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Title: First Measurement of Top Quark Pair Production Cross-Section in Muon Plus Hadronic Tau Final States.
Creator: Sumowidagdo, Suharyo, Adams, Todd, Aldrovandi, Ettore, Wahl, Horst, Reina, Laura, Capstick, Simon, Department of Physics, Florida State University
Abstract/Description: This dissertation presents the first measurement of top quark pair production cross-section in events containing a muon and a tau lepton. The measurement was done with 1 fb−1 of data collected during April 2002 through February 2006 using the DØ detector at the Tevatron proton-antiproton collider, located at Fermi National Accelerator Laboratory (Fermilab), Batavia, Illinois. Events containing one isolated muon, one tau which decays hadronically, missing transverse energy, and two or more...
Show moreThis dissertation presents the first measurement of top quark pair production cross-section in events containing a muon and a tau lepton. The measurement was done with 1 fb−1 of data collected during April 2002 through February 2006 using the DØ detector at the Tevatron proton-antiproton collider, located at Fermi National Accelerator Laboratory (Fermilab), Batavia, Illinois. Events containing one isolated muon, one tau which decays hadronically, missing transverse energy, and two or more jets (at least one of which must be tagged as a heavy flavor jet) were selected.Twenty-nine candidate events were observed with an expected background of 9.16 events. The top quark pair production cross-section is measured to beσ (t¯t) = 8.0+2.8 −2.4 (stat)+1.8−1.7 (syst) ± 0.5 (lumi) pb.Assuming a top quark pair production cross-section of 6.77 pb for Monte Carlo signal top events without a real tau, the measured σ × BR isσ (t¯t) × BR(t¯t μ +τ + 2ν + 2b) = 0.18+0.13−0.11 (stat)+0.09−0.09 (syst) ± 0.01 (lumi) pb.
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Date Issued: 2008
Identifier: FSU_migr_etd-0407
Format: Thesis

Title: Structural Behavior of 157,158,159Dy in the I=30−50L Spin Regime and the High-Spin Domain of 158Er Up to and Above Band Termination.
Creator: Pipidis, Paschalis Akis, Riley, Mark A., Aldrovandi, Ettore, Piekarewicz, Jorge, Reina, Laura, Eugenio, Paul M., Department of Physics, Florida State University
Abstract/Description: The question of how do the properties of nuclei evolve with increasing excitation energy and angular momentum is one of the current frontiers in nuclear physics. State of the art $gamma$-ray detector systems have been used to investigate this question, in a series of rare-earth nuclei with mass extit{A}$sim$158. Significant extensions to the high-spin excitation spectrum of the $N$=91, 92, 93 isotopes $^{157,158,159}$Dy have been achieved using the high-efficiency $gamma$-ray spectrometers...
Show moreThe question of how do the properties of nuclei evolve with increasing excitation energy and angular momentum is one of the current frontiers in nuclear physics. State of the art $gamma$-ray detector systems have been used to investigate this question, in a series of rare-earth nuclei with mass extit{A}$sim$158. Significant extensions to the high-spin excitation spectrum of the $N$=91, 92, 93 isotopes $^{157,158,159}$Dy have been achieved using the high-efficiency $gamma$-ray spectrometers EUROBALL and GAMMASPHERE. These nuclei were populated via weak 3$n$ or $alpha xn$ exit channels in fusion evaporation reactions. In $^{157}$Dy, the yrast band has been extended to extit{I}$^pi$=$frac{101}{2}^{+}$ (tentatively to $frac{105}{2}^{+}$) with four sideband structures (two of which are new) observed in the 35$-$50 $hbar$ spin range. In $^{158}$Dy, three bands have been extended to 42$^{+}$ (44$^{+}$), 40$^{-}$, and 41$^{-}$ (43$^{-}$), while in $^{159}$Dy the yrast band is observed to $frac{81}{2}^{+}$ ($frac{85}{2}^{+}$). A total of 84 (99) new transitions, including 2 new bands, were added to the level schemes of $^{157,158,159}$Dy. The high-spin behavior and band crossing systematics of the Dy isotopes and of the neighboring $N$=91, 92, and 93 isotones are discussed in terms of rotational alignments and shape transitions. Cranked Nilsson-Strutinsky calculations without pairing have been performed for detailed comparisons with the very high-spin states observed in $^{157}$Dy. Results on $^{157,158,159}$Dy have been published in extit{Phys. Rev. C.} Moreover, the angular-momentum induced transition from a deformed state of collective rotation to a non-collective configuration has been studied. In $^{158}$Er this transition manifests itself as favored band termination near extit{I}$approx$45$hbar$. The feeding of these band terminating states has been investigated for the first time using the GAMMASPHERE spectrometer. A large number of weakly populated states, lying at high excitation energy, that decay into these special states have been discovered. Cranked Nilsson-Strutinsky calculations suggest that these states arise from weakly collective configurations that break the $Z$=64 semi-magic core. Additionally, a new frontier of discrete-line $gamma$-ray spectroscopy at ultra-high spin has been opened in the rare-earth nucleus $^{158}$Er. Two rotational structures, displaying high moments of inertia, have been identified, which extend up to spin $sim$65$hbar$ and bypass the band-terminating states in these nuclei near extit{I}$sim$45$hbar$. Cranked Nilsson-Strutinsky calculations suggest that these structures arise from well-deformed triaxial configurations that lie in a valley of favored shell energy, which also includes the well-known triaxial strongly deformed bands in $^{161-167}$Lu. Overall, 182 (209) new transitions, including 10 new bands, were placed in the greatly augmented level scheme of $^{158}$Er, as a result of our work in this thesis. Four of the new bands are based on high$-$ extit{K} quasiparticle excitations, which provide a stringent test of the Cranked Shell Model. This enables the investigation and interpretation of many different quasiparticle configurations from their alignment properties and band crossings systematics. Results on $^{158}$Er have been published in extit{Phys. Rev. Lett.} and extit{Phys. Scr.} Finally, a local experiment, using the FSU tandem accelerator and the FSU $gamma$-ray detectors, was performed to investigate the odd-odd nucleus $^{158}$Tb. Unfortunately, no new significant results on the latter were obtained except for the tentative assignment of a new, strongly-coupled, rotational structure.}
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Date Issued: 2006
Identifier: FSU_migr_etd-0687
Format: Thesis

Title: Quantum Tunneling and Scattering of a Composite Object.
Creator: Ahsan, Naureen, Volya, Alexander, Aldrovandi, Ettore, Piekarewicz, Jorge, Crede, Volker, Xiong, Peng, Department of Physics, Florida State University
Abstract/Description: Reaction physics involving composite objects with internal degrees of freedom is an important subject since it is encountered in the context of nuclear processes like fusion, fission, particle decay, as well as many other branches of science. Quantum tunneling and scattering of a composite object are explored in this work. A few model Hamiltonians are chosen as examples where a two-particle system interacts, in one dimension, with a target that poses a delta-potential or an infinite wall...
Show moreReaction physics involving composite objects with internal degrees of freedom is an important subject since it is encountered in the context of nuclear processes like fusion, fission, particle decay, as well as many other branches of science. Quantum tunneling and scattering of a composite object are explored in this work. A few model Hamiltonians are chosen as examples where a two-particle system interacts, in one dimension, with a target that poses a delta-potential or an infinite wall potential. It is assumed that only one of the two components interacts with the target. The study includes the harmonic oscillator and the infinite square well as examples of intrinsic Hamiltonians that do not allow the projectile to break up, and a finite square well and a delta-well as examples of Hamiltonians that do. The Projection Method and the Variable Phase Method are applied with the aim of an exact solution to the relevant scattering problems. These methods are discussed in the context of the pertinent convergence issues related thereto, and of their applicability. Virtual excitations of the projectile into the classically forbidden energy-domain are found to play a dominant and non-perturbative role in shaping reaction observables, giving rise to enhanced or reduced tunneling in various situations. Cusps and discontinuities are found to appear in observables as manifestations of unitarity and redistribution of flux at the thresholds. The intrinsic structure gives rise to resonance-like behavior in tunneling probabilities. It is also shown that there is charge asymmetry in the scattering of a composite object, unlike in the case of a structureless particle.
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Date Issued: 2011
Identifier: FSU_migr_etd-0142
Format: Thesis

Title: Periods and Motives: Applications in Mathematical Physics.
Creator: Li, Dan, Marcolli, Matilde, Reina, Laura, Aluﬃ, Paolo, Agashe, Amod, Aldrovandi, Ettore, Department of Mathematics, Florida State University
Abstract/Description: The study of periods arose in number theory and algebraic geometry, periods are interesting transcendental numbers like multiple zeta values, on the other hand periods are integrals of algebraic differential forms over domains described by algebraic relations. Viewed as abstract periods, we also consider their relations with motives. In this work, we consider two problems in mathematical physics as applications of the ideas and tools from periods and motives. We first consider the algebro...
Show moreThe study of periods arose in number theory and algebraic geometry, periods are interesting transcendental numbers like multiple zeta values, on the other hand periods are integrals of algebraic differential forms over domains described by algebraic relations. Viewed as abstract periods, we also consider their relations with motives. In this work, we consider two problems in mathematical physics as applications of the ideas and tools from periods and motives. We first consider the algebro-geometric approach to the spectral theory of Harper operators in solid state physics. When the parameters are irrational, the compactification of its Bloch variety is an ind-pro-variety, which is a Cantor-like geometric space and it is compatible with the picture of Hofstadter butterfly. On each approximating component the density of states of the electronic model can be expressed in terms of period integrals over Fermi curves, which can be explicitly computed as elliptic integrals or periods of elliptic curves. The above density of states satisfies a Picard-Fuchs equation, whose solutions are generally given by hypergeometric functions. We use the idea of mirror maps as in mirror symmetry of elliptic curves to derive a q-expansion for the energy level based on the Picard-Fuchs equation. In addition, formal spectral functions such as the partition function are derived as new period integrals. Secondly, we consider generalized Feynman diagram evaluations of an effective noncommutative field theory of the Ponzano-Regge model coupled with matter in loop quantum gravity. We present a parametric representation in a linear k-approximation of the effective field theory derived from a k-deformation of the Ponzano-Regge model and define a generalized Kirchhoff polynomial with k-correction terms. Setting k equal to 1, we verify that the number of points of the corresponding hypersurface of the tetrahedron over finite fields does not fit polynomials with integer coefficients by computer calculations. We then conclude that the hypersurface of the tetrahedron is not polynomially countable, which possibly implies that the hypersurface of the tetrahedron as a motive is not mixed Tate.
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Date Issued: 2012
Identifier: FSU_migr_etd-5390
Format: Thesis

Title: Measurement of the Muon Charge Asymmetry in pp → W + X + → μv + X Events Using the DØ.
Creator: Hoang, Trang Thi Kieu, Blessing, Susan K., Aldrovandi, Ettore, Askew, Andrew, Owens, Joseph, Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: This dissertation describes a measurement of the muon charge asymmetry from W&rarr&mu&nu decay using 7.3 fb-1 of data collected from April 2002 to July 2010 using the D0 detector at Fermi National Accelerator Laboratory. The measurement for muons with pseudorapidity |&eta|
Show moreThis dissertation describes a measurement of the muon charge asymmetry from W&rarr&mu&nu decay using 7.3 fb-1 of data collected from April 2002 to July 2010 using the D0 detector at Fermi National Accelerator Laboratory. The measurement for muons with pseudorapidity |&eta| < 2 probes the charge asymmetry for momentum fraction x from 0.005 to 0.3. The charge asymmetry is compared with the theory predictions generated from RESBOS with CTEQ6.6 parton distribution functions, and from POWHEG with CT10 and MSTW2008 PDFs. The results show good agreement with the electron charge asymmetry measurement from D0. So far, our measurement is the most precise lepton charge asymmetry measurement done at the Tevatron.
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Date Issued: 2012
Identifier: FSU_migr_etd-5363
Format: Thesis

