Browsing by Author "Sharpe, Eric R."
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- Aging processes in complex systemsAfzal, Nasrin (Virginia Tech, 2013-04-27)Recent years have seen remarkable progress in our understanding of physical aging in nondisordered systems with slow, i.e. glassy-like dynamics. In many systems a single dynamical length L(t), that grows as a power-law of time t or, in much more complicated cases, as a logarithmic function of t, governs the dynamics out of equilibrium. In the aging or dynamical scaling regime, these systems are best characterized by two-times quantities, like dynamical correlation and response functions, that transform in a specific way under a dynamical scale transformation. The resulting dynamical scaling functions and the associated non-equilibrium exponents are often found to be universal and to depend only on some global features of the system under investigation. We discuss three different types of systems with simple and complex aging properties, namely reaction diffusion systems with a power growth law, driven diffusive systems with a logarithmic growth law, and a non-equilibrium polymer network that is supposed to capture important properties of the cytoskeleton of living cells. For the reaction diffusion systems, our study focuses on systems with reversible reaction diffusion and we study two-times functions in systems with power law growth. For the driven diffusive systems, we focus on the ABC model and a related domain model and measure two- times quantities in systems undergoing logarithmic growth. For the polymer network model, we explain in some detail its relationship with the cytoskeleton, an organelle that is responsible for the shape and locomotion of cells. Our study of this system sheds new light on the non- equilibrium relaxation properties of the cytoskeleton by investigating through a power law growth of a coarse grained length in our system.
- Algebroids, heterotic moduli spaces and the Strominger systemAnderson, Lara B.; Gray, James A.; Sharpe, Eric R. (Springer, 2014-07-08)In this paper we study compactifications of heterotic string theory on manifolds satisfying the partial derivative(partial derivative) over bar -lemma. We consider the Strominger system description of the low energy supergravity to first order in alpha' and show that the moduli of such compactifications are subspaces of familiar cohomology groups such as H-1 (TX), H-1 (TXV), H-1 (End(0) (V)) and H-1(End(0) (TX)). These groups encode the complex structure, Kahler moduli, bundle moduli and perturbations of the spin connection respectively in the case of a Calabi-Yau compactification. We investigate the fluctuations of only a subset of the conditions of the Strominger system (expected to correspond physically to F-term constraints in the effective theory). The full physical moduli space is, therefore, given by a further restriction on these degrees of freedom which we discuss but do not explicitly provide. This paper is complementary to a previous tree-level worldsheet analysis of such moduli and agrees with that discussion in the limit of vanishing alpha'. The structure we present can be interpreted in terms of recent work in Atiyah and Courant algebroids, and we conjecture links with aspects of Hitchin's generalized geometry to heterotic moduli.
- Analysis of B Meson Decays to Three Charged PionsLi, Yao (Virginia Tech, 2015-12-23)Decays of B mesons to three-body charmless final states probe the properties of the weak interaction through their dependence on the complex quark couplings in the CKM matrix. They also test dynamical models for hadronic B decays. Based on a sample of 772 million BB pairs collected by the Belle experiment, we present a study of direct CP violation in the decay of charged B to three charged pions.
- Anomalies, extensions, and orbifoldsRobbins, Daniel G.; Sharpe, Eric R.; Vandermeulen, Thomas (2021-10-05)We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is classified by cohomology and how extending the orbifold group can remove it. Working with such extensions requires an understanding of the consistent ways in which extending groups can act on the twisted states of the original symmetry, which leads us to a discrete torsionlike choice that exists in orbifolds with trivially acting subgroups. We review a general method for constructing such extensions and investigate its application to orbifolds. Through numerous explicit examples we test the conjecture that consistent extensions should be equivalent to (in general multiple copies of) orbifolds by nonanomalous subgroups.
- Application of Network Reliability to Analyze Diffusive Processes on Graph Dynamical SystemsNath, Madhurima (Virginia Tech, 2019-01-22)Moore and Shannon's reliability polynomial can be used as a global statistic to explore the behavior of diffusive processes on a graph dynamical system representing a finite sized interacting system. It depends on both the network topology and the dynamics of the process and gives the probability that the system has a particular desired property. Due to the complexity involved in evaluating the exact network reliability, the problem has been classified as a NP-hard problem. The estimation of the reliability polynomials for large graphs is feasible using Monte Carlo simulations. However, the number of samples required for an accurate estimate increases with system size. Instead, an adaptive method using Bernstein polynomials as kernel density estimators proves useful. Network reliability has a wide range of applications ranging from epidemiology to statistical physics, depending on the description of the functionality. For example, it serves as a measure to study the sensitivity of the outbreak of an infectious disease on a network to the structure of the network. It can also be used to identify important dynamics-induced contagion clusters in international food trade networks. Further, it is analogous to the partition function of the Ising model which provides insights to the interpolation between the low and high temperature limits.
