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Coset intersection problem and application to 3-nets
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)
Fluctuation and correlation effects in a charged surface immersed in an asymmetric electrolyte solution
Title
Fluctuation and correlation effects in a charged surface immersed in an asymmetric electrolyte solution.
Creator
Acharya, Pramod, Lau, Andy W. C., Graduate College
Date Issued
2013-04-12
PURL
http://purl.flvc.org/fcla/dt/3361263
Subject Headings
Green's functions, Field theory (Physics), Electrostatics
Format
Document (PDF)
Hamiltonian Methods in the Quantization of Gauge Systems
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)
Examination of the R-process in accretion-induced collapse (AIC)
Title
Examination of the R-process in accretion-induced collapse (AIC).
Creator
Davis, Daryl C., Florida Atlantic University, Bruenn, Stephen W.
Abstract/Description
This work is a simulation of the Accretion-Induced Collapse of a 1.37 solar mass white dwarf into a neutron star and the subsequent generation of a neutrino-driven wind, with an examination as to whether the event is a candidate for r-process nucleosynthesis. The simulation utilizes a new radiation hydrodynamic code, RadHyd, to model the AIC event. We examine the process of Accretion-Induced Collapse utilizing two sets of neutrino-scattering and absorption rates: The first, and simpler of the...
Show moreThis work is a simulation of the Accretion-Induced Collapse of a 1.37 solar mass white dwarf into a neutron star and the subsequent generation of a neutrino-driven wind, with an examination as to whether the event is a candidate for r-process nucleosynthesis. The simulation utilizes a new radiation hydrodynamic code, RadHyd, to model the AIC event. We examine the process of Accretion-Induced Collapse utilizing two sets of neutrino-scattering and absorption rates: The first, and simpler of the two has been in use since they were first introduced in 1985. The second includes a more accurate implementation of neutrino-nucleon scattering and nucleon bremsstrahlung. The improved nue - nue-nucleon scattering rate now permits energy to be exchanged between neutrinos and matter by this process, and is therefore important for the numu's and nutau's, as their only channels for exchanging energy in the standard rates was by the relatively weak NES and pair processes. Neutrino-nucleon bremmsstrahlung is also important for numu's and nutau's as this opens another channel (beside pair process) for their production. Both simulations show a neutrino-driven wind being generated after core bounce and shock propagation. We examine the conditions in these winds to ascertain whether the requisite conditions are attained for an r-process. In neither case are these achieved during the time of the simulations (i.e. 2 seconds). However, these simulations need to be carried out at least an order of magnitude longer before firm conclusions can be drawn about the applicability of this site for the r-process.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/12136
Subject Headings
Nuclear astrophysics--Research, Scattering (Physics), Nucleon-nucleon scattering--Research, Field theory (Physics), Stellar winds
Format
Document (PDF)
Simplicial matter in discrete and quantum spacetimes
Title
Simplicial matter in discrete and quantum spacetimes.
Creator
McDonald, Jonathan Ryan., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
A discrete formalism for General Relativity was introduced in 1961 by Tulio Regge in the form of a piecewise-linear manifold as an approximation to (pseudo-)Riemannian manifolds. This formalism, known as Regge Calculus, has primarily been used to study vacuum spacetimes as both an approximation for classical General Relativity and as a framework for quantum gravity. However, there has been no consistent effort to include arbitrary non-gravitational sources into Regge Calculus or examine the...
Show moreA discrete formalism for General Relativity was introduced in 1961 by Tulio Regge in the form of a piecewise-linear manifold as an approximation to (pseudo-)Riemannian manifolds. This formalism, known as Regge Calculus, has primarily been used to study vacuum spacetimes as both an approximation for classical General Relativity and as a framework for quantum gravity. However, there has been no consistent effort to include arbitrary non-gravitational sources into Regge Calculus or examine the structural details of how this is done. This manuscript explores the underlying framework of Regge Calculus in an effort elucidate the structural properties of the lattice geometry most useful for incorporating particles and fields. Correspondingly, we first derive the contracted Bianchi identity as a guide towards understanding how particles and fields can be coupled to the lattice so as to automatically ensure conservation of source. In doing so, we derive a Kirchhoff-like conservation principle that identifies the flow of energy and momentum as a flux through the circumcentric dual boundaries. This circuit construction arises naturally from the topological structure suggested by the contracted Bianchi identity. Using the results of the contracted Bianchi identity we explore the generic properties of the local topology in Regge Calculus for arbitrary triangulations and suggest a first-principles definition that is consistent with the inclusion of source. This prescription for extending vacuum Regge Calculus is sufficiently general to be applicable to other approaches to discrete quantum gravity. We discuss how these findings bear on a quantized theory of gravity in which the coupling to source provides a physical interpretation for the approximate invariance principles of the discrete theory.
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Date Issued
2009
PURL
http://purl.flvc.org/FAU/186691
Subject Headings
Special relativity (Physics), Space and time, Distribution (Probability theory), Global differential geometry, Quantum field theory, Mathematical physics
Format
Document (PDF)