Title: Intersection Numbers of Divisors in Graph Varieties.
Creator: Jones, Deborah, Aluffi, Paolo, Aldrovandi, Ettore, Hironaka., Eriko, Klassen, Eric, Reina, Laura, Department of Mathematics, Florida State University
Abstract/Description: This dissertation studies certain intersection numbers of exceptional divisions arising from blowing up subspaces of lattices associated to graphs. These permit the computation of the Segre class of a scheme associated to the graph/lattice. Explicit formulas are provided for lattices associated to trees and several patterns among these numbers are explored. The problem can be related to the study of so-called Cremona transformations. It is shown that the geometry of such transformations...
Show moreThis dissertation studies certain intersection numbers of exceptional divisions arising from blowing up subspaces of lattices associated to graphs. These permit the computation of the Segre class of a scheme associated to the graph/lattice. Explicit formulas are provided for lattices associated to trees and several patterns among these numbers are explored. The problem can be related to the study of so-called Cremona transformations. It is shown that the geometry of such transformations explain a certain symmetry pattern we discovered.
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Date Issued: 2003
Identifier: FSU_migr_etd-3426
Format: Thesis

Title: Algorithms for Computing Congruences Between Modular Forms.
Creator: Heaton, Randy, Agashe, Amod, Van Hoeij, Mark, Capstick, Simon, Aldrovandi, Ettore, Department of Mathematics, Florida State University
Abstract/Description: Let $N$ be a positive integer. We first discuss a method for computing intersection numbers between subspaces of $S_{2}(Gamma_{0}(N),C)$. Then we present a new method for computing a basis of q-expansions for $S_{2}(Gamma_{0}(N),Q)$, describe an algorithm for saturating such a basis in $S_{2}(Gamma_{0}(N),Z)$, and show how these results have applications to computing congruence primes and studying cancellations in the conjectural Birch and Swinnerton-Dyer formula.
Date Issued: 2012
Identifier: FSU_migr_etd-4904
Format: Thesis

Title: On Elliptic Fibrations and F-Theory Compactifications of String Vacua.
Creator: Fullwood, James, Aluﬃ, Paolo, Reina, Laura, Van Hoeij, Mark, Aldrovandi, Ettore, Hironaka, Eriko, Department of Mathematics, Florida State University
Abstract/Description: We investigate some algebro-geometric aspects of several families of elliptic fibrations relevant for F-theory model building along with some physical applications. In particular, we compute topological invariants of elliptic fibrations via `Sethi-Vafa-Witten formulas', which relate the given invariant of the total space of the fibration to invariants of the base. We find that these invariants can often be computed in a base-independent manner, and moreover, can be computed for all possible...
Show moreWe investigate some algebro-geometric aspects of several families of elliptic fibrations relevant for F-theory model building along with some physical applications. In particular, we compute topological invariants of elliptic fibrations via `Sethi-Vafa-Witten formulas', which relate the given invariant of the total space of the fibration to invariants of the base. We find that these invariants can often be computed in a base-independent manner, and moreover, can be computed for all possible dimensions of a base at once. As such, we construct generating series $f(t)$ corresponding to each invariant such that the coefficient of $t^k$ encodes the invariant of the elliptic fibration over a base of dimension $k$, solely in terms of invariants of the base. From the F-theory perspective, we highlight aspects of elliptic fibrations other than Weierstrass models, and construct a new orientifold limit of F-theory associated with $D_5$ fibrations, i.e., elliptic fibrations whose elliptic fiber is realized via a complete intersection of two quadrics in $\mathbb{P}^3$. We verify tadpole relations as predicted by the (conjectural) equivalence between F-theory and type-IIB, as well as `universal tadpole relations', which are mathematical generalizations of the tadpole relations predicted by the physics of F-theory. We also simplify formulas for invariants of Calabi-Yau fourfolds, and suggest that all Hodge numbers of Calabi-Yau fourfolds depend linearly on $c_1(B)^3$, where $B$ is the base of the fibration.
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Date Issued: 2012
Identifier: FSU_migr_etd-4848
Format: Thesis

Title: Evidence for Single Top Quark Production Using Bayesian Neural Networks.
Creator: Kau, Daekwang, Prosper, Harrison B., Aldrovandi, Ettore, Adams, Todd, Reina, Laura, Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: We present results of a search for single top quark production in pp collisions using a dataset of approximately 1 fb−1 collected with the DØ detector. This analysis considers the muon+jets and electron+jets final states and makes use of Bayesian neural networks to separate the expected signals from backgrounds. The observed excess is associated with a p-value of 0.081%, assuming the background-only hypothesis, which corresponds to an excess over background of 3.2 standard deviations for a...
Show moreWe present results of a search for single top quark production in pp collisions using a dataset of approximately 1 fb−1 collected with the DØ detector. This analysis considers the muon+jets and electron+jets final states and makes use of Bayesian neural networks to separate the expected signals from backgrounds. The observed excess is associated with a p-value of 0.081%, assuming the background-only hypothesis, which corresponds to an excess over background of 3.2 standard deviations for a Gaussian density. The p-value computed using the SM signal cross section of 2.9 pb is 1.6%, corresponding to an expected significance of 2.2 standard deviations. Assuming the observed excess is due to single top production, we measure a single top quark production cross section of _(p¯p ! tb+X, tqb+X) = 4.4±1.5 pb.
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Date Issued: 2007
Identifier: FSU_migr_etd-3296
Format: Thesis

Title: A Model for ππ and πη Photoproduction.
Creator: Kiswandhi, Alvin Stanza, Capstick, Simon, Aldrovandi, Ettore, Piekarewicz, Jorge, Reina, Laura, Eugenio, Paul, Department of Physics, Florida State University
Abstract/Description: We describe a model of general two-to-two-body and two-to-three-body hadronic reaction based on a phenomenological Lagrangian approach that satisfies two-body unitary and is relativistic. This model is used to study πη photoproduction. Unitarity is ensured by using the Lippmann-Schwinger equation to iterate the vertices and dress the propagators to all orders, and by including all possible two-body and quasi-two-body intermediate channels. We also study different approximations of the...
Show moreWe describe a model of general two-to-two-body and two-to-three-body hadronic reaction based on a phenomenological Lagrangian approach that satisfies two-body unitary and is relativistic. This model is used to study πη photoproduction. Unitarity is ensured by using the Lippmann-Schwinger equation to iterate the vertices and dress the propagators to all orders, and by including all possible two-body and quasi-two-body intermediate channels. We also study different approximations of the intermediate momenta in a diagram. Gauge invariance is used as a criterion to choose the best approximation. This model has been tested by investigating the nonresonant interactions of ππ and πη photoproduction, in which significant effects are observed. A preliminary comparison of our calculation to an existing πη photoproduction study is made, and is shown to produce consistent results.
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Date Issued: 2008
Identifier: FSU_migr_etd-2826
Format: Thesis

Title: Braiding and Berry's Phases in Non-Abelian Quantum Hall States.
Creator: Zikos, Georgios, Bonesteel, Nicholas, Aldrovandi, Ettore, Schlottmann, Pedro, Reina, Laura, Chiorescu, Irinel, Department of Physics, Florida State University
Abstract/Description: If one could be built, a quantum computer would be capable of storing and manipulating quantum states with sufficient accuracy to carry out computations that no classical computer can do (most notably factoring integers in polynomial time). The greatest obstacle to building such a device is the problem of error and decoherence. Classical computers can exploit the physical robustness of ordered states to protect classical information (as in, for example, the magnetically ordered state of a...
Show moreIf one could be built, a quantum computer would be capable of storing and manipulating quantum states with sufficient accuracy to carry out computations that no classical computer can do (most notably factoring integers in polynomial time). The greatest obstacle to building such a device is the problem of error and decoherence. Classical computers can exploit the physical robustness of ordered states to protect classical information (as in, for example, the magnetically ordered state of a hard drive). Remarkably, a type of quantum order known as topological order can, in principle, play the same role for quantum information. The best studied topologically ordered states are quantum Hall states. These states arise when a two-dimensional electron gas is placed in a strong magnetic field and cooled to low temperatures. Under the right conditions, the electrons condense into an incompressible quantum liquid whose excitations are particle-like objects with fractional charge (quasiparticles). Certain quantum Hall states are thought to be non Abelian. This means that when a finite number of quasiparticles are present and fixed in space there is a low energy Hilbert space with finite dimension, rather than a unique state. Unitary operations can then be carried out on this Hilbert space by adiabatically dragging quasiparticles around one another so that their world-lines sweep out braids in 2+1 dimensional space time. A quantum computer which stores quantum information in this Hilbert space and computes by braiding is known as a topological quantum computer. In this thesis I review our work on determining precisely how one would carry out a computation on a topological quantum computer. I focus on the so-called Fibonacci anyons--quasiparticles which may exist in the experimentally observed quantum Hall state at Landau level filling fraction ν = 12/5. I give explicit prescriptions for encoding qubits (quantum bits) using Fibonacci anyons, and show how one would carry out a universal set of quantum gates (the quantum analogs of Boolean logic gates) by braiding them. I then focus in particular on my work developing algorithms for performing brute force searches over the space of braids to find braids which produce unitary operations close to any desired operation. These brute force searches are a crucial part of our quantum gate construction, and I show that by using a so-called "load balanced" bidirectional search I can find braids which approximate any desired operation to an accuracy of 1 part in 10 5 . I then turn to my work calculating the Berry's phase obtained when quasiparticles are moved around one another in the Moore-Read state, a non Abelian state generally believed to describe the ν = 5/2 quantum Hall effect. This work is done using variational Monte Carlo, a method which allows one to numerically evaluate the Berry's phase for finite size systems. By exploiting certain properties of the Moore-Read state I have been able to study systems consisting of as many as 150 electrons. In so doing I have verified the conjectured connection between the Berry's phase produced by physically moving quasiparticles around one another and the mathematical phase one obtains by simply analytically continuing the quasiparticle coordinates. An added benefit of these calculations is that we can deduce the length scale which determines the size of the quasiparticles. This length scale dictates how far apart the quasiparticles must be in order to prevent errors when they are used for topological quantum computation.
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Date Issued: 2009
Identifier: FSU_migr_etd-0503
Format: Thesis

Title: Constructing Non-Trivial Elements of the Shafarevich-Tate Group of an Abelian Variety.
Creator: Biswas, Saikat, Agashe, Amod, Aggarwal, Sudhir, Hironaka, Eriko, Van Hoeij, Mark, Aldrovandi, Ettore, Department of Mathematics, Florida State University
Abstract/Description: The Shafarevich-Tate group of an elliptic curve is an important invariant of the curve whose conjectural finiteness can sometimes be used to determine the rank of the curve. The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of a elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non...
Show moreThe Shafarevich-Tate group of an elliptic curve is an important invariant of the curve whose conjectural finiteness can sometimes be used to determine the rank of the curve. The second part of the Birch and Swinnerton-Dyer (BSD) conjecture gives a conjectural formula for the order of the Shafarevich-Tate group of a elliptic curve in terms of other computable invariants of the curve. Cremona and Mazur initiated a theory that can often be used to verify the BSD conjecture by constructing non-trivial elements of the Shafarevich-Tate group of an elliptic curve by means of the Mordell-Weil group of an ambient curve. In this thesis, we extract a general theorem out of Cremona and Mazur's work and give precise conditions under which such a construction can be made. We then give an extension of our result which provides new theoretical evidence for the BSD conjecture. Finally, we prove a theorem that gives an alternative method to potentially construct non-trivial elements of the Shafarevich-Tate group of an elliptic curve by using the component groups of a second curve.
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Date Issued: 2011
Identifier: FSU_migr_etd-3717
Format: Thesis

Title: Closed Form Solutions of Linear Difference Equations.
Creator: Cha, Yongjae, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
Abstract/Description: In this thesis we present an algorithm that finds closed form solutions for homogeneous linear recurrence equations. The key idea is transforming an input operator Linp to an operator Lg with known solutions. The main problem of this idea is how to find a solved equation Lg to which Linp can be reduced. To solve this problem, we use local data of a difference operator, that is invariant under the transformation.
Date Issued: 2011
Identifier: FSU_migr_etd-3960
Format: Thesis

