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Title: Gravitational signature of core-collapse supernova results of CHIMERA simulations.
Creator: Yakunin, Konstantin., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of...
Show moreCore-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state., Based on the results of our simulations, I produced the most realistic gravitational waveforms including all postbounce phases of core-collapse supernovae: the prompt convection, the stationary accretion shock instability, and the corresponding explosion. Additionally, the tracer particles applied in the analysis of the GW signal reveal the origin of low-frequency component in the prompt part of gravitational waveform. Analysis of detectability of the GW signature from a Galactic event shows that the signal is within the band-pass of current and future GW observatories such as AdvLIGO, advanced Virgo, and LCGT.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3322512
Subject Headings: Mathematical physics, Continuum mechanics, Supernovae, Mathematical models
Format: Document (PDF)

Title: Structured flows on manifolds: distributed functional architectures.
Creator: Pillai, Ajay S., Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description: Despite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a...
Show moreDespite the high-dimensional nature of the nervous system, humans produce low-dimensional cognitive and behavioral dynamics. How high-dimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of non-linear dynamical systems and Synergetics and can be used to understand how high-dimensional systems that exhibit multiple time-scale behavior can produce low-dimensional dynamics. Low-dimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The low-dimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion, (removal of nodes) on network dynamics. It is also shown how low-dimensional functional dynamics can be obtained from firing-rate neuron models by placing biologically realistic constraints on the coupling. Finally the theoretical framework is applied to real data. Using the structured flows on manifolds approach we quantify team performance and team coordination and develop objective measures of team performance based on skill level.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/77649
Subject Headings: Manifolds (Mathematics), Differentiable dynamical systems, Mathematical physics
Format: Document (PDF)

Title: THE IDENTIFICATION OF AND SUGGESTED PROVISIONS FOR THE TEACHING OF THE MATHEMATICAL CONCEPTS NECESSARY FOR SUCCESS IN A COURSE OF PSSC PHYSICS.
Creator: DOUTHAT, JAMES ROBERT, JR., Florida Atlantic University
Abstract/Description: This thesis was prepared out of the necessity for an identification of the concepts of mathematics used in PSSC physics. First, a survey of past and current educational journals was used to establish general mathematical prerequisites for PSSC physics. Then the necessary mathematical concepts as conceived by the authors of the PSSC textbook are discussed, with no attempt to state the level of proficiency required in behavioral terms for the identified topics. A survey of the literature was...
Show moreThis thesis was prepared out of the necessity for an identification of the concepts of mathematics used in PSSC physics. First, a survey of past and current educational journals was used to establish general mathematical prerequisites for PSSC physics. Then the necessary mathematical concepts as conceived by the authors of the PSSC textbook are discussed, with no attempt to state the level of proficiency required in behavioral terms for the identified topics. A survey of the literature was made in order to suggest provisions for the teaching of these concepts. These suggestions take the form of mathematics-physics curriculum changes such as integrated mathematics-physics courses, fusion of science applications into the mathematics curriculum, and the institution of a mathematics course specifically designed to prepare students for the study of physics.
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Date Issued: 1971
PURL: http://purl.flvc.org/fcla/dt/13451
Subject Headings: Physics--Study and teaching, Mathematical ability, Mathematical physics
Format: Document (PDF)

Title: Application of QKKR method to complex crystals.
Creator: Wang, Yang, Florida Atlantic University, Faulkner, J. Samuel
Abstract/Description: The QKKR method is a recently invented band theory with remarkable advantages of fast computational speed and no special requirements on the one electron potential. It has been successfully applied to the band structure calculation for simple crystals. A program for QKKR band theory calculations for complex crystals (more than one atom per unit cell) is developed and applied to PdH. It is shown that, compared with the KKR method, the QKKR method is more efficient and yields very accurate...
Show moreThe QKKR method is a recently invented band theory with remarkable advantages of fast computational speed and no special requirements on the one electron potential. It has been successfully applied to the band structure calculation for simple crystals. A program for QKKR band theory calculations for complex crystals (more than one atom per unit cell) is developed and applied to PdH. It is shown that, compared with the KKR method, the QKKR method is more efficient and yields very accurate results in the range of energies in which we are interested. Unlike other band theories, the QKKR requires the expansion of a three dimensional step function in real spherical harmonics. A general method for evaluating this expansion is established in this thesis.
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Date Issued: 1989
PURL: http://purl.flvc.org/fcla/dt/14529
Subject Headings: Crystallography, Mathematical, Multiple scattering (Physics)
Format: Document (PDF)

