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DOE OSTI2015

Spherical collapse for a viscous generalized Chaplygin GaS model

The nonlinear collapse for a viscous generalized Chaplygin gas model (VGCG) is analyzed in the framework of spherical top-hat collapse. Because the VGCG and baryons are essential to form the large-scale structure, we focus on their nonlinear collapse in this paper. We discuss the influence of model parameters α and ζ{sub 0} on the spherical collapse by varying their values and compare with the ΛCDM model. The results show that for the VGCG model, smaller ζ{sub 0} and larger α make the structure formation earlier and faster, and the collapse curves of the VGCG model are almost coincident with those of the ΛCDM model when the model parameter α is less than 10{sup −2}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Superradiance in the Generalized (Non-Wiener) Dicke Model

It is shown that when nonresonant interactions between atoms and a vacuum electromagnetic field are included in analysis of emission of a localized ensemble of identical atoms, a delay must appear in the cooperative radiation pulse emitted by the atomic ensemble that is initially in a half-excited state. At the same time, the emission of cooperative radiation from a completely excited ensemble for certain parameters must begin without any delay. This contradicts the familiar facts of the conventional Dicke superradiance, in the theory of which nonresonant interactions are disregarded. The model taking into account nonresonant interactions along with other factors of the Dicke model is called the generalized Dicke model.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Cosmography of Generalized Ghost Dark Energy Model in f(G) Gravity

This paper is devoted to construction of generalized ghost dark energy f(G) model by using correspondence scheme for both interacting and noninteracting scenarios with pressureless matter and power-law scale factor. We study the cosmological implications of the resulting model through equation of state parameter and ω{sub DE} – ω{sub DE}{sup ′} as well as r – s plane. We also discuss stability of the resulting model through squared speed of sound parameter. The equation of state parameter represents phantom phase of the Universe for both cases while the squared speed of sound indicates stability of this model. The ω{sub DE} – ω{sub DE}{sup ′} plane represents thawing region whereas r – s plane corresponds to phantom and quintessence DE regimes for both interacting and noninteracting cases.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Soliton configurations in generalized Mie electrodynamics

The generalization of the Mie electrodynamics within the scope of the effective 8-spinor field model is suggested, with the Lagrangian including Higgs-like potential and higher degrees of the invariant A{sub Micro-Sign }A{sup Micro-Sign }. Using special Brioschi 8-spinor identity, we show that the model includes the Skyrme and the Faddeev models as particular cases. We investigate the large-distance asymptotic of static solutions and estimate the electromagnetic contribution to the energy of the localized charged configuration.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Generalized landau models with N = 2 worldline supersymmetry

It is a brief review of a new class of N = 2supersymmetric Landau models which generalize the superplane Landau model by extending it to an arbitrary magnetic field on any two-dimensional manifold M{sub 2}. Using an off-shell N = 2 superfield formalism, it is shown that these models are characterized by two independent potentials given on M{sub 2}. The relevant Hamiltonians are factorizable and in the special case, when both the Gauss curvature and the magnetic field are constant over M{sub 2}, admit infinite series of factorization chains, which implies the integrability of the associated systems. For the particular model with the Double-Struck-Capital-C Double-Struck-Capital-P {sup 1} bosonic manifold, the spectrum and eigenvectors are explicitly given.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Raynal–Revai coefficients for a general kinematic rotation

In a three-body system, transitions between different sets of normalized Jacobi coordinates are described as general kinematic transformations that include an orthogonal or a pseudoorthogonal rotation. For such rotations, the Raynal–Revai coefficients execute a unitary transformation between three-body hyperspherical functions. Recurrence relations that make it possible to calculate the Raynal–Revai coefficients for arbitrary angular momenta are derived on the basis of linearized representations of products of hyperspherical functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2013