- Applications of gauged linear sigma modelsChen, Zhuo (Virginia Tech, 2019-05-17)This thesis is devoted to a study of applications of gauged linear sigma models. First, by constructing (0,2) analogues of Hori-Vafa mirrors, we have given and checked proposals for (0,2) mirrors to projective spaces, toric del Pezzo and Hirzebruch surfaces with tangent bundle deformations, checking not only correlation functions but also e.g. that mirrors to del Pezzos are related by blowdowns in the fashion one would expect. Also, we applied the recent proposal for mirrors of non-Abelian (2,2) supersymmetric two-dimensional gauge theories to examples of two-dimensional A-twisted gauge theories with exceptional gauge groups G_2 and E_8. We explicitly computed the proposed mirror Landau-Ginzburg orbifold and derived the Coulomb ring relations (the analogue of quantum cohomology ring relations). We also studied pure gauge theories, and provided evidence (at the level of these topologicalfield-theory-type computations) that each pure gauge theory (with simply-connected gauge group) flows in the IR to a free theory of as many twisted chiral multiplets as the rank of the gauge group. Last, we have constructed hybrid Landau-Ginzburg models that RG flow to a new family of non-compact Calabi-Yau threefolds, constructed as fiber products of genus g curves and noncompact Kahler threefolds. We only considered curves given as branched double covers of P^1. Our construction utilizes nonperturbative constructions of the genus g curves, and so provides a new set of exotic UV theories that should RG flow to sigma models on Calabi-Yau manifolds, in which the Calabi-Yau is not realized simply as the critical locus of a superpotential.
- Applications of Neutrino PhysicsChristensen, Eric Kurt (Virginia Tech, 2014-09-02)Neutrino physics has entered a precision era in which understanding backgrounds and systematic uncertainties is particularly important. With a precise understanding of neutrino physics, we can better understand neutrino sources. In this work, we demonstrate dependency of single detector oscillation experiments on reactor neutrino flux model. We fit the largest reactor neutrino flux model error, weak magnetism, using data from experiments. We use reactor burn-up simulations in combination with a reactor neutrino flux model to demonstrate the capability of a neutrino detector to measure the power, burn-up, and plutonium content of a nuclear reactor. In particular, North Korean reactors are examined prior to the 1994 nuclear crisis and waste removal detection is examined at the Iranian reactor. The strength of a neutrino detector is that it can acquire data without the need to shut the reactor down. We also simulate tau neutrino interactions to determine backgrounds to muon neutrino and electron neutrino measurements in neutrino factory experiments.
- Applications of Numerical Methods in Heterotic Calabi-Yau CompactificationCui, Wei (Virginia Tech, 2020-08-26)In this thesis, we apply the methods of numerical differential geometry to several different problems in heterotic Calabi-Yau compactification. We review algorithms for computing both the Ricci-flat metric on Calabi-Yau manifolds and Hermitian Yang-Mills connections on poly-stable holomorphic vector bundles over those spaces. We apply the numerical techniques for obtaining Ricci-flat metrics to study hierarchies of curvature scales over Calabi-Yau manifolds as a function of their complex structure moduli. The work we present successfully finds known large curvature regions on these manifolds, and provides useful information about curvature variation at general points in moduli space. This research is important in determining the validity of the low energy effective theories used in the description of Calabi-Yau compactifications. The numerical techniques for obtaining Hermitian Yang-Mills connections are applied in two different fashions in this thesis. First, we demonstrate that they can be successfully used to numerically determine the stability of vector bundles with qualitatively different features to those that have appeared in the literature to date. Second, we use these methods to further develop some calculations of holomorphic Chern-Simons invariant contributions to the heterotic superpotential that have recently appeared in the literature. A complete understanding of these quantities requires explicit knowledge of the Hermitian Yang-Mills connections involved. This feature makes such investigations prohibitively hard to pursue analytically, and a natural target for numerical techniques.
- Aspects of SupersymmetryJia, Bei (Virginia Tech, 2014-04-21)This thesis is devoted to a discussion of various aspects of supersymmetric quantum field theories in four and two dimensions. In four dimensions, 𝒩 = 1 supersymmetric quantum gauge theories on various four-manifolds are constructed. Many of their properties, some of which are distinct to the theories on flat spacetime, are analyzed. In two dimensions, general 𝒩 = (2, 2) nonlinear sigma models on S² are constructed, both for chiral multiplets and twisted chiral multiplets. The explicit curvature coupling terms and their effects are discussed. Finally, 𝒩 = (0, 2) gauged linear sigma models with nonabelian gauge groups are analyzed. In particular, various dualities between these nonabelian gauge theories are discussed in a geometric content, based on their Higgs branch structure.