Title: On Picard 2-Stacks and Length 3 Complexes of Abelian Sheaves.
Creator: Tatar, Ahmet Emin, Aldrovandi, Ettore, Capstick, Simon, Agashe, Amod, Aluﬃ, Paolo, Klassen, Eric, Department of Mathematics, Florida State University
Abstract/Description: In Seminaire de Geometrie Algebrique 4 (SGA4), Expose XVIII, Pierre Deligne proves that to any Picard stack one can associate a complex of abelian sheaves of length 2. He also studies the morphisms between such stacks and shows that such a morphism defines a class of fractions in the derived category of complexes of abelian sheaves of length 2. From these two preliminary results, he finally deduces that the derived category of complexes of abelian sheaves of length 2 is equivalent to the...
Show moreIn Seminaire de Geometrie Algebrique 4 (SGA4), Expose XVIII, Pierre Deligne proves that to any Picard stack one can associate a complex of abelian sheaves of length 2. He also studies the morphisms between such stacks and shows that such a morphism defines a class of fractions in the derived category of complexes of abelian sheaves of length 2. From these two preliminary results, he finally deduces that the derived category of complexes of abelian sheaves of length 2 is equivalent to the category of Picard stacks with morphisms being the isomorphism classes. In this dissertation, we generalize his work, following closely his steps in SGA4, to the case of Picard 2-stacks. But this generalization requires first a clear description of a Picard 2-category as well as of a 2-functor between such 2-categories that respects Picard structure. Once this has been done, we can talk about category of Picard 2-stacks and prove that the derived category of complexes of abelian sheaves of length 3 is equivalent to the category of Picard 2-stacks.
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Date Issued: 2010
Identifier: FSU_migr_etd-1674
Format: Thesis

Title: Chern Classes of Sheaves of Logarithmic Vector Fields for Free Divisors.
Creator: Liao, Xia, Aluﬃ, Paolo, Reina, Laura, Klassen, Eric P., Aldrovandi, Ettore, Petersen, Kathleen, Department of Mathematics, Florida State University
Abstract/Description: The thesis work we present here focuses on solving a conjecture raised by Aluffi about Chern-Schwartz-MacPherson classes. Let $X$ be a nonsingular variety defined over an algebraically closed field $k$ of characteristic $0$, $D$ a reduced effective divisor on $X$, and $U = X smallsetminus D$ the open complement of $D$ in $X$. The conjecture states that $c_{textup{SM}}(1_U) = c(textup{Der}_X(-log D)) cap [X]$ in $A_{*}(X)$ for any locally quasi-homogeneous free divisor $D$. We prove a stronger...
Show moreThe thesis work we present here focuses on solving a conjecture raised by Aluffi about Chern-Schwartz-MacPherson classes. Let $X$ be a nonsingular variety defined over an algebraically closed field $k$ of characteristic $0$, $D$ a reduced effective divisor on $X$, and $U = X smallsetminus D$ the open complement of $D$ in $X$. The conjecture states that $c_{textup{SM}}(1_U) = c(textup{Der}_X(-log D)) cap [X]$ in $A_{*}(X)$ for any locally quasi-homogeneous free divisor $D$. We prove a stronger version of this conjecture. We also report on work aimed at studying the Grothedieck class of hypersurfaces of low degree. In this work, we verified the Geometric Chevalley-Warning conjecture in several low dimensional cases.
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Date Issued: 2013
Identifier: FSU_migr_etd-7467
Format: Thesis

Title: Extraction of the Photon Beam Asymmetry Σ in π⁰ Photoproduction off the Proton Using the CBELSA/TAPS Experiment.
Creator: Sparks, Nathan Andrew, Crede, Volker, Aldrovandi, Ettore, Eugenio, Paul, Owens, Joseph, Capstick, Simon, Department of Physics, Florida State University
Abstract/Description: The CBELSA/TAPS experiment at the electron accelerator ELSA, in Bonn, Germany, was used in order to study the photoproduction of neutral pions off the proton with a linearly polarized photon beam; Neutral pions were reconstructed through their dominant decay mode into two photons. The photons were detected in a barrel/forward electromagnetic calorimeter system which covered 99% of the 4π solid angle. The Crystal Barrel CsI(Tl) calorimeter detected photons at polar angles from 30° to 168°,...
Show moreThe CBELSA/TAPS experiment at the electron accelerator ELSA, in Bonn, Germany, was used in order to study the photoproduction of neutral pions off the proton with a linearly polarized photon beam; Neutral pions were reconstructed through their dominant decay mode into two photons. The photons were detected in a barrel/forward electromagnetic calorimeter system which covered 99% of the 4π solid angle. The Crystal Barrel CsI(Tl) calorimeter detected photons at polar angles from 30° to 168°, while TAPS, a BaF2 spectrometer, covered forward polar angles from 5.8° to 30° and served as a fast trigger; Both calorimeters had complete azimuthal angular coverage. Coherent bremsstrahlung of electrons in a diamond radiator was used to produce a linearly polarized beam of photons with a coherent peak at 1305 or 1610 MeV. The analysis of these two datasets allowed for the measurement of the photon beam asymmetry in the beam photon energy range of 920 to 1680 MeV. For the first time, these results cover the very forward polar angles of the neutral pion. The measurements are compared to the SAID, MAID, and BnGa models and to previous measurements. These new measurements of the photon beam asymmetry contribute to the ongoing experimentally-driven exploration of the N and Δ resonances. The study of strange baryons provides a link between the strong interaction physics of the excited nucleons and the heavy flavor baryons. The upcoming GlueX experiment at Jefferson Lab is expected to provide an opportunity to examine strange baryons in much greater detail than ever before. GEANT-based Monte Carlo simulations of Cascade baryons at the GlueX experiment were conducted in order to better understand the capabilities of this experiment. A proposal, "An initial study of mesons and baryons containing strange quarks with GlueX", was submitted to the 40th Jefferson Lab Program Advisory Committee (PAC), in part, supported by these Cascade baryon simulations. 200 days of additional beam time were approved, with the proposal receiving an A scientific rating.
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Date Issued: 2013
Identifier: FSU_migr_etd-8643
Format: Thesis

Title: Clustering Phenomena in the a = 10 T = 1 Isobaric Multiplet.
Creator: Kuchera, Anthony N., Rogachev, Grigory, Tabor, Samuel, Aldrovandi, Ettore, Prosper, Harrison, Volya, Alexander, Department of Physics, Florida State University
Abstract/Description: Clustering of α particles plays an important role in light atomic nuclei. For example, multicenter structures built on the well-known low-lying states of 8Be can be formed. The addition of nucleons to the system may result in covalent-like bonding between the two α-cores. These structures have been called ''nuclear molecules" because of their analog to atomic molecules. Investigation of these exotic nuclear structures is the main subject of this experimental work. Much of the experimental and...
Show moreClustering of α particles plays an important role in light atomic nuclei. For example, multicenter structures built on the well-known low-lying states of 8Be can be formed. The addition of nucleons to the system may result in covalent-like bonding between the two α-cores. These structures have been called ''nuclear molecules" because of their analog to atomic molecules. Investigation of these exotic nuclear structures is the main subject of this experimental work. Much of the experimental and theoretical work for molecular-like states has been done within the Be isotopes, however, despite of significant effort, our knowledge and understanding of molecular-like structures is still deficient. This is due to limited experimental information on the states of interest. The main goal of this work is to provide this information for the unbound T=1 states in A=10 systems and look for signatures of the exotic α:2N:α configurations. The T=1 states in 10B between Ex = 8.7- 12.1 MeV were studied using the 1H(9Be,α)6Li*(T=1, 0+, 3.56 MeV) reaction. An R-matrix analysis was used to extract parameters for the five resonances observed. The widths of the known 2+ resonance at 8.9 MeV have been measured and support the theoretical predictions that it is a highly clustered state and can be identified as a member of the α-np-α rotational band. The 4+ member was not observed in this reaction channel. In a second experiment, 6He+4He elastic scattering was used to probe resonances in 10Be in search of α-2n-α structures. Using the active target detector system, ANASEN, the excitation function was measured from Ex = 9.6 - 15.4 MeV. This was the first experiment in which the new active target detector, ANASEN, was used in filled (active target) mode. The excitation function shows a strong resonance at 10.2 MeV which was identified as 4+ and assigned to the extremely stretched α:2n:α configuration. A broad structure centered at 13.5 MeV was also observed and it may possibly be the 6+ member of this rotational band.
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Date Issued: 2013
Identifier: FSU_migr_etd-8585
Format: Thesis

Title: N-Butterflies: Modeling Weak Morphisms of Strict N-Groups.
Creator: Dungan, Gregory John, Aldrovandi, Ettore, Piekarewicz, Jorge, Agashe, Amod, Aluffi, Paolo, Petersen, Kathleen, Department of Mathematics, Florida State University
Abstract/Description: Butterflies are an algebraic model of the morphisms of the homotopy category of crossed modules and were originally introduced by Behrang Noohi. Crossed complexes are algebraic structures which generalize crossed modules. The following dissertation is concerned with adapting butterflies to the full subcategory of crossed complexes called reduced n-crossed complexes.
Date Issued: 2014
Identifier: FSU_migr_etd-8975
Format: Thesis

Title: Search for Contact Interactions Using the Inclusive Jet √ pT Spectrum in PP Collisions at S = 7 TeV.
Creator: Haas, Jeffrey David, Prosper, Harrison B., Aldrovandi, Ettore, Reina, Laura, Adams, Todd, Eugenio, Paul, Department of Physics, Florida State University
Abstract/Description: Results are reported of a search for a deviation in the jet production cross section from the prediction of perturbative quantum chromodynamics at next-to-leading order. The search is conducted using a 7 TeV proton-proton data sample corresponding to an integrated luminosity of 5.0 fb-1 , collected with the Compact Muon Solenoid detector at the Large Hadron Collider. A deviation could arise from interactions characterized by a mass scale &Lambda too high to be probed directly at the LHC. Such...
Show moreResults are reported of a search for a deviation in the jet production cross section from the prediction of perturbative quantum chromodynamics at next-to-leading order. The search is conducted using a 7 TeV proton-proton data sample corresponding to an integrated luminosity of 5.0 fb-1 , collected with the Compact Muon Solenoid detector at the Large Hadron Collider. A deviation could arise from interactions characterized by a mass scale &Lambda too high to be probed directly at the LHC. Such phenomena can be modeled as contact interactions. No evidence of a deviation is found. Using the CLs criterion, lower limits are set on &Lambda of 9.9 TeV and 14.3 TeV at 95% confidence level for models with destructive and constructive interference, respectively. Limits obtained with a Bayesian method are also reported.
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Date Issued: 2013
Identifier: FSU_migr_etd-7405
Format: Thesis

Title: Physics of Compact Stars.
Creator: Taruna, Jutri, Piekarewicz, Jorge, Aldrovandi, Ettore, Capstick, Simon, Eugenio, Paul, Reina, Laura, Department of Physics, Florida State University
Abstract/Description: This thesis starts with a pedagogical introduction to the study of white dwarfs and neutron stars. We will present a step-by-step study of compact stars in hydrostatic equilibrium leading to the equations of stellar structure. Through the use of a simple finite-difference algorithm, solutions to the equations for stellar structure both for white dwarfs and neutron stars are presented. While doing so, we will also introduce the physics of the equation of state and insights on dealing with...
Show moreThis thesis starts with a pedagogical introduction to the study of white dwarfs and neutron stars. We will present a step-by-step study of compact stars in hydrostatic equilibrium leading to the equations of stellar structure. Through the use of a simple finite-difference algorithm, solutions to the equations for stellar structure both for white dwarfs and neutron stars are presented. While doing so, we will also introduce the physics of the equation of state and insights on dealing with units and rescaling the equations. The next project consists of the development of a 'semi-classical' model to describe the equation of state of neutron-rich matter in the 'Coulomb frustrated' phase known as nuclear pasta. In recent simulations we have resorted to a classical model that, while simple, captures the essential physics of the nuclear pasta, which consists of the interplay between long range Coulomb repulsion and short range nuclear attraction. However, for the nuclear pasta the de Broglie wavelength is comparable to the average inter-particle separation. Therefore, fermionic correlations are expected to become important. In an effort to address this challenge, a fictitious 'Pauli potential' is introduced to mimic the fermionic correlations. In this thesis we will examine two issues. First, we will address some of the inherent difficulties in a widely used version of the Pauli potential. Second, we will refine the potential in a manner consistent with the most basic properties of a degenerate free Fermi gas, such as its momentum distribution and its two-body correlation function. With the newly refined potential, we study various physical observables, such as the two-body correlation function via Metropolis Monte-Carlo simulations.
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Date Issued: 2008
Identifier: FSU_migr_etd-1687
Format: Thesis

