crowd videos, with the aim that this will help in the quantitative validation of simulations. The first approach was to use a simple linear proportionality relation, with a single coefficient, alpha, between velocity vector of the optical flow and observed velocity of crowd members in a video or simulation. Since there are many variables that affect alpha, an attempt was made to find the best possible conditions for determining alpha, by varying experimental and optical flow settings. The measure of a good alpha was chosen to be that alpha does not vary excessively over a number of video frames. Best conditions of low coefficient of variation of alpha using the Lucas-Kanade optical flow algorithm were found to be when a larger aperture of 15x15 pixels was used, combined with a smaller threshold. Adequate results were found at cell size 40x40 pixels; the improvement in detecting details when smaller cells are used did not reduce the variability of alpha, and required much more computing power. Reduction in variability of alpha can be obtained by spreading the tracked location of a crowd member from a pixel into a rectangle. The Particle Image Velocimetry optical flow algorithm had better correspondence with the velocity vectors of manually tracked crowd members than results obtained using the Lukas-Kanade method. Here, also, it was found that 40x40 pixel cells were better than 15x15. A second attempt at quantifying the correlation between optical flow and actual crowd member velocities was studied using simulations. Two processes were researched, which utilized geometrical correction of the perspective distortion of the crowd videos. One process geometrically corrects the video, and then obtains optical flow data. The other obtains optical flow data from video, and then geometrically corrects the data. The results indicate that the first process worked better. Correlation was calculated between sets of data obtained from the average of twenty frames. This was found to be higher than calculating correlations between the velocities of cells in each pair of frames. An experiment was carried out to predict crowd tracks using optical flow and a calculated parameter, beta, seems to give promising results.
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Date Issued
2011
Identifier
CFE0004024, ucf:49175
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004024
OPTICAL PROPAGATION OF SELF-SUSTAINING WAVEFRONTS AND NONLINEAR DYNAMICS IN PARABOLIC MULTIMODE FIBERS
Title
OPTICAL PROPAGATION OF SELF-SUSTAINING WAVEFRONTS AND NONLINEAR DYNAMICS IN PARABOLIC MULTIMODE FIBERS.
Creator
Mills, Matthew, Christodoulides, Demetrios, Hagan, David, Dogariu, Aristide, Kaup, David, University of Central Florida
Abstract / Description
The aim of this thesis is to introduce my work which has generally been focused on opticalwavefronts that have the unusual property of resisting commonplace phenomena such as diffraction and dispersion. Interestingly, these special beams are found both in linear and nonlinear situations. For example, in the linear regime, localized spatio-temporal waves which resemble the spherical harmonic symmetries of the hydrogen quantum orbitals can simultaneously negotiate both diffractive and...
Show moreThe aim of this thesis is to introduce my work which has generally been focused on opticalwavefronts that have the unusual property of resisting commonplace phenomena such as diffraction and dispersion. Interestingly, these special beams are found both in linear and nonlinear situations. For example, in the linear regime, localized spatio-temporal waves which resemble the spherical harmonic symmetries of the hydrogen quantum orbitals can simultaneously negotiate both diffractive and dispersiveeffects. In the nonlinear regime, dressed optical filaments can be arranged to propagate multi-photon produced plasma channels orders of magnitude longer than expected.The first portion of this dissertation will begin by surveying the history of diffraction-free beamsand introducing some of their mathematical treatments. Interjected throughout this discussion will be several relevant concepts which I explored during my first years a CREOL. The discussion will then be steered into a detailed account of diffraction/dispersion free wavefronts which display hydrogen-like symmetries. The second segment of the document will cover the highly nonlinear process of optical filamentation. This chapter will almost entirely investigate the idea of the dressed filament, an entity which allows for substantial prolongation of this light string. I will then conclude by delving into the topicof supercontinuum generation in parabolic multimode fibers which, in the upcoming years, has great potential of becoming important in optics.
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Date Issued
2015
Identifier
CFE0005977, ucf:50767
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005977
Modeling the Standard and Poor's 500 Index via Wave Analytics: Harnessing Lag for Intraday Utilizations
Title
Modeling the Standard and Poor's 500 Index via Wave Analytics: Harnessing Lag for Intraday Utilizations.