Title: Coset intersection problem and application to 3-nets.
Creator: Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all...
Show moreIn a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3355866
Subject Headings: Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
Format: Document (PDF)

Title: First-principles study of metastable phases and structural anomalies of Fe, Al, Zn, and Cd under pressure.
Creator: Apostol, Florin., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Stable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of...
Show moreStable and metastable phases of Fe and Al and structural anomalies of Zn and Cd have been studied by epitaxial Bain path (EBP) and minimum path (MNP) first-principles procedures, based on finding equilibrium structures from minimizing the Gibbs free energy G with respect to structure at a given hydrostatic pressure p and temperature T . The main accomplishments are as follows. (1) This dissertation illustrates the effectiveness of the MNP procedure for finding stable and metastable phases of an element by studying four Bravais phases of Fe including body-centered tetragonal (bct), body-centered cubic (bcc), face-centered cubic (fcc) and rhombohedral (rh) phases. The determination of absolute stability using MNP is new; MNP finds all the elastic constants cjj of a given state and the eigenvalues of the elastic constants matrix, which determine the absolute stability of the state., (2) We have extended our search for stable and metastable phases from zero temperature to finite temperature, which requires the calculations of the Debye temperature Od from cjj in the case of no symmetry. The Debye theory is modified by introducing a parameter B2 that gives the fraction of the full Debye zero-point energy possessed by the actual dispersive mode frequencies. The value of the lattice parameter of fcc Al at low temperatures,a(T) , is shown to be accurately determined by the modified Debye theory of lattice vibrations and first-principles total energy band calculations with the MNP procedure. (3) The existence of structural anomalies in hcp Zn and Cd has been shown from first-principles total-energy calculations using WIEN2k with the EBP procedure., Evaluation of the pressure dependence of various elastic quantities which are much more sensitive to the anomaly shows that the anomalies in hcp Zn and hcp Cd exist over a considerable range of pressure; several abrupt changes in the electron distribution are thereby indicated in that pressure range. (4) Calculations on the zone-center transverse optical phonon frequencies Vto(p) of hcp Zn, which found oscillatory behavior of Vto(p) in the pressure range of the anomalies, support the conclusions made in (3) on the structural anomalies. Based on this dissertation research four papers have been published in refereed journals.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/186334
Subject Headings: Epitaxy, Mathematical physics, Metals, Electric properties, Phase transformation (Statistical physics)
Format: Document (PDF)

Title: MODIFIED f(R) THEORY OF GRAVITY: AN ALTERNATIVE GRAVITY THEORY.
Creator: Saiedi, Hamidreza, Wille, Luc T., Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description: Through the variational principle, we review the gravitational field equations in Einstein gravity and modified f(R) gravity theories. Metric and Palatini formalisms are two different approaches that are employed to obtain the field equations in the context of f(R) theory of gravity. In this framework, we attempt to investigate the energy conditions in Friedmann-Lemaitre-Robertson-Walker (FLRW) metric using the Raychaudhuri equation. Then, we focus on wormhole geometries and their...
Show moreThrough the variational principle, we review the gravitational field equations in Einstein gravity and modified f(R) gravity theories. Metric and Palatini formalisms are two different approaches that are employed to obtain the field equations in the context of f(R) theory of gravity. In this framework, we attempt to investigate the energy conditions in Friedmann-Lemaitre-Robertson-Walker (FLRW) metric using the Raychaudhuri equation. Then, we focus on wormhole geometries and their thermodynamics behavior in Palatini and metric versions of modified f(R) gravity, separately. To violate the null and the weak energy conditions, wormhole spacetimes need an exotic matter. It has been shown that in f(R) gravity the matter threading the wormholes serves the energy conditions, and it is the derivative terms of the higher order curvature that may be explained as a gravitational fluid, that supports these geometries. Therefore, in f(R) gravity theory it is not required to introduce exotic matter in order to have traversable wormholes. In the framework of metric and Palatini f(R) gravity, we investigate the thermodynamic properties of evolving wormholes. We obtain an expression for the variation of the total entropy to discuss the thermodynamic behavior of wormhole spacetimes. The investigation has been extended to the apparent and event horizons. Eventually, we apply the radius of these horizons to determine the validity of the generalized second law of thermodynamics. This law states that the rate of change of total entropy is positive.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00013879
Subject Headings: Gravity, Gravitational fields--Mathematics, Wormholes (Physics)
Format: Document (PDF)