Title: Chern-Schwartz-Macpherson Classes of Graph Hypersurfaces and Schubert Varieties.
Creator: Stryker, Judson P., Aluﬃ, Paolo, Van Engelen, Robert, Aldrovandi, Ettore, Hironaka, Eriko, Van Hoeij, Mark, Department of Mathematics, Florida State University
Abstract/Description: This dissertation finds some partial results in support of two positivity conjectures regarding the Chern-Schwartz-MacPherson (CSM) classes of graph hypersurfaces (conjectured by Aluffi and Marcolli) and Schubert varieties (conjectured by Aluffi and Mihalcea). Direct calculations of some of these CSM classes are performed. Formulas for CSM classes of families of both graph hypersurfaces and coefficients of Schubert varieties are developed. Additionally, the positivity of the CSM class of...
Show moreThis dissertation finds some partial results in support of two positivity conjectures regarding the Chern-Schwartz-MacPherson (CSM) classes of graph hypersurfaces (conjectured by Aluffi and Marcolli) and Schubert varieties (conjectured by Aluffi and Mihalcea). Direct calculations of some of these CSM classes are performed. Formulas for CSM classes of families of both graph hypersurfaces and coefficients of Schubert varieties are developed. Additionally, the positivity of the CSM class of certain families of these varieties is proven. The first chapter starts with an overview and introduction to the material along with some of the background material needed to understand this dissertation. In the second chapter, a series of equivalences of graph hypersurfaces that are useful for reducing the number of cases that must be calculated are developed. A table of CSM classes of all but one graph with 6 or fewer edges are explicitly computed. This table also contains Fulton Chern classes and Milnor classes for the graph hypersurfaces. Using the equivalences and a series of formulas from a paper by Aluffi and Mihalcea, a new series of formulas for the CSM classes of certain families of graph hypersurfaces are deduced. I prove positivity for all graph hypersurfaces corresponding to graphs with first Betti number of 3 or less. Formulas for graphs equivalent to graphs with 6 or fewer edges are developed (as well as cones over graphs with 6 or fewer edges). In the third chapter, CSM classes of Schubert varieties are discussed. It is conjectured by Aluffi and Mihalcea that all Chern classes of Schubert varieties are represented by effective cycles. This is proven in special cases by B. Jones. I examine some positivity results by analyzing and applying combinatorial methods to a formula by Aluffi and Mihalcea. Positivity of what could be considered the ``typical' case for low codimensional coefficients is found. Some other general results for positivity of certain coefficients of Schubert varieties are found. This technique establishes positivity for some known cases very quickly, such as the codimension 1 case as described by Jones, as well as establishing positivity for codimension 2 and families of cases that were previously unknown. An unexpected connection between one family of cases and a second order PDE is also found. Positivity is shown for all cases of codimensions 1-4 and some higher codimensions are discussed. In both the graph hypersurfaces and Schubert varieties, all calculated Chern-Schwartz-MacPherson classes were found to be positive.
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Date Issued: 2011
Identifier: FSU_migr_etd-1531
Format: Thesis

Title: Phenomenology of Supergravity Models with Non-Universal Scalar Masses.
Creator: Mustafayev, Azar, Baer, Howard, Aldrovandi, Ettore, Reina, Laura, Wahl, Horst D., Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: Supersymmetry (SUSY) is one of the most compelling theoretical extensions of the Standard Model. Many physicists believe that the discovery of SUSY may be imminent and that current and upcoming experiments will finally be able to observe it. Because of the large number of parameters and limited information about physics at very high energy, one should combine all available experimental results with cosmological date in order to determine viable models. One of the major unknowns in SUSY is the...
Show moreSupersymmetry (SUSY) is one of the most compelling theoretical extensions of the Standard Model. Many physicists believe that the discovery of SUSY may be imminent and that current and upcoming experiments will finally be able to observe it. Because of the large number of parameters and limited information about physics at very high energy, one should combine all available experimental results with cosmological date in order to determine viable models. One of the major unknowns in SUSY is the origin and pattern of the supersymmetry breaking scalar masses. For the sake of simplicity, they are usually taken to be universal at the grand unification (GUT) scale. In this study, we discuss theoretical motivations for scalar mass non-universality and explore its experimental signatures. We show that the seemingly innocuous deviation from universality in scalar masses can significantly alter our expectations in terms of dark matter as well as (s)particle physics phenomenology. This dissertation is devoted to the analysis of scalar mass non-universality in supergravity models and consists of two parts. After a brief review of phenomenology of models with universality, in the first part, we relax universality of scalar mass terms between generations at GUT scale. This should be done with great care - breaking generational universality of the GUT-scale soft masses induces flavor-violating processes at the weak scale. We find that recent constraints from b →sγ, (g −2)μ and relic density of neutralino Dark Matter can be simultaneously satisfied if one makes the third generation scalar masses heavier than the degenerate first and second generation scalar masses. This scenario has light sleptons that yield large rates for multilepton processes that, as we have shown in our study, make it testable at the LHC, LC and possibly at the Tevatron. In the second part, we have examined the possibility that the soft SUSY breaking mass parameters in the Higgs sector are unrelated to the matter scalar masses mo. We conducted extensive investigation of one and two parameter models of this type. Previously it was known that making Higgs mass squared parameters independent of mo and positive can lower relic density for almost any mSUGRA point. In this study we have found for the first time the particular correlation of Higgs mass squared parameters with other SUSY parameters and experimental observables in the viable parameter space. For example, we have found that allowing Higgs mass squared parameters to take negative values can decrease the axial Higgs boson mass to the A-funnel (2mZ1 mA) with a neutralino relic density in accord with WMAP results even at low tanβ. This wasn't possible for positive Higgs mass squared parameters. We also study implications of these models for Dark Matter detection experiments and collider searches.
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Date Issued: 2006
Identifier: FSU_migr_etd-2158
Format: Thesis

Title: Direct and Indirect Detection of Neutralino Dark Matter.
Creator: O’Farrill, Jorge A., Baer, Howard, Aldrovandi, Ettore, Prosper, Harrison, Hagopian, Vasken, Kemper, Kirby, Department of Physics, Florida State University
Abstract/Description: This dissertation examines the observability of neutralino dark matter in the context of supersymmetric models constrained constrained by the recent WMAP data on the relic density of cold dark matter. The neutralino-nucleon scattering cross-section is calculated and used to derive the rate of interaction for neutralinos scattering from nuclei as well as different modes of indirect detection. Indirect detection of neutralinos is made possible through the annihilation of neutralino pairs into...
Show moreThis dissertation examines the observability of neutralino dark matter in the context of supersymmetric models constrained constrained by the recent WMAP data on the relic density of cold dark matter. The neutralino-nucleon scattering cross-section is calculated and used to derive the rate of interaction for neutralinos scattering from nuclei as well as different modes of indirect detection. Indirect detection of neutralinos is made possible through the annihilation of neutralino pairs into Standard Model (SM) particles. Four different avenues of indirect detection will be covered, including: neutralino annihilation to positrons in the galactic halo, antiprotons from neutralino annihilation in the halo, gamma rays from neutralino annihilation near the core of the galaxy and neutrinos from neutralino annihilation in the core of the sun and the earth. The reaches of various proposed collider experiments will also be calculated. There are many viable supersymmetric models and this dissertation will cover only a few. Most of the rates will be calculated for the mSUGRA model. Results for direct detection will also be given for Yukawa unified SO(10) models with non-universal scalar masses, and 5-dimensional gauge mediated SUSY GUTS. Results for indirect detection will be given for mSUGRA as well as mSUGRA with non-universal gaugino masses. These results will be compared to the sensitivities of ongoing as well as proposed dark matter experiments. Given the precision of the WMAP data, it will be shown that nearly all of the mSUGRA parameter space satisfying the WMAP constraints can be covered by a combination of direct, indirect and collider searches for neutralinos.
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Date Issued: 2004
Identifier: FSU_migr_etd-2311
Format: Thesis

Title: Threshold Resummation in Direct Photon Production.
Creator: Sato, Nobuo, Owens, Joseph Francis, Aldrovandi, Ettore, Reina, Laura, Prosper, Harrison, Schlottmann, Pedro, Department of Physics, Florida State University
Abstract/Description: In this work, we study the phenomenology of direct photon production using theoretical predictions at next-to-leading order with threshold resummation up to next-to-leading- logarithmic accuracy . By analyzing the global data sets of direct photons, we have found a good agreement between the theory and the data for a wide range of energies (√s = 23 GeV up to 7 TeV) if we exclude the data from E706 experiment. We have study the potential impact of direct photon data on parton distribution...
Show moreIn this work, we study the phenomenology of direct photon production using theoretical predictions at next-to-leading order with threshold resummation up to next-to-leading- logarithmic accuracy . By analyzing the global data sets of direct photons, we have found a good agreement between the theory and the data for a wide range of energies (√s = 23 GeV up to 7 TeV) if we exclude the data from E706 experiment. We have study the potential impact of direct photon data on parton distribution functions using Bayesian reweighting approach. A reduction of 10% around 0.3 < x < 0.6 is observed in the uncertainties of the gluon distribution.
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Date Issued: 2014
Identifier: FSU_migr_etd-9085
Format: Thesis

Title: Solutions of Second Order Recurrence Relations.
Creator: Levy, Giles, Van Hoeij, Mark, Van Engelen, Robert A., Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
Abstract/Description: This thesis presents three algorithms each of which returns a transformation from a base equation to the input using transformations that preserve order and homogeneity (referred to as gt-transformations). The first and third algorithm are new and the second algorithm is an improvement over prior algorithms for the second order case. The first algorithm `Find 2F1' finds a gt-transformation to a recurrence relation satisfied by a hypergeometric series u(n) = hypergeom([a+n, b],[c],z), if such...
Show moreThis thesis presents three algorithms each of which returns a transformation from a base equation to the input using transformations that preserve order and homogeneity (referred to as gt-transformations). The first and third algorithm are new and the second algorithm is an improvement over prior algorithms for the second order case. The first algorithm `Find 2F1' finds a gt-transformation to a recurrence relation satisfied by a hypergeometric series u(n) = hypergeom([a+n, b],[c],z), if such a transformation exists. The second algorithm `Find Liouvillian' finds a gt-transformation to a recurrence relation of the form u(n+2) + b(n)u(n) = 0 for some b(n) in C(n), if such a transformation exists. The third algorithm `Database Solver' takes advantage of a large database of sequences, `The On-Line Encyclopedia of Integer Sequences' maintained by Neil A. J. Sloane at AT&T Labs Research. It employs this database by using the recurrence relations that they satisfy as base equations from which to return a gt-transformation, if such a transformation exists.
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Date Issued: 2010
Identifier: FSU_migr_etd-3099
Format: Thesis

Title: Supersymmetry at pp¯, pp and e+e− Colliders in Light of Wmap Measurements of the Dark Matter Density of the Universe.
Creator: Krupovnickas, Tadas, Baer, Howard, Aldrovandi, Ettore, Reina, Laura, Adams, Todd, Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: The Standard Model (SM) describes almost all the particle physics experiments with a high accuracy. However, the SM has a lot of conceptual problems (spontaneous symmetry breaking is introduced by hand, the Higgs boson mass has to be very finely fine-tuned, there is no explanation for the number of generations or particle quantum numbers, there are at least 19 arbitrary model parameters). Therefore, it is reasonable to search for theories solving some or all of the problems that the SM has....
Show moreThe Standard Model (SM) describes almost all the particle physics experiments with a high accuracy. However, the SM has a lot of conceptual problems (spontaneous symmetry breaking is introduced by hand, the Higgs boson mass has to be very finely fine-tuned, there is no explanation for the number of generations or particle quantum numbers, there are at least 19 arbitrary model parameters). Therefore, it is reasonable to search for theories solving some or all of the problems that the SM has. One class of such theories is based on an assumption that at some large energy scale Nature chooses the maximal possible space-time symmetry, called supersymmetry (SUSY). Once the theory is constructed, it has to be tested against the experiment. This dissertation explores various collider signals in the framework of minimal Supergravity model (mSUGRA) and gaugino mediated SUSY breaking model (inoMSB). We calculate whether the signal predicted by these models could be detected at the Fermilab Tevatron and at the CERN LHC hadronic colliders, and also explore the capabilities of a future electron-positron Linear Collider. We show the collider reach contours in the mSUGRA parameter space, combined with constraints from other experiments. We also devise new cuts, optimizing the signal to background ratio in the regions where no such work was previously done.
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Date Issued: 2004
Identifier: FSU_migr_etd-2897
Format: Thesis

