Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Group Theory and Generalizations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Some effects of time usage patterns on the productivity of engineers

The performance of the 1500+ engineers at MSFC is critical to the Center's mission. Worker's performance, however, is a variable affected by ability, motivation, role understanding, and other factors. Managing subordinates' performance is a great challenges to managers. Special challenges confront the managers of engineers because engineers often work with general goals, long deadlines, and considerable autonomy. The productivity of a team or branch is a function of the productivity of each of its members. While many managers have personal theories about how to run their work group, surprisingly little systematic scientific knowledge exerts about the effects of various factors on engineers' productivity. This study is intended to help lay the foundation for such a program of research.

Jackson, Conrad N.↗

Generalization of QCD3 symmetry-breaking and flavored quiver dualities

We extend the recently proposed symmetry breaking scenario of QCD 3 to the so-called “master” (2 + 1)d bosonization duality, which has bosonic and fermionic matter on both ends. Using anomaly arguments, a phase diagram emerges with several novel regions. We then construct 2+1 dimensional dualities for flavored quivers using node-by-node dualization. Such dualities are applicable to theories which live on domain walls in QCD 4 -like theories with dynamical quarks. We also derive dualities for quivers based on orthogonal and symplectic gauge groups. Lastly, we support the conjectured dualities using holographic constructions, even though several aspects of this holographic construction remain mostly qualitative.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A model of persistent breaking of continuous symmetry

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Mass loss parameters for typical Shuttle materials

The weight loss of twenty different typical Shuttle materials was measured with a thermogravimetric analyzer as the material temperature was increased from ambient to 300 C. An additional ten tests were performed where conditioning of the material varied. The materials were selected from each general grouping such as adhesives, coatings, lubricants, encapsulants, elastomers, and resins. Care was taken in the preparation, curing, and preconditioning of the materials to simulate flight use. Making the assumption that the weight loss follows first order rate theory, the source outgassing parameters for these thirty materials is presented.

Muscari, J. A.↗

Background independent quantum field theory and gravitating vacuum fluctuations

The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein’s equation. Self-consistent background spacetimes are scale dependent, and therefore “going on-shell” at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this “rigid picture” breaks down after a very short RG time already (less than one decade of scales) because of a “scale horizon” that forms. Furthermore, we critically reanalyze and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

$\mathrm{BPS}$ coherent states and localization

We introduce coherent states averaged over a gauge group action to study correlators of half BPS states in $\mathcal{N}$= 4 SYM theory. The overlaps of these averaged coherent states are a generating function of correlators and can be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We show that this formula immediately leads to a computation of the normalization of two point functions in terms of characters obtained originally in the work of Corley, Jevicki and Ramgoolam. We also find various generalizations for A n–1 quivers that follow directly from other solvable integrals over unitary groups. All of these can be computed using localization methods. When we promote the parameters of the generating function to collective coordinates, there is a dominant saddle that controls the effective action of these coherent states in the regime where they describe single AdS giant gravitons. We also discuss how to add open strings to this formulation. These will produce calculations that rely on correlators of matrix components of unitaries in the ensemble that is determined by the HCIZ integral to determine anomalous dimensions. We also discuss how sphere giants arise from Grassman integrals, how one gets a dominant saddle and how open strings are added in that case. The fact that there is a dominant saddle helps to understand how a 1/N expansion arises for open strings. We generalize the coherent state idea to study 1/4 and 1/8 BPS states as more general integrals over unitary groups.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Homotopy characterization of non-Hermitian Hamiltonians

We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called “point-gap” and “line-gap” schemes. However, simple Hamiltonians without band degeneracies can be constructed which correspond to neither of the two schemes. Here, we resolve this shortcoming of the existing classifications by developing the most general topological characterization of non-Hermitian bands for systems without a symmetry. Our approach, which is based on homotopy theory, makes no particular assumptions on the band gap, and predicts significant extensions to the previous classification frameworks. In particular, we show that the one-dimensional invariant generalizes from $\mathbb{Z}$ winding number to the non-Abelian braid group, and that depending on the braid group invariants, the two-dimensional invariants can be cyclic groups $\mathbb{Z}_n$ (rather than $\mathbb{Z}$ Chern number). Finally, we interpret these results in terms of a correspondence with gapless systems, and we illustrate them in terms of analogies with other problems in band topology, namely, the fragile topological invariants in Hermitian systems and the topological defects and textures of nematic liquids.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

On the determination of the coefficients of the Gaussian general theory of the Earth's magnetism for the year 1885 and about the relationship of the three Earth-magnetic elements

An attempt is made to judge the value of the Gaussian series for the Earth's magnetism. The computation employed to do this uses the method of the least and greatest coefficients. The number of unknown which had to be calculated from the individual groups was at most only four. All symbols of Gauss were retained.

Fritsche, H.↗

Is There a Cosmological Constant?