Title: Neural field dynamics under vari ation of local and global connectivity and finite t ransmission speeds.
Creator: Qubbaj, Murad R., Florida Atlantic University, Jirsa, Viktor K., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Spatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous...
Show moreSpatially continuous networks with heterogeneous connections are ubiquitous in biological systems, in part icular neural systems. To understand the mutual effects of locally homogeneous and globally heterogeneous connectivity, the st ability of the steady state activity of a neural field as a fun ction of its connectivity is investigated. The variation of the connectivity is operationalized through manipulation of a heterogeneous two-point connection embedded into the otherwise homogeneous connectivity matrix and by variation of connectivity strength and transmission speed. A detailed discussion of the example of the real Ginzburg-Land au equation with an embedded two-point heterogeneous connection in addition to the homogeneous coupling due to the diffusion term is performed. The system is reduced to a set of delay differential equations and the stability di agrams as a function of the time delay and the local and global coupling strengths are computed. The major finding is that the stability of the heterogeneously connected elements with a well-defined velocity defines a lower bound for the stabil ity of the entire system . Diffusion and velocity dispersion always result in increased stability. Various other local architectures represented by exponentially decaying connectivity fun ctions are also discussed. The analysis shows that developmental changes such as the myelination of the cortical large-scale fib er system generally result in the stabilization of steady state activity via oscillatory instabilities independent of the local connectivity. Non-oscillatory (Turing) instabilities are shown to be independent of any influences of time delay.
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Date Issued: 2007
PURL: http://purl.flvc.org/fau/fd/FA00000873
Subject Headings: Mathematical physics, Connections (Mathematics), Superconductivity--Mathematics, Neural networks (Computer science)
Format: Document (PDF)

Title: Spin-foam dynamics of general relativity.
Creator: Chaharsough Shirazi, Atousa, Engle, Jonathan S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: In this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic...
Show moreIn this dissertation the dynamics of general relativity is studied via the spin-foam approach to quantum gravity. Spin-foams are a proposal to compute a transition amplitude from a triangulated space-time manifold for the evolution of quantum 3d geometry via path integral. Any path integral formulation of a quantum theory has two important parts, the measure factor and a phase part. The correct measure factor is obtained by careful canonical analysis at the continuum level. The basic variables in the Plebanski-Holst formulation of gravity from which spin-foam is derived are a Lorentz connection and a Lorentz-algebra valued two-form, called the Plebanski two-form. However, in the final spin-foam sum, one usually sums over only spins and intertwiners, which label eigenstates of the Plebanski two-form alone. The spin-foam sum is therefore a discretized version of a Plebanski-Holst path integral in which only the Plebanski two-form appears, and in which the conne ction degrees of freedom have been integrated out. Calculating the measure factor for Plebanksi Holst formulation without the connection degrees of freedom is one of the aims of this dissertation. This analysis is at the continuum level and in order to be implemented in spin-foams one needs to properly discretize and quantize this measure factor. The correct phase is determined by semi-classical behavior. In asymptotic analysis of the Engle-Pereira-Rovelli-Livine spin-foam model, due to the inclusion of more than the usual gravitational sector, more than the usual Regge term appears in the asymptotics of the vertex amplitude. As a consequence, solutions to the classical equations of motion of GR fail to dominate in the semi-classical limit. One solution to this problem has been proposed in which one quantum mechanically imposes restriction to a single gravitational sector, yielding what has been called the “proper” spin-foam model. However, this revised model of quantum gravity, like any proposal for a theory of quantum gravity, must pass certain tests. In the regime of small curvature, one expects a given model of quantum gravity to reproduce the predictions of the linearized theory. As a consistency check we calculate the graviton two-point function predicted by the Lorentzian proper vertex and examine its semiclassical limit.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004488, http://purl.flvc.org/fau/fd/FA00004488
Subject Headings: General relativity (Physics), Gravitation, Mass (Physics), Mathematical physics, Quantum gravity, Quantum theory
Format: Document (PDF)

Title: Algebraic and combinatorial aspects of group factorizations.
Creator: Bozovic, Vladimir., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number...
Show moreThe aim of this work is to investigate some algebraic and combinatorial aspects of group factorizations. The main contribution of this dissertation is a set of new results regarding factorization of groups, with emphasis on the nonabelian case. We introduce a novel technique for factorization of groups, the so-called free mappings, a powerful tool for factorization of a wide class of abelian and non-abelian groups. By applying a certain group action on the blocks of a factorization, a number of combinatorial and computational problems were noted and studied. In particular, we analyze the case of the group Aut(Zn) acting on blocks of factorization of Zn. We present new theoretical facts that reveal the numerical structure of the stabilizer of a set in Zn, under the action of Aut(Zn). New algorithms for finding the stabilizer of a set and checking whether two sets belong to the same orbit are proposed.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/107805
Subject Headings: Physical measurements, Mapping (Mathematics), Combinatorial enumeration problems, Algebra, Abstract
Format: Document (PDF)