- B-branes and supersymmetric quivers in 2dClosset, Cyril; Guo, Jirui; Sharpe, Eric R. (Springer, 2018-02-08)We study 2d N = (0, 2) supersymmetric quiver gauge theories that describe the low-energy dynamics of D1-branes at Calabi-Yau fourfold (CY4) singularities. On general grounds, the holomorphic sector of these theories - matter content and (classical) superpotential interactions - should be fully captured by the topological B-model on the CY4. By studying a number of examples, we confirm this expectation and flesh out the dictionary between B-brane category and supersymmetric quiver, the matter content of the supersymmetric quiver is encoded in morphisms between B-branes (that is, Ext groups of coherent sheaves), while the superpotential interactions are encoded in the A(infinity) algebra satisfied by the morphisms. This provides us with a derivation of the supersymmetric quiver directly from the CY4 geometry. We also suggest a relation between triality of N = (0, 2) gauge theories and certain mutations of exceptional collections of sheaves. 0d N = 1 supersymmetric quivers, corresponding to D-instantons probing CY5 singularities, can be discussed similarly.
- Chiral operators in two-dimensional (0,2) theories and a test of trialityGuo, Jirui; Jia, Bei; Sharpe, Eric R. (Springer, 2015-06-30)In this paper we compute spaces of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories, and apply them to check recent duality conjectures. The fact that in a nonlinear sigma model, the Fock vacuum can act as a section of a line bundle on the target space plays a crucial role in our (0,2) computations, so we begin with a review of this property. We also take this opportunity to show how even in (2,2) theories, the Fock vacuum encodes in this way choices of target space spin structures, and discuss how such choices enter the A and B model topological field theories. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the recent Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. We find that different UV theories in the same proposed universality class do not necessarily have the same space of chiral operators - but, the mismatched operators do not contribute to elliptic genera and are in non-integrable representations of the proposed IR affine symmetry groups, suggesting that the mismatched states become massive along RG flow. We find this state matching in examples not only of different geometric phases of the same GLSMs, but also in phases of different GLSMs, indirectly verifying the triality proposal, and giving a clean demonstration that (0,2) chiral rings are not topologically protected. We also check proposals for enhanced IR affine E-6 symmetries in one such model, verifying that (matching) chiral states in phases of corresponding GLSMs transform as 27's, (27) over bar.
- Chiral Rings of Two-dimensional Field Theories with (0,2) SupersymmetryGuo, Jirui (Virginia Tech, 2017-04-26)This thesis is devoted to a thorough study of chiral rings in two-dimensional (0,2) theories. We first discuss properties of chiral operators in general two-dimensional (0,2) nonlinear sigma models, both in theories twistable to the A/2 or B/2 model, as well as in non-twistable theories. As a special case, we study the quantum sheaf cohomology of Grassmannians as a deformation of the usual quantum cohomology. The deformation corresponds to a (0,2) deformation of the nonabelian gauged linear sigma model whose geometric phase is associated with the Grassmannian. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. Supersymmetric localization is also applicable in this case, which proves to be efficient in computing A/2 correlation functions. We then compute chiral operators in general (0,2) nonlinear sigma models, and apply them to the Gadde-Gukov-Putrov triality proposal, which says that certain triples of (0,2) GLSMs should RG flow to nontrivial IR fixed points. As another application, we extend previous works to construct (0,2) Toda-like mirrors to the sigma model engineering Grassmannians.
- Constraining New Physics with Colliders and NeutrinosSun, Chen (Virginia Tech, 2017-06-06)In this work, we examine how neutrino and collider experiments can each and together put constraints on new physics more stringently than ever. Constraints arise in three ways. First, possible new theoretical frameworks are reviewed and analyzed for the compatibility with collider experiments. We study alternate theories such as the superconnection formalism and non-commutative geometry (NCG) and show how these can be put to test, if any collider excess were to show up. In this case, we use the previous diboson and diphoton statistical excess as examples to do the analysis. Second, we parametrize low energy new physics in the neutrino sector in terms of non-standard interactions (NSI), which are constrained by past and proposed future neutrino experiments. As an example, we show the capability of resolving such NSI with the OscSNS, a detector proposed for Oak Ridge National Lab and derive interesting new constraints on NSI at very low energy (≲ 50 MeV). Apart from this, in order to better understand the NSI matter effect in long baseline experiments such as the future DUNE experiment, we derive a new compact formula to describe the effect analytically, which provides a clear physical picture of our understanding of the NSI matter effect compared to numerical computations. Last, we discuss the possibility of combining neutrino and collider data to get a better understanding of where the new physics is hidden. In particular, we study a model that produces sizable NSI to show how they can be constrained by past collider data, which covers a distinct region of the model parameter space from the DUNE experiment. In combining the two, we show that neutrino experiments are complementary to collider searches in ruling out models such as the ones that utilize a light mediator particle. More general procedures in constructing such models relevant to neutrino experiments are also described.