Title: Topics in Physics Beyond the Standard Model.
Creator: Köpp, Karoline, Okui, Takemichi, Aldrovandi, Ettore, Reina, Laura, Adams, Todd, Gerardy, Christopher, Department of Physics, Florida State University
Abstract/Description: In this work, topics in physics beyond the standard model of high energy phyics relevant to the experimental studies at the Large Hadron Collider (LHC) at CERN are discussed. We introduce an effective theory to describe the dynamics of heavy Majorana particles, whose existence is predicted in many extensions of the standard model. Further, it is demonstrated how by combining the two independent concepts of a weakly interacting massive particle accounting for the dark matter observed in our...
Show moreIn this work, topics in physics beyond the standard model of high energy phyics relevant to the experimental studies at the Large Hadron Collider (LHC) at CERN are discussed. We introduce an effective theory to describe the dynamics of heavy Majorana particles, whose existence is predicted in many extensions of the standard model. Further, it is demonstrated how by combining the two independent concepts of a weakly interacting massive particle accounting for the dark matter observed in our universe and gauge coupling unification, strong phenomenological trends can be inferred. The scenario we present predicts new colored states within LHC reach that can be either collider stable or decay promptly to final states including a Higgs particle. In both cases, interesting LHC signatures are expected. The LHC discovery of the long predicted Higgs boson as well as new lower bounds on supersymmetric particle masses provide motivation to re-evaluate the issue of fine-tuning in supersymmetric theories. We provide an overview of the current state of this ongoing discussion. In the last part of this work we introduce an alternative approach termed stable near-criticality, in which the standard limits on superparticle masses stemming from fine-tuning considerations are relaxed. This approach requires specific and robust correlations among soft mass terms. We discuss how reduced fine-tuning can be achieved even if the gauge and Yukawa couplings are considered variable parameters. Finally, we illustrate our findings with a possible model implementation and demonstrate the validity of our approach by analysing a representative benchmark point.
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Date Issued: 2013
Identifier: FSU_migr_etd-7451
Format: Thesis

Title: An Analysis of Conjugate Harmonic Components of Monogenic Functions and Lambda Harmonic Functions.
Creator: Ballenger-Fazzone, Brendon Kerr, Nolder, Craig, Harper, Kristine, Aldrovandi, Ettore, Case, Bettye Anne, Quine, J. R. (John R.), Ryan, John Barry, Florida State University,...
Show moreBallenger-Fazzone, Brendon Kerr, Nolder, Craig, Harper, Kristine, Aldrovandi, Ettore, Case, Bettye Anne, Quine, J. R. (John R.), Ryan, John Barry, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: Clifford analysis is seen as the higher dimensional analogue of complex analysis. This includes a rich study of Clifford algebras and, in particular, monogenic functions, or Clifford-valued functions that lie in the kernel of the Cauchy-Riemann operator. In this dissertation, we explore the relationships between the harmonic components of monogenic functions and expand upon the notion of conjugate harmonic functions. We show that properties of the even part of a Clifford-valued function...
Show moreClifford analysis is seen as the higher dimensional analogue of complex analysis. This includes a rich study of Clifford algebras and, in particular, monogenic functions, or Clifford-valued functions that lie in the kernel of the Cauchy-Riemann operator. In this dissertation, we explore the relationships between the harmonic components of monogenic functions and expand upon the notion of conjugate harmonic functions. We show that properties of the even part of a Clifford-valued function determine properties of the odd part and vice versa. We also explore the theory of functions lying in the kernel of a generalized Laplace operator, the λ-Laplacian. We explore the properties of these so-called λ-harmonic functions and give the solution to the Dirichlet problem for the λ-harmonic functions on annular domains in Rⁿ.
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Date Issued: 2016
Identifier: FSU_2016SP_BallengerFazzone_fsu_0071E_13136
Format: Thesis

Title: Third Order A-Hypergeometric Functions.
Creator: Xu, Wen, Hoeij, Mark van, Reina, Laura, Agashe, Amod S. (Amod Sadanand), Aldrovandi, Ettore, Aluffi, Paolo, Florida State University, College of Arts and Sciences, Department of...
Show moreXu, Wen, Hoeij, Mark van, Reina, Laura, Agashe, Amod S. (Amod Sadanand), Aldrovandi, Ettore, Aluffi, Paolo, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: To solve globally bounded order $3$ linear differential equations with rational function coefficients, this thesis introduces a partial $_3F_2$-solver (Section~\ref{3F2 type solution}) and $F_1$-solver (Chapter~\ref{F1 solver}), where $_3F_2$ is the hypergeometric function $_3F_2(a_1,a_2,a_3;b_1,b_2\,|\,x)$ and $F_1$ is the Appell's $F_1(a,b_1,b_2,c\,|\,x,y).$ To investigate the relations among order $3$ multivariate hypergeometric functions, this thesis presents two multivariate tools:...
Show moreTo solve globally bounded order $3$ linear differential equations with rational function coefficients, this thesis introduces a partial $_3F_2$-solver (Section~\ref{3F2 type solution}) and $F_1$-solver (Chapter~\ref{F1 solver}), where $_3F_2$ is the hypergeometric function $_3F_2(a_1,a_2,a_3;b_1,b_2\,|\,x)$ and $F_1$ is the Appell's $F_1(a,b_1,b_2,c\,|\,x,y).$ To investigate the relations among order $3$ multivariate hypergeometric functions, this thesis presents two multivariate tools: compute homomorphisms (Algorithm~\ref{hom}) of two $D$-modules, where $D$ is a multivariate differential ring, and compute projective homomorphisms (Algorithm~\ref{algo ProjHom}) using the tensor product module and Algorithm~\ref{hom}. As an application, all irreducible order $2$ subsystems from reducible order $3$ systems turn out to come from Gauss hypergeometric function $_2F_1(a,b;c\,|\,x)$ (Chapter~\ref{chapter applications}).
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Date Issued: 2017
Identifier: FSU_FALL2017_XU_fsu_0071E_14234
Format: Thesis

Title: Algorithms for Solving Linear Differential Equations with Rational Function Coefficients.
Creator: Imamoglu, Erdal, van Hoeij, Mark, van Engelen, Robert, Agashe, Amod S. (Amod Sadanand), Aldrovandi, Ettore, Aluffi, Paolo, Florida State University, College of Arts and Sciences...
Show moreImamoglu, Erdal, van Hoeij, Mark, van Engelen, Robert, Agashe, Amod S. (Amod Sadanand), Aldrovandi, Ettore, Aluffi, Paolo, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: This thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1 searches for solutions of type: exp(∫ r dx) ⋅ ₂F₁ (a₁,a₂;b₁;f) and Algorithm 5.2.1 searches for solutions of type exp(∫ r dx) (r₀ ⋅ ₂F₁(a₁,a₂;b₁;f) + r₁ ⋅ ₂F´₁ (a₁,a₂;b₁;f)) where f, r, r₀, r₁ ∈ ℚ̅(̅x̅)̅ and a₁,a₂,b₁ ∈ ℚ and denotes the Gauss hypergeometric function. The algorithms use modular...
Show moreThis thesis introduces two new algorithms to find hypergeometric solutions of second order regular singular differential operators with rational function or polynomial coefficients. Algorithm 3.2.1 searches for solutions of type: exp(∫ r dx) ⋅ ₂F₁ (a₁,a₂;b₁;f) and Algorithm 5.2.1 searches for solutions of type exp(∫ r dx) (r₀ ⋅ ₂F₁(a₁,a₂;b₁;f) + r₁ ⋅ ₂F´₁ (a₁,a₂;b₁;f)) where f, r, r₀, r₁ ∈ ℚ̅(̅x̅)̅ and a₁,a₂,b₁ ∈ ℚ and denotes the Gauss hypergeometric function. The algorithms use modular reduction, Hensel lifting, rational function reconstruction, and rational number reconstruction to do so. Numerous examples from different branches of science (mostly from combinatorics and physics) showed that the algorithms presented in this thesis are very effective. Presently, Algorithm 5.2.1 is the most general algorithm in the literature to find hypergeometric solutions of such operators. This thesis also introduces a fast algorithm (Algorithm 4.2.3) to find integral bases for arbitrary order regular singular differential operators with rational function or polynomial coefficients. A normalized (Algorithm 4.3.1) integral basis for a differential operator provides us transformations that convert the differential operator to its standard forms (Algorithm 5.1.1) which are easier to solve.
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Date Issued: 2017
Identifier: FSU_SUMMER2017_Imamoglu_fsu_0071E_13942
Format: Thesis

Title: Characteristic Classes and Local Invariants of Determinantal Varieties and a Formula for Equivariant Chern-Schwartz-MacPherson Classes of Hypersurfaces.
Creator: Zhang, Xiping, Aluffi, Paolo, Piekarewicz, Jorge, Aldrovandi, Ettore, Petersen, Kathleen L., Hoeij, Mark van, Florida State University, College of Arts and Sciences, Department...
Show moreZhang, Xiping, Aluffi, Paolo, Piekarewicz, Jorge, Aldrovandi, Ettore, Petersen, Kathleen L., Hoeij, Mark van, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: Determinantal varieties parametrize spaces of matrices of given ranks. The main results of this dissertation are computations of intersection-theoretic invariants of determinantal varieties. We focus on the Chern-Mather and Chern-Schwartz-MacPherson classes, on the characteristic cycles, and on topologically motivated invariants such as the local Euler obstruction. We obtain explicit formulas in both the ordinary and the torus-equivariant setting, and formulate a conjecture concerning the...
Show moreDeterminantal varieties parametrize spaces of matrices of given ranks. The main results of this dissertation are computations of intersection-theoretic invariants of determinantal varieties. We focus on the Chern-Mather and Chern-Schwartz-MacPherson classes, on the characteristic cycles, and on topologically motivated invariants such as the local Euler obstruction. We obtain explicit formulas in both the ordinary and the torus-equivariant setting, and formulate a conjecture concerning the effectiveness of the Chern-Schwartz-MacPherson classes of determinantal varieties. We also prove a vanishing property for the Chern-Schwartz-MacPherson classes of general group orbits. As applications we obtain formulas for the sectional Euler characteristic of determinantal varieties and the microlocal indices of their intersection cohomology sheaf complexes. Moreover, for a close embedding we define the equivariant version of the Segre class and prove an equivariant formula for the Chern-Schwartz-MacPherson classes of hypersurfaces of projective varieties.
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Date Issued: 2018
Identifier: 2018_Sp_Zhang_fsu_0071N_14521
Format: Thesis

Title: The 1-Type of Algebraic K-Theory as a Multifunctor.
Creator: Valdes, Yaineli, Aldrovandi, Ettore, Rawling, John Piers, Agashe, Amod S., Aluffi, Paolo, Petersen, Kathleen L., Hoeij, Mark van, Florida State University, College of Arts and...
Show moreValdes, Yaineli, Aldrovandi, Ettore, Rawling, John Piers, Agashe, Amod S., Aluffi, Paolo, Petersen, Kathleen L., Hoeij, Mark van, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: It is known that the category of Waldhausen categories is a closed symmetric multicategory and algebraic K-theory is a multifunctor from the category of Waldhuasen categories to the category of spectra. By assigning to any Waldhausen category the fundamental groupoid of the 1-type of its K-theory spectrum, we get a functor from the category of Waldhausen categories to the category of Picard groupoids, since stable 1-types are classified by Picard groupoids. We prove that this functor is a...
Show moreIt is known that the category of Waldhausen categories is a closed symmetric multicategory and algebraic K-theory is a multifunctor from the category of Waldhuasen categories to the category of spectra. By assigning to any Waldhausen category the fundamental groupoid of the 1-type of its K-theory spectrum, we get a functor from the category of Waldhausen categories to the category of Picard groupoids, since stable 1-types are classified by Picard groupoids. We prove that this functor is a multifunctor to a corresponding multicategory of Picard groupoids.
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Date Issued: 2018
Identifier: 2018_Sp_Valdes_fsu_0071E_14374
Format: Thesis