Creator
Cardenas, John, Morrow, Patricia Bockelman, Kaup, David, Akbas, Mustafa, University of Central Florida
Abstract / Description
ABSTRACT Modeling and simulation of financial instruments is accomplished from multiple approaches but most completely from an engineering perspective. Aeronautical engineering yields a wave model created for stock indices in the 1970s. This comprehensive methodology models stock markets as waves for the intention of trading or investing yet has not been applied on time periods smaller than daily or weekly, known as intraday. Stakeholders trading intraday waves need to utilize wave analysis...
Show moreABSTRACT Modeling and simulation of financial instruments is accomplished from multiple approaches but most completely from an engineering perspective. Aeronautical engineering yields a wave model created for stock indices in the 1970s. This comprehensive methodology models stock markets as waves for the intention of trading or investing yet has not been applied on time periods smaller than daily or weekly, known as intraday. Stakeholders trading intraday waves need to utilize wave analysis for price capture, analytics, and profitability. It is the purpose of this thesis to present a model to harness wave analytics for the needs of traders seeking price capture of the Standard and Poor's 500 Index on an hourly and minute time periods, or intraday. This paper applies wave analytics in time frames never accomplished before for the sufficing the needs of index day traders.
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Date Issued
2018
Identifier
CFE0007394, ucf:52055
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007394
Non-Hermitian Optics
Title
Non-Hermitian Optics.
Creator
Ulhassan, Absar, Christodoulides, Demetrios, Khajavikhan, Mercedeh, Likamwa, Patrick, Kaup, David, University of Central Florida
Abstract / Description
From the viewpoint of quantum mechanics, a system must always be Hermitian since all its corresponding eigenvalues must be real. In contrast, the eigenvalues of open systems-unrestrained because of either decay or amplification-can be in general complex. Not so long ago, a certain class of non-Hermitian Hamiltonians was discovered that could have a completely real eigenvalue spectrum. This special class of Hamiltonians was found to respect the property of commutation with the parity-time (PT)...
Show moreFrom the viewpoint of quantum mechanics, a system must always be Hermitian since all its corresponding eigenvalues must be real. In contrast, the eigenvalues of open systems-unrestrained because of either decay or amplification-can be in general complex. Not so long ago, a certain class of non-Hermitian Hamiltonians was discovered that could have a completely real eigenvalue spectrum. This special class of Hamiltonians was found to respect the property of commutation with the parity-time (PT) operator. Translated into optics, this implies a balance between regions exhibiting gain and loss. Traditionally, loss has been perceived as a foe in optics and something that needs to be avoided at all costs. As we will show, when used in conjunction with gain, the presence of loss can lead to a host of counterintuitive outcomes in such non-Hermitian configurations that would have been otherwise unattainable in standard arrangements. We will study PT symmetric phase transitions in various optical settings that include semiconductor microrings and coupled fiber cavities, and show how they can allow mode-selectivity in lasers. One of the key outcomes of this effort was the realization of higher order degeneracies in a three-cavity laser configuration that can exhibit orders-of-magnitude larger sensitivity to external perturbations. We will also consider systems that display nonlinear effects such as gain saturation, thus allowing novel phase transitions. Some interesting properties associated with degeneracies in non-Hermitian settings will be investigated as well. Such degeneracies, called exceptional points (EPs), are much more drastic compared to standard degeneracies of eigenvalues because the corresponding eigenvectors also coalesce, which in turn reduces the dimensionality of the phase space. We will show that dynamic parameter contours enclosing or close to EPs can lead to a robust chiral mode conversion process (-) something that can be potentially used to realize omni-polarizing optical devices.
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Date Issued
2018
Identifier
CFE0007259, ucf:52182
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007259
Non-Hermitian and Space-Time Mode Management
Title
Non-Hermitian and Space-Time Mode Management.
Creator
Nye, Nicholas, Christodoulides, Demetrios, Khajavikhan, Mercedeh, Abouraddy, Ayman, Kaup, David, University of Central Florida
Abstract / Description
In the last few years, optics has witnessed the emergence of two fields namely metasurfaces and parity-time (PT) symmetry. Optical metasurfaces are engineered structures that provide unique responses to electromagnetic waves, absent in natural materials. On the other hand, PT symmetry has emerged from quantum mechanics, when a new class of non-Hermitian Hamiltonian quantum systems was shown to have real eigenvalues. In this work, we demonstrate how PT-symmetric diffractive structures are...