- Contribution of the First Electronically Excited State of Molecular Nitrogen to Thermospheric Nitric OxideYonker, Justin David (Virginia Tech, 2013-05-13)The chemical reaction of the first excited electronic state of molecular nitrogen, N₂(A), with ground state atomic oxygen is an important contributor to thermospheric nitric oxide (NO). The importance is assessed by including this reaction in a one-dimensional photochemical model. The method is to scale the photoelectron impact ionization rate of molecular nitrogen by a Gaussian centered near 100 km. Large uncertainties remain in the temperature dependence and branching ratios of many reactions important to NO production and loss. Similarly large uncertainties are present in the solar soft x-ray irradiance, known to be the fundamental driver of the low-latitude NO. To illustrate, it is shown that the equatorial, midday NO density measured by the Student Nitric Oxide Explorer (SNOE) satellite near the Solar Cycle 23 maximum can be recovered by the model to within the 20% measurement uncertainties using two rather different but equally reasonable chemical schemes, each with their own solar soft-xray irradiance parameterizations. Including the N₂(A) changes the NO production rate by an average of 11%, but the NO density changes by a much larger 44%. This is explained by tracing the direct, indirect, and catalytic contributions of N₂(A) to NO, finding them to contribute 40%, 33%, and 27% respectively. The contribution of N₂(A) relative to the total NO production and loss is assessed by tracing both back to their origins in the primary photoabsorption and photoelectron impact processes. The photoelectron impact ionization of N₂ is shown to be the main driver of the midday NO production while the photoelectron impact dissociation of N₂ is the main NO destroyer. The net photoelectron impact excitation rate of N₂, which is responsible for the N₂(A) production, is larger than the ionization and dissociation rates and thus potentially very important. Although the conservative assumptions regarding the level-specific NO yield from the N₂(A)+O reaction results in N₂(A) being a somewhat minor contributor, N₂(A) production is found to be the most efficient producer of NO among the thermospheric energy deposition processes.
- Corrections to and Applications of the Antineutrino Spectrum Generated by Nuclear ReactorsJaffke, Patrick John (Virginia Tech, 2015-11-16)In this work, the antineutrino spectrum as specifically generated by nuclear reactors is studied. The topics covered include corrections and higher-order effects in reactor antineutrino experiments, one of which is covered in Ref. [1] and another contributes to Ref. [2]. In addition, a practical application, antineutrino safeguards for nuclear reactors, as summarized in Ref. [3,4] and Ref. [5], is explored to determine its viability and limits. The work will focus heavily on theory, simulation, and statistical analyses to explain the corrections, their origins, and their sizes, as well as the applications of the antineutrino signal from nuclear reactors. Chapter [1] serves as an introduction to neutrinos. Their origin is briefly covered, along with neutrino properties and some experimental highlights. The next chapter, Chapter [2], will specifically cover antineutrinos as generated in nuclear reactors. In this chapter, the production and detection methods of reactor neutrinos are introduced as well as a discussion of the theories behind determining the antineutrino spectrum. The mathematical formulation of neutrino oscillation will also be introduced and explained. The first half of this work focuses on two corrections to the reactor antineutrino spectrum. These corrections are generated from two specific sources and are thus named the spent nuclear fuel contribution and the non-linear correction for their respective sources. Chapter [3] contains a discussion of the spent fuel contribution. This correction arises from spent nuclear fuel near the reactor site and involves a detailed application of spent fuel to current reactor antineutrino experiments. Chapter [4] will focus on the non-linear correction, which is caused by neutron-captures within the nuclear reactor environment. Its quantification and impact on future antineutrino experiments are discussed. The research projects presented in the second half, Chapter [5], focus on neutrino applications, specifically reactor monitoring. Chapter [5] is a comprehensive examination of the use of antineutrinos as a reactor safeguards mechanism. This chapter will include the theory behind safeguards, the statistical derivation of power and plutonium measurements, the details of reactor simulations, and the future outlook for non-proliferation through antineutrino monitoring.