Title: Search for New and Unusual Strangeonia States Using γp → pφη with GlueX at Thomas Jefferson National Accelerator Facility.
Creator: Cannon, Bradford Emerson, Eugenio, Paul Michael, Aldrovandi, Ettore, Capstick, Simon, Wahl, Horst, Crede, Volker, Ostrovidov, Alexander, Florida State University, College of...
Show moreCannon, Bradford Emerson, Eugenio, Paul Michael, Aldrovandi, Ettore, Capstick, Simon, Wahl, Horst, Crede, Volker, Ostrovidov, Alexander, Florida State University, College of Arts and Sciences, Department of Physics
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Abstract/Description: We perform an analysis dedicated to the search for new and unusual strangeonium states produced in the reaction γp → pφη. The data used for this analysis was recorded during the Spring 2017 physics run for Hall D of Thomas Jefferson National Accelerator Facility, where the GlueX experiment is located. The GlueX experiment uses a linearly polarized coherent bremsstrahlung beam of up to 12 GeV in energy. This photon beam interacts with a stationary liquid hydrogen target located inside the...
Show moreWe perform an analysis dedicated to the search for new and unusual strangeonium states produced in the reaction γp → pφη. The data used for this analysis was recorded during the Spring 2017 physics run for Hall D of Thomas Jefferson National Accelerator Facility, where the GlueX experiment is located. The GlueX experiment uses a linearly polarized coherent bremsstrahlung beam of up to 12 GeV in energy. This photon beam interacts with a stationary liquid hydrogen target located inside the GlueX detector. The subsequent photoproduction will provide final states ideal for studying both exotic and non-exotic ss ̄ mesons. After all cuts, a total of four different selection methods were used to study the φη parent state. Three of these methods used an event by event probabilistic weighting method in order to separate signal from background, and the fourth method was simply an elliptical subtraction which did not utilize probabilistic weighting. After comparing the φη invariant mass spectra for all selection methods, two structures were consistently observed. One of the structures was found to have a mass of (m = 1.657 ± 0.008)GeV/c^2 and a width of (σ = 0.190 ± 0.024)GeV/^2 ; and the second structure was found to have a mass of (m = 1.879 ± 0.004)GeV/c^2 and a width of (σ = 0.042 ± 0.014)GeV/c^2 .
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Date Issued: 2019
Identifier: 2019_Spring_Cannon_fsu_0071E_15063
Format: Thesis

Title: Finding All Bessel Type Solutions for Linear Differential Equations with Rational Function Coefficients.
Creator: Yuan, Quan, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
Abstract/Description: A linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bessel functions, change of variables, algebraic operations and exponential integrals. For second order equations with rational function coefficients, the function f of change of variables must be a rational function or the square root of a rational function. An algorithm was given by Debeerst, van Hoeij, and Koepf, that can compute Bessel type solutions if and only if...
Show moreA linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bessel functions, change of variables, algebraic operations and exponential integrals. For second order equations with rational function coefficients, the function f of change of variables must be a rational function or the square root of a rational function. An algorithm was given by Debeerst, van Hoeij, and Koepf, that can compute Bessel type solutions if and only if change of variables is a rational function. In this thesis we extend this work to the square root case, resulting in a complete algorithm to find all Bessel type solutions. This algorithm can be easily extended to a Whittaker/Kummer solver. Combine the two algorithms, we can get a complete algorithm for all 0F1 and 1F1 type solutions. We also use our algorithm to analyze the relation between Bessel functions and Heun functions.
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Date Issued: 2012
Identifier: FSU_migr_etd-5296
Format: Thesis

Title: Solving Linear Differential Equations in Terms of Hypergeometric Functions by ₂-Descent.
Creator: Fang, Tingting, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
Abstract/Description: Let L be a linear ordinary differential equation with coefficients in C(x). This thesis presents algorithms to solve L in closed form. The key part of this thesis is 2-descent method, which is used to reduce L to an equation that is easier to solve. The starting point is an irreducible L, and the goal of 2-descent is to decide if L is projectively equivalent to another equation $\tilde{L}$ that is defined over a subfield C(f) of C(x). Although part of the mathematics for 2-descent has already...
Show moreLet L be a linear ordinary differential equation with coefficients in C(x). This thesis presents algorithms to solve L in closed form. The key part of this thesis is 2-descent method, which is used to reduce L to an equation that is easier to solve. The starting point is an irreducible L, and the goal of 2-descent is to decide if L is projectively equivalent to another equation $\tilde{L}$ that is defined over a subfield C(f) of C(x). Although part of the mathematics for 2-descent has already been treated before, a complete implementation could not be given because it involved a step for which we do not have a complete implementation. Our key novelty is to give an approach that is fully implementable. We describe and implement the algorithm for order 2, and show by examples that the same also work for higher order. By doing 2-descent for L, the number of true singularities drops to at most n/2 + 2 (n is the number of true singularities of L). This provides us ways to solve L in closed form(e.g.in terms of hypergeometric funtions).
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Date Issued: 2012
Identifier: FSU_migr_etd-5350
Format: Thesis

Title: An Analytic Approach to Estimating the Required Surplus, Benchmark Profit, and Optimal Reinsurance Retention for an Insurance Enterprise.
Creator: Boor, Joseph A. (Joseph Allen), Born, Patricia, Case, Bettye Anne, Tang, Qihe, Rogachev, Grigory, Okten, Giray, Aldrovandi, Ettore, Paris, Steve, Department of Mathematics,...
Show moreBoor, Joseph A. (Joseph Allen), Born, Patricia, Case, Bettye Anne, Tang, Qihe, Rogachev, Grigory, Okten, Giray, Aldrovandi, Ettore, Paris, Steve, Department of Mathematics, Florida State University
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Abstract/Description: This paper presents an analysis of the capital needs, needed return on capital, and optimum reinsurance retention for insurance companies, all in the context where claims are either paid out or known with certainty within or soon after the policy period. Rather than focusing on how to estimate such values using Monte Carlo simulation, it focuses on closed form expressions and approximations for key quantities that are needed for such an analysis. Most of the analysis is also done using a...
Show moreThis paper presents an analysis of the capital needs, needed return on capital, and optimum reinsurance retention for insurance companies, all in the context where claims are either paid out or known with certainty within or soon after the policy period. Rather than focusing on how to estimate such values using Monte Carlo simulation, it focuses on closed form expressions and approximations for key quantities that are needed for such an analysis. Most of the analysis is also done using a distribution-free approach with respect to the loss severity distribution, so minimal or no assumptions surrounding the specific distribution are needed when analyzing the results. However, one key parameter, that is treated via an exhaustion of cases, involves the degree of parameter uncertainty, the number of separate lines of business involved. This is done for the no parameter uncertainty monoline compound Poisson distribution as well as situations involving (lognormal) severity parameter uncertainty, (gamma/negative binomial) count parameter uncertainty, the multiline compound Poisson case, and the compound Poisson scenario with parameter uncertainty, and especially parameter uncertainty correlated across the lines of business. It shows how the risk of extreme aggregate losses that is inherent in insurance operations may be understood (and, implicitly, managed) by performing various calculations using the loss severity distribution, and, where appropriate, key parameters driving the parameter uncertainty distributions. Formulas are developed that estimate the capital and surplus needs of a company(using the VaR approach), and therefore the profit needs of a company that involve tractable calculations. As part of that the process the benchmark loading for profit, reflecting both the needed financial support for the amount of capital to adequately secure to a given one year survival probability, and the amount needed to recompense investors for diversifiable risk is discussed. An analysis of whether or not the loading for diversifiable risk is needed is performed. Approximations to the needed values are performed using the moments of the capped severity distribution and analytic formulas from the frequency distribution as inputs into method of moments normal and lognormal approximations to the percentiles of the aggregate loss distribution. An analysis of the optimum reinsurance retention/policy limit is performed as well, with capped loss distribution/frequency distribution equations resulting from the relationship that the marginal profit (with respect to the loss cap) should be equal to the marginal expense and profit dollar loading with respect to the loss cap. Analytical expressions are developed for the optimum reinsurance retention. Approximations to the optimum retention based on the normal distribution were developed and their error analyzed in great detail. The results indicate that in the vast majority of practical scenarios, the normal distribution approximation to the optimum retention is acceptable. Also included in the paper is a brief comparison of the VaR (survival probability) and expected policyholder deficit (EPD) and TVaR approaches to surplus adequacy (which conclude that the VaR approach is superior for most property/casualty companies); a mathematical analysis of the propriety of insuring the upper limits of the loss distribution, which concludes that, even if unlimited funds were available to secure losses in capital and reinsurance, it would not be in the insured's best interest to do so. Further inclusions to date include a illustrative derivation of the generalized collective risk equation and a method for interpolating ``along'' a mathematical curve rather than directly using the values on the curve. As a prelude to a portion of the analysis, a theorem was proven indicating that in most practical situations, the n-1st order derivatives of a suitable probability mass function at values L, when divided by the product of L and the nth order derivative, generate a quotient with a limit at infinity that is less than 1/n.
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Date Issued: 2012
Identifier: FSU_migr_etd-4726
Format: Thesis

Title: Principal Elements of Mixed-Sign Coxeter Systems.
Creator: Armstrong, Johnathon Kyle, Hironaka, Eriko, Petersen, Kathleen, Chicken, Eric, Aldrovandi, Ettore, Bellenot, Steven, Van Hoeij, Mark, Department of Mathematics, Florida State...
Show moreArmstrong, Johnathon Kyle, Hironaka, Eriko, Petersen, Kathleen, Chicken, Eric, Aldrovandi, Ettore, Bellenot, Steven, Van Hoeij, Mark, Department of Mathematics, Florida State University
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Abstract/Description: In this thesis we generalize results from classical Coxeter systems to mixed-sign Coxeter systems which are denoted by a triple (W,S,B)consisting of a reflection group W, a distinguished set of generators Sfor the group for W, and a bilinear form Bon R n. A generator s i in the set S is defined to negate the ith basis vector of R n and fix the set of vectors v which are orthogonal relative to B. Classical Coxeter theory works in this fashion, here we generalize this notion to encompass both...
Show moreIn this thesis we generalize results from classical Coxeter systems to mixed-sign Coxeter systems which are denoted by a triple (W,S,B)consisting of a reflection group W, a distinguished set of generators Sfor the group for W, and a bilinear form Bon R n. A generator s i in the set S is defined to negate the ith basis vector of R n and fix the set of vectors v which are orthogonal relative to B. Classical Coxeter theory works in this fashion, here we generalize this notion to encompass both Coxeter systems in addition to mixed-sign Coxeter systems. As in classical Coxeter theory, we show that the bilinear form may be used to compute an element of the reflection group called a principal element. In classical Coxeter groups, the principal elements have been shown to have special properties. The so-called deletion condition is a property of classical Coxeter systems which allows Coxeter groups to have a presentation which only depends on pairwise relationships between generators. Here, we show that mixed-sign Coxeter systems do not generally have the deletion condition. We give a correspondence between a graph $\Gamma$ and the reflection system (W,S,B). We refer to the reflection group associated to &Gamma by W (&Gamma). We show an isomorphism of mixed-sign Coxeter groups; explicitly if &Gamma is a bipartite mixed-sign Coxeter graph and &Gamma is the mixed-sign Coxeter graph with all the nodes of &Gamma- negated then (W,S,B(&Gamma)) and (W,S,B(&Gamma-)) are conjugate reflection systems. Furthermore, we indicate the the bipartite condition is necessary. We show a class of examples; odd cycles with all negative nodes where negating all the nodes gives a reflection system which is not conjugate. Additionally, we show that the spectral radius of mixed-sign Coxeter elements are not bounded below by the bipartite eigenvalue of the mixed-sign Coxeter system, this is another distinguishing feature of mixed-sign Coxeter systems from their classical counterparts and provides an interesting avenue of research to pursue in the future.
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Date Issued: 2012
Identifier: FSU_migr_etd-4697
Format: Thesis