Show moreIn the last few years, optics has witnessed the emergence of two fields namely metasurfaces and parity-time (PT) symmetry. Optical metasurfaces are engineered structures that provide unique responses to electromagnetic waves, absent in natural materials. On the other hand, PT symmetry has emerged from quantum mechanics, when a new class of non-Hermitian Hamiltonian quantum systems was shown to have real eigenvalues. In this work, we demonstrate how PT-symmetric diffractive structures are capable of eliminating diffraction orders in specific directions, while maintaining/enhancing the remaining orders. In the second part of this work, we emphasize on supersymmetry (SUSY) and its applications in optics. Even though the full ramification of SUSY in high-energy physics is still a matter of debate that awaits experimental validation, supersymmetric techniques have already found their way into low-energy physics. In this work, we apply certain isospectral techniques in order to achieve single mode lasing in multi-element waveguide systems, where multimode chaotic emission is expected. In the third part of this dissertation, we emphasize on dynamically reconfigurable nanoparticle platforms. By exploiting the dielectrophoresis effect, we demonstrate how controllable lasing can be achieved in random photonic arrangements. Although this work focuses on the case of controlling random lasers, we expect that the proposed nanoparticle architecture can incorporate heterogeneous materials of a wide range of optical functionalities, including gain, scattering, plasmonic resonance, and nonlinearity. In the last part of the dissertation, we demonstrate the capability of synthesizing space-time (ST) wave packets, based on new propagation-invariant elementary solutions of the wave equation identified through a complexification of the spatial and temporal degrees of freedom. By establishing the connection between ST propagation-invariant pulses and tilted-pulse-front pulses, a path is opened to exploiting the unique attributes of such wave packets both in nonlinear and quantum optics.
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Date Issued
2019
Identifier
CFE0007896, ucf:52780
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007896
Non-Reciprocal Wave Transmission in Integrated Waveguide Array Isolators
Title
Non-Reciprocal Wave Transmission in Integrated Waveguide Array Isolators.
Creator
Ho, Yat, Likamwa, Patrick, Christodoulides, Demetrios, Vanstryland, Eric, Kaup, David, University of Central Florida
Abstract / Description
Non-reciprocal wave transmission is a phenomenon witnessed in certain photonic devices when the wave propagation dynamics through the device along one direction differs greatly from the dynamics along the counter-propagating direction. Specifically, it refers to significant power transfer occurring in one direction, and greatly reduced power transfer in the opposite direction. The resulting effect is to isolate the directionality of wave propagation, allowing transmission to occur along one...
Show moreNon-reciprocal wave transmission is a phenomenon witnessed in certain photonic devices when the wave propagation dynamics through the device along one direction differs greatly from the dynamics along the counter-propagating direction. Specifically, it refers to significant power transfer occurring in one direction, and greatly reduced power transfer in the opposite direction. The resulting effect is to isolate the directionality of wave propagation, allowing transmission to occur along one direction only.Given the popularity of photonic integrated circuits (PIC), in which all the optical components are fabricated on the same chip so that the entire optical system can be made more compact, it is desirable to have an easily integrated optical isolator. Common free-space optical isolator designs, which rely on the Faraday effect, are limited by the availability of suitable magnetic materials. This research proposes a novel integrated optical isolator based on an array of closely spaced, identical waveguides. Because of the nonlinear optical properties of the material, this device exploits the differing behaviors of such an array when illuminated with either a high power or a low power beam to achieve non-reciprocal wave transmission in the forwards and backwards directions, respectively. The switching can be controlled electro-optically via an integrated gain section which provides optical amplification before the input to the array. The design, fabrication, characterization and testing of this optical isolator are covered in this dissertation. We study the switching dynamics of this device and present its optimum operating conditions. ?
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Date Issued
2012
Identifier
CFE0004305, ucf:49495
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004305
Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic
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 steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison 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 steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison 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.
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Date Issued
2015
Identifier
CFE0005831, ucf:50903
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005831
Modeling Network Worm Outbreaks
Title
Modeling Network Worm Outbreaks.
Creator
Foley, Evan, Shuai, Zhisheng, Kaup, David, Nevai, A, University of Central Florida
Abstract / Description
Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible,...