Generalized parton distributions from meson leptoproduction

Generalized parton distributions (GPDs) extracted from exclusive meson leptoproduction within the handbag approach are briefly reviewed. Only the GPD E is discussed in some detail. Applications of these GPDs to virtual Compton scattering (DVCS) and to Ji’s sum rule are also presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model

Wess-Zumino-Novikov-Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2D) rational conformal field theories (RCFTs). A WZNW chiral state space is a finite direct sum of integrable representations of the corresponding affine (current) algebra, and the correlation functions of primary fields are monodromy invariant combinations of left times right sector conformal blocks solving the Knizhnik-Zamolodchikov equation. However, even in this very well understood case of 2D RCFT, the “internal” (gauge) symmetry that governs the ensuing fusion rules remains unclear. On the other hand, the canonical approach to the classical chiral WZNW theory developed by Faddeev, Alekseev, Shatashvili, Gawedzki and Falceto reveals its Poisson-Lie symmetry. After a covariant quantization, the latter gives rise to an associated quantum group symmetry which naturally requires an extension of the state space. This paper contains a review of earlier work on the subject with a special emphasis, in the case G = SU(n), on the emerging chiral “WZNW zero modes” which provide an adequate algebraic description of the internal symmetry structure of the model. Combining further left and right zero modes, one obtains a specific dynamical quantum group, the structure of its Fock representation resembling the axiomatic approach to gauge theories in which a “restricted” quantum group plays the role of a generalized gauge symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Quantum groups as generalized gauge symmetries in WZNW models. Part II. The quantized model

This is the second part of a paper dealing with the “internal” (gauge) symmetry of the Wess-Zumino-Novikov-Witten (WZNW) model on a compact Lie group G. It contains a systematic exposition, for G = SU(n), of the canonical quantization based on the study of the classical model (performed in the first part) following the quantum group symmetric approach first advocated by L.D. Faddeev and collaborators. The internal symmetry of the quantized model is carried by the chiral WZNW zero modes satisfying quadratic exchange relations and an n-linear determinant condition. For generic values of the deformation parameter the Fock representation of the zero modes’ algebra gives rise to a model space of U{sub q}(sl(n)). The relevant root of unity case is studied in detail for n = 2 when a “restricted” (finite dimensional) quotient quantum group is shown to appear in a natural way. The module structure of the zero modes’ Fock space provides a specific duality with the solutions of the Knizhnik-Zamolodchikov equation for the four point functions of primary fields suggesting the existence of an extended state space of logarithmic CFT type. Combining left and right zero modes (i.e., returning to the 2D model), the rational CFT structure shows up in a setting reminiscent to covariant quantization of gauge theories in which the restricted quantum group plays the role of a generalized gauge symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Generalized Bohm’s criterion and negative anode voltage fall in electric discharges

The value of the voltage fall across the anode sheath is found as a function of the current density. Analytic solutions are obtained in a wide range of the ratio of the directed velocity of plasma electrons v{sub 0} to their thermal velocity v{sub T}. It is shown that the voltage fall in a one-dimensional collisionless anode sheath is always negative. At the small values of v{sub 0}/v{sub T}, the obtained expression asymptotically transforms into the Langmuir formula. Generalized Bohm’s criterion for an electric discharge with allowance for the space charge density ρ(0), electric field E(0), ion velocity v{sub i}(0), and ratio v{sub 0}/v{sub T} at the plasma-sheath interface is formulated. It is shown that the minimum value of the ion velocity v{sub i}{sup *}(0) corresponds to the vanishing of the electric field at one point inside the sheath. The dependence of v{sub i}{sup *} (0) on ρ(0), E(0), and v{sub 0}/v{sub T} determines the boundary of the existence domain of stationary solutions in the sheath. Using this criterion, the maximum possible degree of contraction of the electron current at the anode is determined for a short high-current vacuum arc discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Online Adaptive Algorithm for Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method