Title: Hypergeometric Solutions of Linear Differential Equations with Rational Function Coefficients.
Creator: Kunwar, Vijay Jung, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Hironaka, Eriko, Petersen, Kathleen, Department of Mathematics, Florida State...
Show moreKunwar, Vijay Jung, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Hironaka, Eriko, Petersen, Kathleen, Department of Mathematics, Florida State University
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Abstract/Description: Let L be a second order linear differential equation with rational function coefficients. We want to find a solution (if that exists) of L in terms of 2F1-hypergeometric function. This thesis presents two algorithms to find such solution in the following cases: 1. L has five regular singularities where at least one of them is logarithmic. 2. L has hypergeometric solution of degree three, i.e, L is solvable in terms of 2F1(a,b;c | f) where f is a rational function of degree three.
Date Issued: 2014
Identifier: FSU_migr_etd-9021
Format: Thesis

Title: Exotic Smoothness, Branched Covering Spaces, Andquantum Gravity.
Creator: Duston, Christopher Levi, Marcolli, Matilde, Reina, Laura, Klassen, Eric, Prosper, Harrison, Vafek, Oskar, Aldrovandi, Ettore, Hironaka, Eriko, Department of Physics, Florida...
Show moreDuston, Christopher Levi, Marcolli, Matilde, Reina, Laura, Klassen, Eric, Prosper, Harrison, Vafek, Oskar, Aldrovandi, Ettore, Hironaka, Eriko, Department of Physics, Florida State University
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Abstract/Description: This thesis addresses the role of topology and geometry in quantum gravity. A major topic will be how inequivalent differentiable structures (exotic smoothness) can play a physically significant role in both semiclassical gravity and loop quantum gravity. We will discuss the result of including these structures into a physical theory, and describe some approaches to fully account for them. We will also be able to use our construction to study the topology of loop quantum gravity. In our...
Show moreThis thesis addresses the role of topology and geometry in quantum gravity. A major topic will be how inequivalent differentiable structures (exotic smoothness) can play a physically significant role in both semiclassical gravity and loop quantum gravity. We will discuss the result of including these structures into a physical theory, and describe some approaches to fully account for them. We will also be able to use our construction to study the topology of loop quantum gravity. In our framework, topology change will be a natural part of the theory. The approaches discussed in this thesis will be inspired by novel mathematical results, applied to established physical models. It is hoped that the methods described herein will lead to a greater understanding of the deep connection between geometry and physics, particularly as it relates to the geometrical nature of the gravitational field.
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Date Issued: 2013
Identifier: FSU_migr_etd-7363
Format: Thesis

Title: Threshold Resummation and the Determination of Parton Distribution Functions.
Creator: Westmark, David, Owens, Joseph F., Aldrovandi, Ettore, Reina, Laura, Blessing, Susan K., Roberts, Winston, Florida State University, College of Arts and Sciences, Department of...
Show moreWestmark, David, Owens, Joseph F., Aldrovandi, Ettore, Reina, Laura, Blessing, Susan K., Roberts, Winston, Florida State University, College of Arts and Sciences, Department of Physics
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Abstract/Description: Precise knowledge of parton distribution functions (PDFs) is necessary to the accurate calculation of QCD observables initiated by hadrons. The deep inelastic scattering (DIS) and lepton pair production (LPP) processes are primary sources of information on PDFs. Recent global fits for PDFs have used DIS data from the large Bjorken $x$, moderate $Q^{2}$ region. It is known that there are large logarithms in this kinematic region that can be resummed using threshold resummation techniques. The...
Show morePrecise knowledge of parton distribution functions (PDFs) is necessary to the accurate calculation of QCD observables initiated by hadrons. The deep inelastic scattering (DIS) and lepton pair production (LPP) processes are primary sources of information on PDFs. Recent global fits for PDFs have used DIS data from the large Bjorken $x$, moderate $Q^{2}$ region. It is known that there are large logarithms in this kinematic region that can be resummed using threshold resummation techniques. The purpose of this study is to investigate the effects of simultaneously including DIS and LPP threshold resummation in the determinations of PDFs. The analysis includes a study of the effects of the choice of resummation prescription and of current resummation methods used in the LPP rapidity and $x_{F}$ distributions. It is demonstrated theoretically and phenomenologically that the current resummation methods for such distributions are approximations that lose accuracy at high rapidities or $x_{F}$. The unapproximated resummation formalism is extended to the $\overline{\mathrm{MS}}$ scheme in the minimal and Borel prescriptions and used in conjunction with resummation in DIS to perform a global fit. The resultant PDF sets that correspond to two choices of resummation prescription are analyzed to determine the effect of threshold resummation on PDF fits and its theoretical uncertainties.
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Date Issued: 2015
Identifier: FSU_migr_etd-9485
Format: Thesis

Title: Edge Spin Excitations and Reconstructions of Quantum Hall Liquids.
Creator: Zhang, Yuhui, Yang, Kun, Aldrovandi, Ettore, Piekarewicz, Jorge, Engel, Lloyd W., Bonesteel, N. E., Florida State University, College of Arts and Sciences, Department of Physics
Abstract/Description: In this dissertation, we investigate the edge spin excitations and reconstructions of quantum Hall (QH) liquids. Edge spin reconstructions reflect the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of QH liquids. The main method used in this dissertation is the exact diagonalization calculation for finite size systems. The QH liquids studied in this dissertation are classified into three kinds, based on their topological properties and...
Show moreIn this dissertation, we investigate the edge spin excitations and reconstructions of quantum Hall (QH) liquids. Edge spin reconstructions reflect the interplay of confining potential, electron-electron interaction, and Zeeman splitting at the edges of QH liquids. The main method used in this dissertation is the exact diagonalization calculation for finite size systems. The QH liquids studied in this dissertation are classified into three kinds, based on their topological properties and statistics of quasiparticles (quasiholes). The first kind of QH liquids is spin-polarized QH liquids. The QH liquids with filling factors ν = 1 and 1/3 are studied in this kind. We find the low-energy excitations of the ν = 1 and 1/3 are bosonic edge spin waves. Instabilities of these ferromagnetic state with altering confinement strength result from the softening of these spin waves and formation of edge spin textures. A microscopic trial wave function is used to study the edge instabilities of larger systems with particle number up to 40, and the obtained results are consistent to the ones calculated by exact diagonalization. The second kind of QH liquids is spin-unpolarized QH liquids. The liquids with ν = 2, 2/5 and 2/3 are studied in this kind. When ν = 2, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appearing between two compact states are their edge spin waves. The initial ν = 2 instability is toward the compact state with total spin 1. At ν = 2/5, the edge instabilities is also triggered by softening of the edge spin waves with smoother confinement. The situation of ν = 2/3 unpolarized QH liquids is a little different, because it has one backward-moving edge spin wave mode and one forward-moving magnetoplasmon mode. There is no mystery about what kind of instability would occur with stronger or smoother confinement. The exact diagonalization calculation of finite systems can reproduce the instability induced by edge spin wave at the stronger confinement side and gives an estimate about the critical value of confining potential. But instability due to edge magnetoplasmon mode can not be realized in small size systems because of the high velocity of this mode. The last kind is the non-Abelian QH liquid (at ν = 5/2). Its edge instability triggered by softening of edge magnetoplasmon excitations with smoother confinement. Three different confinements are compared in the study of integer QH liquids in finite size systems. And some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit. The effect of Zeeman splitting to the edge instabilities is also considered in this dissertation.
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Date Issued: 2014
Identifier: FSU_migr_etd-9274
Format: Thesis

Title: Lagrangian Specialization via Log Resolutions and Schwartz-MacPherson Chern Classes.
Creator: Adams, William J. L. (William James Louis), Aluffi, Paolo, Rawling, J. Piers, Aldrovandi, Ettore, Kim, Kyounghee, Agashe, Amod Sadanand, Florida State University, College of...
Show moreAdams, William J. L. (William James Louis), Aluffi, Paolo, Rawling, J. Piers, Aldrovandi, Ettore, Kim, Kyounghee, Agashe, Amod Sadanand, Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: This dissertation covers several topics around the idea of the Schwartz-MacPherson Chern classes, which were independently constructed by M.H. Schwartz around 1965 and R. MacPherson in the early 1970's. First we review a more recent construction of Schwartz-MacPherson Chern class due to G. Kennedy using projective Lagrangian conormals and make explicit some details not found in that work. Around 1980, J.-L. Verdier obtained a specialization formula for Schwartz-MacPherson Chern classes, which...
Show moreThis dissertation covers several topics around the idea of the Schwartz-MacPherson Chern classes, which were independently constructed by M.H. Schwartz around 1965 and R. MacPherson in the early 1970's. First we review a more recent construction of Schwartz-MacPherson Chern class due to G. Kennedy using projective Lagrangian conormals and make explicit some details not found in that work. Around 1980, J.-L. Verdier obtained a specialization formula for Schwartz-MacPherson Chern classes, which was recovered by Kennedy again using the Lagrangian setting and Fulton-MacPherson intersection theory, elaborating on work of C. Sabbah. A verbatim reading of this approach reveals several subtleties. We introduce an alternate blow-up construction to address some of these subtleties, as well as an alternate definition based upon the work of C. Sabbah. We then prove that either of these constructions indeed provides a complete alternative proof of Verdier's specialization formula. In the early 2010's P. Aluffi revisited Verdier's work and developed a more calculable approach to specialization utilizing constructible functions and the Weak Factorization Theorem of Abramovich, Karu, Matsuki, and Wl􏰀odarczyk. Aluffi's construction gives an explicit formula when in the case of a divisor with normal crossings and nonsingular components. We take those ideas to the Lagrangian setting to define a new Langrangian cycle, the Asp cycle. All of the proofs in that section utilize Langrangians. We prove that the Asp cycle agrees with the specialization cycle introduced by Sabbah and Kennedy in the special case in which the subvariety is the central fiber of a family over a smooth curve. Thus the Asp cycle may be viewed as a generalization of the Kennedy-Sabbah cycle. We give a corresponding generalization of Verdier's specialization formula.
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Date Issued: 2015
Identifier: FSU_migr_etd-9535
Format: Thesis

Title: Predegree Polynomials of Plane Configurations in Projective Space.
Creator: Tzigantchev, Dimitre G. (Dimitre Gueorguiev), Aluﬃ, Paolo, Reina, Laura, Aldrovandi, Ettore, Klassen, Eric, Seppälä, Mika, Department of Mathematics, Florida State University
Abstract/Description: We work over an algebraically closed ground field of characteristic zero. The group of PGL(4) acts naturally on the projective space P^N parameterizing surfaces of a given degree d in P^3. The orbit of a surface under this action is the image of a rational map from P^15 to P^N. The closure of the orbit is a natural and interesting object to study. Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above map restricted to a general P^j , j being the...
Show moreWe work over an algebraically closed ground field of characteristic zero. The group of PGL(4) acts naturally on the projective space P^N parameterizing surfaces of a given degree d in P^3. The orbit of a surface under this action is the image of a rational map from P^15 to P^N. The closure of the orbit is a natural and interesting object to study. Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above map restricted to a general P^j , j being the dimension of the orbit. We find the predegrees and other invariants for all surfaces supported on unions of planes. The information is encoded in the so-called adjusted predegree polynomials, which possess nice multiplicative properties allowing us to easily compute the predegree (polynomials) of various special plane configurations. The predegree has both a combinatorial and geometric significance. The results obtained in this thesis would be a necessary step in the solution of the problem of computing predegrees for all surfaces.
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Date Issued: 2006
Identifier: FSU_migr_etd-1747
Format: Thesis