Title: The Circular Restricted Four Body Problem is Non-Integrable: A Computer Assisted Proof.
Creator: Kepley, Shane, Kalies, William D., Mireles-James, Jason D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Gravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important...
Show moreGravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important role in the discussion. In the last fty years the study of numerical methods for computing invariant objects has matured into a thriving sub-discipline. This growth is driven at least in part by the needs of the world's space programs. Recent work on validated numerical methods has begun to unify the computational and analytical perspectives, enriching both aspects of the subject. Many of these results use computer assisted proofs, a tool which has become increasingly popular in recent years. This thesis presents a proof that the circular restricted four body problem is non-integrable. The proof of this result is obtained as an application of more general rigorous numerical methods in nonlinear analysis.
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Date Issued: 2017
PURL: http://purl.flvc.org/fau/fd/FA00004997
Subject Headings: Dissertations, Academic -- Florida Atlantic University, Mathematical physics., Invariants., Dynamical systems
Format: Document (PDF)

Title: Synchronization and phase dynamics of oscillating foils.
Creator: Finkel, Cyndee L., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: In this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air...
Show moreIn this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air{bearings. The position of the apparatus in the channel was regulated with a linear, closed loop PI controller. Thrust/drag forces were measured with strain gauges and particle image velocimetry (PIV) was used to examine the wake structure that develops. The Strouhal number of the oscillating airfoil was compared to the values observed in nature as the system transitions between the accelerated and steady states... As suggested by previous work, this self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. The limit cycles were used to examine the synchronous conditions due to the coupling of the foil and wake vortices. Noise is a factor that can mask details of the synchronization. In order to control its effect, we study the locking conditions using an analytic technique that only considers the phases.. The results suggest that Strouhal number selection in steady forward natural swimming and flying is the result of a limit cycle process and not actively controlled by an organism. An implication of this is that only relatively simple sensory and control hardware may be necessary to control the steady forward motion of man-made biomimetically propelled vehicles.
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Date Issued: 2013
PURL: http://purl.flvc.org/fcla/dt/3362333
Subject Headings: Mathematical physics, Fluid dynamics, Unsteady flow (Fluid dynamics), Aerofoils, Aerodynamics
Format: Document (PDF)

Title: Boundary Layer Control on a Circular Cylindrical Body through Oscillating Lorentz Forcing.
Creator: Seltzer, Ryan K., Dhanak, Manhar R., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: Boundary layer control on a circular cylindrical body through oscillating Lorentz forcing is studied by means of numerical simulation of the vorticity-stream function formulation of the Navier-Stokes equations. The model problem considers axisymmetric seawater flow along an infinite cylinder controlled by an idealized radially directed Lorentz force oscillating spatially and temporally. Under optimum forcing parameters, it is shown that sustainable Lorentz induced vortex rings can travel...
Show moreBoundary layer control on a circular cylindrical body through oscillating Lorentz forcing is studied by means of numerical simulation of the vorticity-stream function formulation of the Navier-Stokes equations. The model problem considers axisymmetric seawater flow along an infinite cylinder controlled by an idealized radially directed Lorentz force oscillating spatially and temporally. Under optimum forcing parameters, it is shown that sustainable Lorentz induced vortex rings can travel along the cylinder at a speed equivalent to the phase speed of forcing . Wall stress is shown to locally change sign in the region adjacent to the vortex, considerably decreasing net viscous drag . Adverse flow behaviors are revealed as a result of studying the effects of the Reynolds numbers, strength of the Lorentz force, and phase speed of forcing for boundary layer control. Adverse flow behaviors inc I ude complex vortex configurations found for suboptimal forcing resulting in a considerable increase in wall stress.
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Date Issued: 2007
PURL: http://purl.flvc.org/fau/fd/FA00012549
Subject Headings: Mathematical physics, Lorentz transformations, Boundary layer control, Fluid dynamics
Format: Document (PDF)