- D-branes and K-homologyJia, Bei (Virginia Tech, 2013-04-19)In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,\phi]$ represents a D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.
- The Daya Bay Reactor Neutrino ExperimentHor, Yuenkeung (Virginia Tech, 2014-09-18)The Daya Bay experiment has determined the last unknown mixing angle $theta_{13}$. This thesis describes the layout of the experiment and the detector design. The analysis presented in the thesis covered the water attenuation, spent fuel neutrino and electron anti-neutrino spectrum. Other physics analysis and impact to future experiments are also discussed.
- Detection of Antineutrinos at the North Anna Nuclear Generating StationLi, Shengchao (Virginia Tech, 2020-10-28)Nuclear reactors have played an essential role in developing our current understanding of neutrinos. The precision measurement of these high-flux, pure-flavor and controllable artificial neutrino sources shed lights on a wide range of fundamental questions in physics. Specifically, the Reactor Antineutrino Anomaly hints that there may exist a novel eV-scale sterile neutrino, which requires new physics beyond the Standard Model. Performing reactor neutrino spectrum measurements at very-short baseline will improve our imperfect understanding of antineutrino emission from fissile material. CHANDLER is a new-generation neutrino experiment aiming for reactor antineutrino spectrum measurements, to test the eV-scale sterile neutrino oscillation hypothesis unambiguously. The second prototype detector, MiniCHANDLER, was deployed 25 meters from a $2.9~GW_{th}$ commercial nuclear reactor in North Anna, Virginia. To fight against the overwhelming background arising from its surface-level deployment, CHANDLER detectors adopt a novel design using lithium-6 ($^6$Li) loaded zinc sulfide (ZnS) scintillator to tag neutron capture events, which significantly improves the IBD detection efficiency. The use of the Raghavan optical lattice brings enormous enhancement of light collection towards high energy resolution, which unlocks reconstruction of event topology to further suppress backgrounds. The ability of measuring reactor antineutrino spectra enables the potential application of CHANDLER technology in nuclear nonproliferation. This thesis features the prototype detectors instrumentation, data analysis development and Monte Carlo study for the CHANDLER experiment during 2016 to 2020. The detector calibration and energy reconstruction with vertical muon forms a core piece of this thesis. We report our observation of IBD spectrum with 5.5$sigma$ significance with a four month deployment of the minimal shielded MiniCHANDLER prototype at North Anna. The application of separation cuts and topological selections in the analysis are instrumental for a segmented plastic scintillator detector. We also present our results from the proton scintillation quenching measurement at Triangle Universities Nuclear Laboratory, with the deployment of the first prototype detector, MicroCHANDLER, at a neutron beam.
- Duality group actions on fermionsPantev, Tony; Sharpe, Eric R. (Springer, 2016-11-29)In this short paper we look at the action of T-duality and string duality groups on fermions, in maximally-supersymmetric theories and related theories. Briefly, we argue that typical duality groups such as SL( 2, Z) have sign ambiguities in their actions on fermions, and propose that pertinent duality groups be extended by Z 2, to groups such as the metaplectic group. Specifically, we look at duality groups arising from mapping class groups of tori in M theory compactifications, T-duality, ten-dimensional type IIB S-duality, and ( briefly) four-dimensional N = 4 super Yang-Mills, and in each case, propose that the full duality group is a nontrivial Z 2 extension of the duality group acting on bosonic degrees of freedom, to more accurately describe possible actions on fermions. We also walk through U-duality groups for toroidal compactifications to nine, eight, and seven dimensions, which enables us to perform cross-consistency tests of these proposals.
- Dynamics of Driven Vortices in Disordered Type-II SuperconductorsChaturvedi, Harshwardhan Nandlal (Virginia Tech, 2019-01-22)We numerically investigate the dynamical properties of driven magnetic flux vortices in disordered type-II superconductors for a variety of temperatures, types of disorder and sample thicknesses. We do so with the aid of Langevin molecular dynamics simulations of a coarsegrained elastic line model of flux vortices in the extreme London limit. Some original findings of this doctoral work include the discovery that flux vortices driven through random point disorder show simple aging following drive quenches from the moving lattice state to both the pinned glassy state (non-universal aging) and near the critical depinning region (universal aging); estimations of experimentally consistent critical scaling exponents for the continuous depinning phase transition of vortices in three dimensions; and an estimation of the boundary curve separating regions of linear and non-linear electrical transport for flux lines driven through planar defects via novel direct measurements of vortex excitations.
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