The grant contributed to the publication of 18 refereed papers and 5 conference proceedings. The primary uses of the funding have been for page charges, travel for invited talks related to the grant research, and the support of a graduate student, Charles Keeton. The refereed papers address four of the primary goals of the proposal: (1) the statistics of radio lenses as a probe of the cosmological model (#1), (2) the role of spiral galaxies as lenses (#3), (3) the effects of dust on statistics of lenses (#7, #8), and (4) the role of groups and clusters as lenses (#2, #6, #10, #13, #15, #16). Four papers (#4, #5, #11, #12) address general issues of lens models, calibrations, and the relationship between lens galaxies and nearby galaxies. One considered cosmological effects in lensing X-ray sources (#9), and two addressed issues related to the overall power spectrum and theories of gravity (#17, #18). Our theoretical studies combined with the explosion in the number of lenses and the quality of the data obtained for them is greatly increasing our ability to characterize and understand the lens population. We can now firmly conclude both from our study of the statistics of radio lenses and our survey of extinctions in individual lenses that the statistics of optically selected quasars were significantly affected by extinction. However, the limits on the cosmological constant remain at lambda < 0.65 at a 2-sigma confidence level, which is in mild conflict with the results of the Type la supernova surveys. We continue to find that neither spiral galaxies nor groups and clusters contribute significantly to the production of gravitational lenses. The lack of group and cluster lenses is strong evidence for the role of baryonic cooling in increasing the efficiency of galaxies as lenses compared to groups and clusters of higher mass but lower central density. Unfortunately for the ultimate objective of the proposal, improved constraints on the cosmological constant, the next large survey for gravitational lenses did not release its results during the term of the proposal. The research supported the career development. of six graduate students (polar, Fletcher, Herold, Keeton, Deng and Rusin) and two post-docs (Labor and Munoz).

Kochanek, Christopher↗

Conservation laws in coupled cluster dynamics at finite temperature

We extend the finite-temperature Keldysh non-equilibrium coupled cluster theory (Keldysh-CC) [A. F. White and G. K.-L. Chan, J. Chem. Theory Comput. 15, 6137–6253 (2019)] to include a time-dependent orbital basis. When chosen to minimize the action, such a basis restores local and global conservation laws (Ehrenfest’s theorem) for all one-particle properties while remaining energy conserving for time independent Hamiltonians. We present the time-dependent Keldysh orbital-optimized coupled cluster doubles method in analogy with the formalism for zero-temperature dynamics, extended to finite temperatures through the time-dependent action on the Keldysh contour. To demonstrate the conservation property and understand the numerical performance of the method, we apply it to several problems of nonequilibrium finite-temperature dynamics: a 1D Hubbard model with a time-dependent Peierls phase, laser driving of molecular H2, driven dynamics in warm-dense silicon, and transport in the single impurity Anderson model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

System theory as applied differential geometry

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Hermann, R.↗

Aging and the complexity of cardiovascular dynamics

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Non-NASA Center↗

Resurgence of the renormalization group equation

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

97 MATHEMATICS AND COMPUTING↗

Branches, quivers, and ideals for knot complements

We generalize the F K invariant, i.e. Z^ for the complement of a knot K in the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an F K invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these F K invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N = 2 theory T[M 3 ] and to the data of the associated modular tensor category MTC[M 3 ].

97 MATHEMATICS AND COMPUTING↗

Separation of variables in the WZW models

We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers-Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Conformal correlators on the Lorentzian torus

The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus LT 2 which arises as the conformal boundary of the group manifold SL ( 2 , R ) ≃ AdS 3 / Z . We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to celestial holography, for which the LT 2 at the boundary of Klein space is the home of the putative celestial CFT. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Development of Two-Step Method for Fast Chloride MSR Neutronics

This work presents neutronics models of a small and large fast-spectrum molten chloride-salt reactor. The models are similar to designs being pursued by industry, and they may serve as generic preconceptual and simplified neutronics models that provide information for decision making in licensing-related areas. Here, the two models were created using Serpent, a Monte Carlo neutron transport code, and Moltres, a neutron diffusion core simulator tool. Specifically, this study focused on exploring the applicability of diffusion theory to fast molten salt reactor (MSR) models, the capabilities of an open-source, MSR-oriented simulation tool (Moltres), and optimal energy-group structures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Small circle expansion for adjoint QCD 2 with periodic boundary conditions

We study 1 + 1-dimensional SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumference L. Using periodic boundary conditions, we derive the effective action for the quantum mechanics of the holonomy and the fermion zero modes in perturbation theory up to order (gL) 3 . When the adjoint fermion mass-squared is tuned to g 2 N/(2π), the effective action is found to be an example of supersymmetric quantum mechanics with a nontrivial superpotential. We separate the states into the ℤN center symmetry sectors (universes) labeled by p = 0, . . . , N – 1 and show that in one of the sectors the supersymmetry is unbroken, while in the others it is broken spontaneously. These results give us new insights into the (1, 1) supersymmetry of adjoint QCD 2 , which has previously been established using light-cone quantization. When the adjoint mass is set to zero, our effective Hamiltonian does not depend on the fermions at all, so that there are 2 N−1 degenerate sectors of the Hilbert space. This construction appears to provide an explicit realization of the extended symmetry of the massless model, where there are 2 2N−2 operators that commute with the Hamiltonian. We also generalize our results to other gauge groups G, for which supersymmetry is found at the adjoint mass-squared g 2 h ∨ /(2π), where h ∨ is the dual Coxeter number of G.

effective field theories↗