Here in this research, we propose an online basis enrichment strategy within the framework of a recently developed constraint energy minimizing generalized multiscale discontinuous Galerkin method. Combining the technique of oversampling, one makes use of the information of the current residuals to adaptively construct basis functions in the online stage to reduce the error of multiscale approximation. A complete analysis of the method is presented, which shows the proposed online enrichment leads to a fast convergence from multiscale approximation to the fine-scale solution. The error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Further, the convergence rate of the enrichment algorithm depends on a factor of exponential decay regarding the number of oversampling layers and a user-defined parameter. Numerical results are provided to demonstrate the effectiveness and efficiency of the proposed online adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Exploring baryon resonances with transition generalized parton distributions: status and perspectives

QCD gives rise to a rich spectrum of excited baryon states. Understanding their internal structure is important for many areas of nuclear physics, such as nuclear forces, dense matter, and neutrino-nucleus interactions. Generalized parton distributions (GPDs) are an established tool for characterizing the QCD structure of the ground-state nucleon. They are used to create 3D tomographic images of the quark/gluon structure and quantify the mechanical properties such as the distribution of mass, angular momentum, and forces in the system. Transition GPDs extend these concepts to N → N* transitions and can be used to characterize the 3D structure and mechanical properties of baryon resonances. They can be probed in high-momentum-transfer exclusive electroproduction processes with resonance transitions e + N → e' + M + N*, such as deeply-virtual Compton scattering (M = γ) or meson production (M = π, K, etc.), and in related photon/hadron-induced processes. This White Paper describes a research program aiming to explore baryon resonance structure with transition GPDs. This includes the properties and interpretation of the transition GPDs, theoretical methods for structures and processes, first experimental results from JLab 12 GeV, future measurements with existing and planned facilities (JLab detector and energy upgrades, COMPASS/AMBER, EIC, EicC, J-PARC, LHC ultraperipheral collisions), and the theoretical and experimental developments needed to realize this program.

Experimental Nuclear Physics↗
DOE OSTI2011

Measurement of the generalized form factors near pion threshold via gamma*p --> npi^+ in CLAS

We extracted the multipoles near pion threshold for the first time at high momentum transfers (Q2) in the nπ+ final state channel. The dominance of the S-wave transverse multipole (E0+) is expected in this region, which allows us to access the new generalized form factors G1, G2 within the Light-Cone-Sum-Rule (LCSR) framework. In this analysis, we used one of the recent CLAS experimental data sets which utilized the high-energy polarized electron beam on unpolarized proton target using the 4π detector coverage. We measured the differential cross sections and extracted the multipoles using two methods, LCSR and multipole fit. Both methods show consistent results, which are almost Q2 independent.

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

New model for nucleon generalized parton distributions

We describe a new type of models for nucleon generalized parton distributions (GPDs) H and E. They are heavily based on the fact nucleon GPDs require to use two forms of double distribution (DD) representations. The outcome of the new treatment is that the usual DD+D-term construction should be amended by an extra term, {xi} E{sub +}{sup 1} (x,{xi}) which has the DD structure {alpha}/{beta} e({beta},{alpha}, with e({beta},{alpha}) being the DD that generates GPD E(x,{xi}). We found that this function, unlike the D-term, has support in the whole -1 <= x <= 1 region. Furthermore, it does not vanish at the border points |x|={xi}.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Studies of Analytic Evolution of Two-Photon Generalized Distribution Amplitude in QCD

We extend our method of analytic ERBL evolution for the case of distribution amplitudes that have jumps at some points x = {zeta}{sub I} inside the support region 0 < x < 1. As an application of the method, we use it for evolution of the two-photon generalized distribution amplitude. Our approach has advantages over the standard method of expansion in Gegenbauer polynomials, which requires infinite number of terms in order to accuretly reproduce functions in the vicinity of singular points, and over the method of straightforward iteration of initial distribution with evolution kernel which produces logarithmically divergent terms at each iteration. In our method, the logarithmic singularities are summed from the start, which immediately produces a continuous curve, with only one or two iterations needed afterwards in order to get precise results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