Show moreDue to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across the infection period, while pouring resources into treating susceptible computers decreases the total amount of infections throughout the infection period. This is assuming both methods are receiving resources without loss. This result reveals an interesting notion of balance between protecting computers and removing computers from infections, ultimately depending on the business executives' goals and/or preferences.
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Date Issued
2015
Identifier
CFE0005948, ucf:50816
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005948
Comparing the Variational Approximation and Exact Solutions of the Straight Unstaggered and Twisted Staggered Discrete Solitons
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 Bose-Einstein condensates which are trapped in deep optical-lattice 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 Bose-Einstein condensates which are trapped in deep optical-lattice 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 on-site-centered 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 unstaggered-twisted 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.
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Date Issued
2016
Identifier
CFE0006350, ucf:51570
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006350
Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related to Musical Instruments
Title
Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related to Musical Instruments.
Creator
Adams, Christine, Nashed, M, Mohapatra, Ram, Kaup, David, University of Central Florida
Abstract / Description
The central theme of this thesis deals with problems related to the question, (")Can one hear the shape of a drum?(") first posed formally by Mark Kac in 1966. More precisely, can one determine the shape of a membrane with fixed boundary from the spectrum of the associated differential operator? For this paper, Kac received both the Lester Ford Award and the Chauvant Prize of the Mathematical Association of America. This problem has received a great deal of attention in the past forty years...
Show moreThe central theme of this thesis deals with problems related to the question, (")Can one hear the shape of a drum?(") first posed formally by Mark Kac in 1966. More precisely, can one determine the shape of a membrane with fixed boundary from the spectrum of the associated differential operator? For this paper, Kac received both the Lester Ford Award and the Chauvant Prize of the Mathematical Association of America. This problem has received a great deal of attention in the past forty years and has led to similar questions in completely different contexts such as (")Can one hear the shape of a graph associated with the Schr(&)#246;dinger operator?("), (")Can you hear the shape of your throat?("), (")Can you feel the shape of a manifold with Brownian motion?("), (")Can one hear the crack in a beam?("), (")Can one hear into the sun?("), etc. Each of these topics deals with inverse eigenvalue problems or related inverse problems. For inverse problems in general, the problem may or may not have a solution, the solution may not be unique, and the solution does not necessarily depend continuously on perturbation of the data. For example, in the case of the drum, it has been shown that the answer to Kac's question in general is (")no.(") However, if we restrict the class of drums, then the answer can be yes. This is typical of inverse problems when a priori information and restriction of the class of admissible solutions and/or data are used to make the problem well-posed. This thesis provides an analysis of shapes for which the answer to Kac's question is positive and a variety of interesting questions on this problem and its variants, including cases that remain open. This thesis also provides a synopsis and perspectives of other types of (")can one hear(") problems mentioned above. Another part of this thesis deals with aspects of direct problems related to musical instruments.
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Date Issued
2013
Identifier
CFE0004643, ucf:49886
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004643
Nonlinear Dynamics in Multimode Optical Fibers
Title
Nonlinear Dynamics in Multimode Optical Fibers.
Creator
Eftekhar, Mohammad Amin, Christodoulides, Demetrios, Amezcua Correa, Rodrigo, Li, Guifang, Kaup, David, University of Central Florida
Abstract / Description
Multimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. The complex nature of heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we have studied nonlinear dynamics in multimode optical fibers (MMFs) in both the normal...
Show moreMultimode optical fibers have recently reemerged as a viable platform for addressing a number of long-standing issues associated with information bandwidth requirements and power-handling capabilities. The complex nature of heavily multimoded systems can be effectively exploited to observe altogether novel physical effects arising from spatiotemporal and intermodal linear and nonlinear processes. Here, we have studied nonlinear dynamics in multimode optical fibers (MMFs) in both the normal and anomalous dispersion regimes. In the anomalous dispersion regime, the nonlinearity leads to a formation of spatiotemporal 3-D solitons. Unlike in single-mode fibers, these solitons are not unique and their properties can be modified through the additional degrees of freedom offered by these multimoded settings. In addition, soliton related processes such as soliton fission and dispersive wave generation will be also drastically altered in such multimode systems. Our theoretical work unravels some of the complexities of the underlying dynamics and helps us better understand these effects. The nonlinear dynamics in such multimode systems can be accelerated through a judicious fiber design. A cancelation of Raman self-frequency shifts and Blue-shifting multimode solitons were observed in such settings as a result of an acceleration of intermodal oscillations. Spatiotemporal instabilities in parabolic-index multimode fibers will also be discussed. In the normal dispersion regime, this effect can be exploited to generate an ultrabroad and uniform supercontinuum that extends more than 2.5 octaves. To do so, the unstable spectral regions are pushed away from the pump, thus sweeping the entire spectrum. Multimode parabolic pulses were also predicted and observed in passive normally dispersive tapered MMFs. These setting can obviate the harsh bandwidth limitation present in single-mode system imposed by gain medium and be effectively used for realizing high power multimode fiber lasers. Finally, an instant and efficient second-harmonic generation was observed in the multimode optical fibers. Through a modification of initial conditions, the efficiency of this process could be enhanced to a record high of %6.5.