Title: Factoring Univariate Polynomials over the Rationals.
Creator: Novocin, Andrew, Van Hoeij, Mark, Van Engelen, Robert, Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
Abstract/Description: This thesis presents an algorithm for factoring polynomials over the rationals which follows the approach of the van Hoeij algorithm. The key theoretical novelty in our approach is that it is et up in a way that will make it possible to prove a new complexity result for this algorithm which was actually observed on prior algorithms. One difference of this algorithm from prior algorithms is the practical improvement which we call early termination. Our algorithm should outperform prior...
Show moreThis thesis presents an algorithm for factoring polynomials over the rationals which follows the approach of the van Hoeij algorithm. The key theoretical novelty in our approach is that it is et up in a way that will make it possible to prove a new complexity result for this algorithm which was actually observed on prior algorithms. One difference of this algorithm from prior algorithms is the practical improvement which we call early termination. Our algorithm should outperform prior algorithms in many common classes of polynomials (including irreducibles).
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Date Issued: 2008
Identifier: FSU_migr_etd-2515
Format: Thesis

Title: Dark Matter Detection in Supersymmetric Models with Non-Universal Gaugino Masses.
Creator: Park, Eun-Kyung, Baer, Howard, Aldrovandi, Ettore, Reina, Laura, Prosper, Harrison, Volya, Alexander, Department of Physics, Florida State University
Abstract/Description: SUSY is one of the most promising new physics ideas, and will soon be tested at high energy accelerators like the CERN LHC. Moreover SUSY provides a good candidate for cold dark matter (CDM). In this dissertation, we investigated phenomenology of SUSY models with non-universal gaugino masses (NUGM) at colliding experiments using event generators such as ISAJET and examined direct and indirect detection rates of relic neutralino CDM in the universe. The motivation of these models is that in...
Show moreSUSY is one of the most promising new physics ideas, and will soon be tested at high energy accelerators like the CERN LHC. Moreover SUSY provides a good candidate for cold dark matter (CDM). In this dissertation, we investigated phenomenology of SUSY models with non-universal gaugino masses (NUGM) at colliding experiments using event generators such as ISAJET and examined direct and indirect detection rates of relic neutralino CDM in the universe. The motivation of these models is that in most of mSUGRA parameter space, the relic density $Omega_{ z_1}h^2$ is considerably larger than the WMAP measurement, and it is well known that if non-universal gaugino masses are allowed, then qualitatively new possibilities arise that are not realized in the mSUGRA model. Our first NUGM attempt is to allow a mixed wino-bino lightest SUSY particle (LSP) by lowering $SU(2)$ gaugino mass $M_2$ at the weak scale from its mSUGRA value while keeping the hypercharge gaugino mass $M_1$ fixed ({it Mixed Wino Dark Matter}). In this model, wino-like $ ilde{Z_1}$ with sufficiently low $M_2$ compared to $M_1$ enhances $ ilde{Z_1} ilde{Z_1} ightarrow W_{1}^{+} W_{1}^{-}$ annihilations to reach the WMAP measured relic density. The second attempt is study on the NUGM model with different signs of $M_1$ and $M_2$ ({it Bino-Wino Co-Annihilation Scenario}). In this case, there is little mixing, so that $ ilde{Z_1}$ remains nearly a pure bino or a pure wino. By increasing $M_1 simeq M_2$, enhanced bino-wino co-annihilation can achieve the relic neutralino abundance. The final attempt of NUGM models is lowering the $SU(3)$ gaugino mass to diminish the effect of the large top quark Yukawa coupling in the running of the higgs mass, so that the value of superpotential $mu$ parameter gets efficiently low to give rise to mixed higgsino dark matter ({it Mixed Higgsino Dark Matter}). Consequences of these NUGM model studies show us that relaxing universality of gaugino masses in SUSY models leads to enhanced direct and indirect dark matter detection rates and reduced $m_{ ilde{Z_2}}-m_{ ilde{Z_1}}$ mass gap so that the LHC and ILC can distinguish each NUGM model from others. Finally, we found that models with well-tempered neutralinos, where the composition of the neutralino is adjusted to give observed relic density, yield target cross sections which are detectable at proposed experiments.
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Date Issued: 2007
Identifier: FSU_migr_etd-2254
Format: Thesis

Title: Effective Methods in Intersection Theory and Combinatorial Algebraic Geometry.
Creator: Harris, Corey S. (Corey Scott), Chicken, Eric, Aldrovandi, Ettore, Kim, Kyounghee, Petersen, Kathleen L., Florida State University, College of Arts and Sciences, Department of...
Show moreHarris, Corey S. (Corey Scott), Chicken, Eric, Aldrovandi, Ettore, Kim, Kyounghee, Petersen, Kathleen L., Florida State University, College of Arts and Sciences, Department of Mathematics
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Abstract/Description: This dissertation presents studies of effective methods in two main areas of algebraic geometry: intersection theory and characteristic classes, and combinatorial algebraic geometry. We begin in chapter 2 by giving an effective algorithm for computing Segre classes of subschemes of arbitrary projective varieties. The algorithm presented here comes after several others which solve the problem in special cases, where the ambient variety is for instance projective space. To our knowledge, this...
Show moreThis dissertation presents studies of effective methods in two main areas of algebraic geometry: intersection theory and characteristic classes, and combinatorial algebraic geometry. We begin in chapter 2 by giving an effective algorithm for computing Segre classes of subschemes of arbitrary projective varieties. The algorithm presented here comes after several others which solve the problem in special cases, where the ambient variety is for instance projective space. To our knowledge, this is the first algorithm to be able to compute Segre classes in projective varieties with arbitrary singularities. In chapter 3, we generalize an algorithm by Goward for principalization of monomial ideals in nonsingular varieties to work on any scheme of finite type over a field, proving that the more general class of r.c. monomial subschemes in arbitrarily singular varieties can be principalized by a sequence of blow-ups at codimension 2 r.c. monomial centers. The main result of chapter 4 is a classification of the monomial Cremona transformations of the plane up to conjugation by certain linear transformations. In particular, an algorithm for enumerating all such maps is derived. In chapter 5, we study the multiview varieties and compute their Chern-Mather classes. As a corollary we derive a polynomial formula for their Euclidean distance degree, partially addressing a conjecture of Draisma et al. [35]. In chapter 6, we discuss the classical problem of counting planes tangent to general canonical sextic curves at three points. We investigate the situation for real and tropical sextics. In chapter 6, we explicitly compute equations of an Enriques surface via the involution on a K3 surface.
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Date Issued: 2017
Identifier: FSU_2017SP_Harris_fsu_0071E_13829
Format: Thesis

Title: Nuclear Structure of Neutron Rich ²⁶Na and the Lifetimes and Electromagnetic Transitions in Neutron Rich ²²F.
Creator: Lee, Sangjin, Tabor, Samuel L., Aldrovandi, Ettore, Prosper, Harrison B., Riley, Mark, Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: The 14C(14C,d) reaction at 22 MeV was used to study Tz=2 26Na. Charged particles were detected with a Si detector telescope at 0º, and γ transitions in coincidence were detected with an array of three Compton-suppressed "clover" detectors and seven Compton-suppressed single Ge crystals. The d- γ and d- γ - γ coincidence data were analyzed to study the structure of 26Na. New levels were found and precise energies and γ decay patterns were determined for many states previously observed in...
Show moreThe 14C(14C,d) reaction at 22 MeV was used to study Tz=2 26Na. Charged particles were detected with a Si detector telescope at 0º, and γ transitions in coincidence were detected with an array of three Compton-suppressed "clover" detectors and seven Compton-suppressed single Ge crystals. The d- γ and d- γ - γ coincidence data were analyzed to study the structure of 26Na. New levels were found and precise energies and γ decay patterns were determined for many states previously observed in charge-exchange reactions. Candidates were observed for the 1+ state missing in β decay. Mixing ratios were determined for some γ transitions from angular distribution information. There is reasonable agreement with the s-d shell model using the USD interaction. Electromagnetic transitions in 22F were investigated using the 9Be(14C,p) reaction at Elab = 22 MeV. Proton- γ and proton- γ - γ coincidences were measured using a segmented E - ΔE Si telescope and the FSU γ detector array. γ -ray energies, intensities, and branching ratios were measured and mean lifetimes were inferred using the Doppler-shift attenuation method. Several new states and many new decay modes were observed. The results are compared with sd shell model calculations using the USD, USDA, and USDB interactions. The excitation energies of the states below 2 MeV agree well with the calculations using the USD interaction, while the levels between 2 and 4 MeV agree much better with those using the newer USDA and USDB interactions. The branching ratios and mean lifetimes show no clear preference among these interactions.
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Date Issued: 2008
Identifier: FSU_migr_etd-3173
Format: Thesis

Title: Beta Decay Studies of Neutron-Rich ³⁰,³¹Al and in-Beam Studies of Neutron-Rich ³⁰Al.
Creator: Hinners, Trisha, Tabor, Samuel L., Aldrovandi, Ettore, Blessing, Susan, Riley, Mark, Piekarewicz, Jorge, Department of Physics, Florida State University
Abstract/Description: Low-spin states were studied in 30Al following the β decay of 30Mg produced in the fragmentation of 140 MeV/AMU 48Ca. Analysis of the β-γ and β-γ-γ coincidences revealed a new 1+ state at 2413 keV, confirmation of the level scheme, and a more accurate half life measurement of 315(6)ms for the 30Mg ground state. Higher-spin states were investigated in the reaction of 14C on 18O at 22 MeV. Protons and deuterons were detected in a segmented E-Δ E Si telescope in coincidence with one or two gamma...
Show moreLow-spin states were studied in 30Al following the β decay of 30Mg produced in the fragmentation of 140 MeV/AMU 48Ca. Analysis of the β-γ and β-γ-γ coincidences revealed a new 1+ state at 2413 keV, confirmation of the level scheme, and a more accurate half life measurement of 315(6)ms for the 30Mg ground state. Higher-spin states were investigated in the reaction of 14C on 18O at 22 MeV. Protons and deuterons were detected in a segmented E-Δ E Si telescope in coincidence with one or two gamma rays in the FSU Ge detector array. A comparison of the resulting level and decay scheme with predictions of the sd shell model shows good agreement with all but 6 of the states in both excitation energy and γ decay branching ratios. The RMS deviations in energy of these states using the older USD and newer USDA and USDB interactions were 265, 176, and 173 keV respectively. The remaining 6 states are well described as 4-to 7- states, similar in relative energy to those in 28Al but shifted down by about 1200 keV. These states also agree well with the predictions of shell model calculations using the WBP interaction. A comparison of the lowest 4- states in even A Na, Al, and P isotopes shows a systematic decrease in energy with increasing N and with decreasing Z. The energies of the 4- states are almost identical in nuclei with the same N - Z values. In addition to the study of 30Al, 31Al was also produced following the β decay of 31Mg in the fragmentation of 140 MeV/AMU 48Ca. The β-γ and β-γ-γ coincidences were able to show all previously known work. However, no new transitions were observed.
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Date Issued: 2008
Identifier: FSU_migr_etd-4033
Format: Thesis

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text (48)	+ -
doctoral thesis (5)	+ -
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Aldrovandi, Ettore (48)	+ -
Florida State University (48)	+ -
Department of Mathematics (25)	+ -
Department of Physics (23)	+ -
Reina, Laura (20)	+ -

Piekarewicz, Jorge (13)	+ -
Aluﬃ, Paolo (11)	+ -
Van Hoeij, Mark (11)	+ -
Agashe, Amod (10)	+ -
College of Arts and Sciences (10)	+ -
Aluffi, Paolo (7)	+ -
Capstick, Simon (7)	+ -
Hironaka, Eriko (6)	+ -
Adams, Todd (5)	+ -
Prosper, Harrison (5)	+ -
Van Engelen, Robert A. (5)	+ -
Baer, Howard (4)	+ -
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Prosper, Harrison B. (3)	+ -
Volya, Alexander (3)	+ -
Agashe, Amod S. (Amod Sadanand) (2)	+ -
Blessing, Susan K. (2)	+ -
Case, Bettye Anne (2)	+ -
Chicken, Eric (2)	+ -
Kim, Kyounghee (2)	+ -

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