Title: Hamiltonian Methods in the Quantization of Gauge Systems.
Creator: Vaulin, Ruslan, Florida Atlantic University, Miller, Warner A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: The new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework...
Show moreThe new formalism for quantization of gauge systems based on the concept of the dynamical Hamiltonian recently introduced as a basis for the canonical theory of quantum gravity was considered in the context of general gauge theories. This and other Hamiltonian methods, that include Dirac's theory of extended Hamiltonian and the Hamiltonian reduction formalism were critically examined. It was established that the classical theories of constrained gauge systems formulated within the framework of either of the approaches are equivalent. The central to the proof of equivalence was the fact that the gauge symmetries resuIt in the constraints of the first class in Dirac's terminology that Iead to redundancy of equations of motion for some of the canonica variables. Nevertheless, analysis of the quantum theories showed that in general, the quantum theory of the dynamical Hamiltonian is inequivalent to those of the extended Hamiltonian and the Hamiltonian reduction. The new method of quantization was applied to a number of gauge systems, including the theory of relativistic particle, the Bianchi type IX cosmological model and spinor electrodynamics along side with the traditional methods of quantization. In all of the cases considered the quantum theory of the dynamical Hamiltonian was found to be well-defined and to possess the appropriate classical limit. In particular, the quantization procedure for the Bianchi type IX cosmological spacetime did not run into any of the known problems with quantizing the theory of General Relativity. On the other hand, in the case of the quantum electrodynamics the dynamical Hamiltonian approach led to the quantum theory with the modified self-interaction in the matter sector. The possible consequence of this for the quantization of the full theory of General Relativity including the matter fields are discussed.
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Date Issued: 2006
PURL: http://purl.flvc.org/fau/fd/FA00000882
Subject Headings: Quantum field theory, Mathematical physics, Evolution equations, Nonlinear, Hamiltonian systems
Format: Document (PDF)

Title: COMPUTATIONAL ASPECTS OF QUANTUM GRAVITY: NUMERICAL METHODS IN SPINFOAM MODELS.
Creator: Qu, Dongxue, Han, Muxin, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description: Quantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing...
Show moreQuantum Gravity attempts to unify general relativity (GR) and quantum theory, and is one of the challenging research areas in theoretical physics. LQG is a background-independent and non-perturbative approach towards the theory of quantum gravity. The spinfoam formulation gives the covariant path integral formulation of LQG. The spinfoam amplitude plays a crucial role in the spinfoam formulation by defining the transition amplitude of covariant LQG. It is particularly interesting for testing the semiclassical consistency of LQG, because of the connection between the semiclassical approximation of path integral and the stationary phase approximation. The recent semiclassical analysis reveals the interesting relation between spinfoam amplitudes and the Regge calculus, which discretizes GR on triangulations. This relation makes the semiclassical consistency of covariant LQG promising. The spinfoam formulation also provides ways to study the n-point functions of quantum-geometry operators in LQG. Despite the novel and crucial analytic results in the spinfoam formulation, the computational complexity has been obstructed further explorations in spinfoam models. Nevertheless, numerical approaches to spinfoams open new windows to circumvent this obstruction. There has been enlightening progress on numerical computation of the spinfoam amplitudes and the two-point function. The numerical technology should expand the toolbox to investigate LQG.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00013878
Subject Headings: Quantum gravity, Quantum theory, Quantum gravity--Mathematics, Theoretical physics
Format: Document (PDF)

Title: Nonlinear Phenomena from a Reinjected Horseshoe.
Creator: Fontaine, Marcus, Kalies, William D., Naudot, Vincent, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to...
Show moreA geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004591
Subject Headings: Nonlinear theories., Computational dynamics., Attractors (Mathematics), Chaotic behavior in systems., Mathematical physics.
Format: Document (PDF)

Title: Science fiction girlfriends transgender politics and US science fiction television, 1990–present.
Creator: Cava, Peter, Scodari, Christine, Florida Atlantic University, Dorothy F. Schmidt College of Arts and Letters, School of Communication and Multimedia Studies
Abstract/Description: The 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation....
Show moreThe 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation. The method is multiperspectival cultural studies, which considers how the production, content, and reception of media texts and their metatexts collectively determine the texts’ meaning. The data include trade articles about the television industry; published interviews with producers; 3,175 hours of televisual content; commercial advertisements for television programs; films, novels, and webisodes (Web episodes) in selected media franchises; professional reviews; online discussion boards; fan fiction; and fan videos.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004435, http://purl.flvc.org/fau/fd/FA00004435
Subject Headings: Computer science., Computers., Artificial intelligence., Applied mathematics., Engineering mathematics., Statistical physics., Dynamical systems., Vibration., Dynamics., Computer Science.
Format: Document (PDF)