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Date Issued
2018
Identifier
CFE0007399, ucf:52063
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007399
An Integrated Framework for Automated Data Collection and Processing for Discrete Event Simulation Models
Title
An Integrated Framework for Automated Data Collection and Processing for Discrete Event Simulation Models.
Creator
Rodriguez, Carlos, Kincaid, John, Karwowski, Waldemar, O'Neal, Thomas, Kaup, David, Mouloua, Mustapha, University of Central Florida
Abstract / Description
Discrete Events Simulation (DES) is a powerful tool of modeling and analysis used in different disciplines. DES models require data in order to determine the different parameters that drive the simulations. The literature about DES input data management indicates that the preparation of necessary input data is often a highly manual process, which causes inefficiencies, significant time consumption and a negative user experience.The focus of this research investigation is addressing the manual...
Show moreDiscrete Events Simulation (DES) is a powerful tool of modeling and analysis used in different disciplines. DES models require data in order to determine the different parameters that drive the simulations. The literature about DES input data management indicates that the preparation of necessary input data is often a highly manual process, which causes inefficiencies, significant time consumption and a negative user experience.The focus of this research investigation is addressing the manual data collection and processing (MDCAP) problem prevalent in DES projects. This research investigation presents an integrated framework to solve the MDCAP problem by classifying the data needed for DES projects into three generic classes. Such classification permits automating and streamlining the preparation of the data, allowing DES modelers to collect, update, visualize, fit, validate, tally and test data in real-time, by performing intuitive actions. In addition to the proposed theoretical framework, this project introduces an innovative user interface that was programmed based on the ideas of the proposed framework. The interface is called DESI, which stands for Discrete Event Simulation Inputs.The proposed integrated framework to automate DES input data preparation was evaluated against benchmark measures presented in the literature in order to show its positive impact in DES input data management. This research investigation demonstrates that the proposed framework, instantiated by the DESI interface, addresses current gaps in the field, reduces the time devoted to input data management within DES projects and advances the state-of-the-art in DES input data management automation.
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Date Issued
2015
Identifier
CFE0005878, ucf:50861
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005878
Nonlinear dispersive partial differential equations of physical relevance with applications to vortex dynamics
Title
Nonlinear dispersive partial differential equations of physical relevance with applications to vortex dynamics.
Creator
VanGorder, Robert, Kaup, David, Vajravelu, Kuppalapalle, Nevai, Andrew, Mohapatra, Ram, Kassab, Alain, University of Central Florida
Abstract / Description
Nonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex partial differential equations, vector partial differential equations, and finally non-local integro-differential equations. For physically interesting families of these equations, we demonstrate the existence (and, when possible, stability) of specific solutions which are relevant for applications....
Show moreNonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex partial differential equations, vector partial differential equations, and finally non-local integro-differential equations. For physically interesting families of these equations, we demonstrate the existence (and, when possible, stability) of specific solutions which are relevant for applications. While multiple application areas are considered, the primary application that runs through the work would be the nonlinear dynamics of vortex filaments under a variety of physical models. For instance, we are able to determine the structure and time evolution of several physical solutions, including the planar, helical, self-similar and soliton vortex filament solutions in a quantum fluid. Properties of such solutions are determined analytically and numerically through a variety of approaches. Starting with complex scalar equations (often useful for studying two-dimensional motion), we progress through more complicated models involving vector partial differential equations and non-local equations (which permit motion in three dimensions). In many of the examples considered, the qualitative analytical results are used to verify behaviors previously observed only numerically or experimentally.
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Date Issued
2014
Identifier
CFE0005272, ucf:50545
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005272