Title: Modeling strategic resource allocation in probabilistic global supply chain system with genetic algorithm.
Creator: Damrongwongsiri, Montri., Florida Atlantic University, Han, Chingping (Jim), College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: Effective and efficient supply chain management is essential for domestic and global organizations to compete successfully in the international market. Superior inventory control policies and product distribution strategies along with advanced information technology enable an organization to collaborate distribution and allocation of inventory to gain a competitive advantage in the world market. Our research establishes the strategic resource allocation model to capture and encapsulate the...
Show moreEffective and efficient supply chain management is essential for domestic and global organizations to compete successfully in the international market. Superior inventory control policies and product distribution strategies along with advanced information technology enable an organization to collaborate distribution and allocation of inventory to gain a competitive advantage in the world market. Our research establishes the strategic resource allocation model to capture and encapsulate the complexity of the modern global supply chain management problem. A mathematical model was constructed to depict the stochastic, multiple-period, two-echelon inventory with the many-to-many demand-supplier network problem. The model simultaneously constitutes the uncertainties of inventory control and transportation parameters as well as the varying price factors. A genetic algorithm (GA) was applied to derive optimal solutions through a two-stage optimization process. Practical examples and solutions from three sourcing strategies (single sourcing, multiple sourcing, and dedicated system) were included to illustrate the GA based solution procedure. Our model can be utilized as a collaborative supply chain strategic planning tool to efficiently determine the appropriate inventory allocation and a dynamic decision making process to effectively manage the distribution plan.
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Date Issued: 2003
PURL: http://purl.flvc.org/fcla/dt/12056
Subject Headings: Business logistics--Mathematical models, Physical distribution of goods--Management, Inventory control--Mathematical models, Genetic algorithms
Format: Document (PDF)

Title: Spectral decomposition of grid data.
Creator: Donovan, Andrew., Harriet L. Wilkes Honors College
Abstract/Description: Spectral decomposition is a method of expressing functions as a harmonic series, and can be used for the simplification of complicated physical problems. This type of analysis requires knowledge of the function at all points on a circle or sphere. In problems where the function is known only at discreet points, regular intervals in a rectangular grid, for example, numerical methods must be employed to compute approximate coefficients for the harmonic expansion. In this paper, we investigate...
Show moreSpectral decomposition is a method of expressing functions as a harmonic series, and can be used for the simplification of complicated physical problems. This type of analysis requires knowledge of the function at all points on a circle or sphere. In problems where the function is known only at discreet points, regular intervals in a rectangular grid, for example, numerical methods must be employed to compute approximate coefficients for the harmonic expansion. In this paper, we investigate numerical methods for computing Fourier coefficients of a two dimensional function at a fixed radius, and spherical harmonic coefficients in three dimensions on a sphere of fixed radius.
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Date Issued: 2005
PURL: http://purl.flvc.org/FAU/11572
Subject Headings: Inverse problems (Differential equations), Boundary value problems, Differential equations, Partial, Mathematical physics, Harmonic analysis
Format: Document (PDF)

Title: Characterizing magnetic noise of AUV for use in towed magnetometer study of internal waves.
Creator: Tilley, Dylan., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: As part of a project to study internal waves, FAU plans to utilize an AUV to tow a magnetometer to study electromagnetic signatures from internal waves. This research is focused on the electromagnetic noise issues related to using an AUV to tow the magnetic sensor package. There are active sources of electromagnetic noise caused by an AUV that are present in addition to those induced by the Earth's magnetic field and permanent magnets. To characterize the magnetic noise associated with the...
Show moreAs part of a project to study internal waves, FAU plans to utilize an AUV to tow a magnetometer to study electromagnetic signatures from internal waves. This research is focused on the electromagnetic noise issues related to using an AUV to tow the magnetic sensor package. There are active sources of electromagnetic noise caused by an AUV that are present in addition to those induced by the Earth's magnetic field and permanent magnets. To characterize the magnetic noise associated with the AUV magnetometer tow system, the various active source elements were identified, the orientation sensitivity of the sensors being used was determined, and the magnetic anomaly of a similar AUV which may be eventually be used in a magnetic sensing arrangement was measured. The results are used to show the proposed sensing arrangement will likely not achieve the necessary sensitivity to measure subtle internal wave signals.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3352881
Subject Headings: Automatic control, Mathematical models, Electromagnetic measurements, Fluctuations (Physics), Oceanographic submersibles, Underwater acoustics
Format: Document (PDF)

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