Search NASA⌕ Search

SEARCH · Search NASA

Results for “Lie brackets”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Localization and the Weyl algebras

Let W{sub n}(ℝ) be the Weyl algebra of index n. It is well known that so(p, q) Lie algebras can be viewed as quadratic polynomial (Lie) algebras in W{sub n}(ℝ) for p + q = n with the Lie algebra multiplication being given by the bracket [a, b] = ab − ba for a, b quadratic polynomials in W{sub n}(ℝ). What does not seem to be so well known is that the converse statement is, in a certain sense, also true, namely, that, by using extension and localization, it is possible, at least in some cases, to construct homomorphisms of W{sub n}(ℝ) onto its image in a localization of U(so(p + 2, q)), the universal enveloping algebra of so(p + 2, q), and m = p + q. Since Weyl algebras are simple, these homomorphisms must either be trivial or isomorphisms onto their images. We illustrate this remark for the so(2, q) case and construct a mappping from W{sub q}(ℝ) onto its image in a localization of U(so(2, q)). We prove that this mapping is a homomorphism when q = 1 or q = 2. Some specific results about representations for the lowest dimensional case of W{sub 1}(ℝ) and U(so(2, 1)) are given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Reheating predictions in single field inflation

Reheating is a transition era after the end of inflation, during which the inflaton is converted into the particles that populate the Universe at later times. No direct cosmological observables are normally traceable to this period of reheating. Indirect bounds can however be derived. One possibility is to consider cosmological evolution for observable CMB scales from the time of Hubble crossing to the present time. Depending upon the model, the duration and final temperature after reheating, as well as its equation of state, may be directly linked to inflationary observables. For single-field inflationary models, if we approximate reheating by a constant equation of state, one can derive relations between the reheating duration (or final temperature), its equation of state parameter, and the scalar power spectrum amplitude and spectral index. While this is a simple approximation, by restricting the equation of state to lie within a broad physically allowed range, one can in turn bracket an allowed range of n{sub s} and r for these models. The added constraints can help break degeneracies between inflation models that otherwise overlap in their predictions for n{sub s} and r.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

REEXAMINING THE LITHIUM DEPLETION BOUNDARY IN THE PLEIADES AND THE INFERRED AGE OF THE CLUSTER

Moderate-dispersion (R ∼ 5400), optical spectroscopy of seven brown dwarf candidate members of the Pleiades was obtained using the Echellette Spectrograph and Imager on the Keck II telescope. The proper motion and photometrically selected sample lies on the single-star main sequence of the cluster and effectively brackets the established lithium depletion boundary. The brown dwarf candidates range in spectral type from M6 to M7, implying effective temperatures between ∼2800 and 2650 K. All sources exhibit Hα emission, consistent with enhanced chromospheric activity that is expected for young, very low-mass stars and brown dwarfs. Li i λ6708 absorption is confidently detected in the photospheres of two of the seven sources. A revised lithium depletion boundary is established in the near-infrared where the effects of extinction and variability are minimized. This lithium depletion edge occurs near K{sub o} = 14.45 or M{sub K} = 8.78 mag (UKIRT Infrared Deep Sky Survey), assuming the most accurate and precise distance estimate for the cluster of 136.2 pc. From recent theoretical evolutionary models, a revised age of τ = 112 ± 5 Myr is determined for the Pleiades. Accounting for the effects of magnetic activity on the photospheres of these very low-mass stars and brown dwarfs, however, would imply an even younger age for the cluster of ∼100 Myr.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

L ∞ algebras and field theory

In this paper, we review and develop the general properties of L ∞ algebras focusing on the gauge structure of the associated field theories. Motivated by the L ∞ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the L ∞ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an L ∞ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full L ∞ algebra for the interacting theory. The analysis suggests that L ∞ algebras provide a classification of perturbative gauge invariant classical field theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

On non-autonomous dynamical systems

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A novel method for the measurement of the von Neumann spike in detonating high explosives

We present detonation wave profiles measured in T2 (97 wt. % TATB) and TX1 (52 wt. % TATB and 45 wt. % HMX) high explosives. The experiments consisted in initiating a detonation wave in a 15 mm diameter cylinder of explosive using an explosive wire detonator and an explosive booster. Free surface velocity wave profiles were measured at the explosive/air interface using a Photon Doppler Velocimetry system. We demonstrate that a comparison of these free surface wave profiles with those measured at explosive/window interfaces in similar conditions allows to bracket the von Neumann spike in a narrow range. For T2, our measurements show that the spike pressure lies between 35.9 and 40.1 GPa, whereas for TX1, it lies between 42.3 and 47.0 GPa. The numerical simulations performed in support to these measurements show that they can be used to calibrate reactive burn models and also to check the accuracy of the detonation products equation of state at low pressure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Derivation of the Hall and extended magnetohydrodynamics brackets

There are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and two-fluid theory, with Hall and Extended MHD being two important examples. In this paper, we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed Eulerian-Lagrangian, actions that have appeared previously. As an important step in this process, we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Lie-dragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the Euler-Lagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.

Hamiltonian mechanics↗
DOE OSTI2025

Information divergences to parametrize astrophysical uncertainties in dark matter direct detection

Astrophysical uncertainties in dark matter direct detection experiments are typically addressed by parametrizing the velocity distribution in terms of a few uncertain parameters that vary around some central values. Here we propose a method to optimize over all velocity distributions lying within a given distance measure from a central distribution. We discretize the dark matter velocity distribution as a superposition of streams and use a variety of information divergences to parametrize its uncertainties. With this, we bracket the limits on the dark matter–nucleon and dark matter–electron scattering cross sections, when the true dark matter velocity distribution deviates from the commonly assumed Maxwell-Boltzmann form. The methodology pursued is general and could be applied to other physics scenarios where a given physical observable depends on a function that is uncertain.

particle astrophysics↗
NASA NTRS2006

Past and Future SOHO-Ulysses Quadratures

With the launch of SOHO, it again became possible to carry out quadrature observations. In comparison with earlier observations, the new capabilities of coronal spectroscopy with UVCS and in situ ionization state and composition with Ulysses/SWICS enabled new types of studies. Results from two studies serve as examples: (i) The acceleration profile of wind from small coronal holes. (ii) A high-coronal reconnecting current sheet as the source of high ionization state Fe in a CME at Ulysses. Generally quadrature observations last only for a few days, when Ulysses is within ca. 5 degrees of the limb. This means luck is required for the phenomenon of interest to lie along the radial direction to Ulysses. However, when Ulysses is at high southern latitude in winter 2007 and high northern latitude in winter 2008, there will be unusually favorable configurations for quadrature observations with SOHO and corresponding bracketing limb observations from STEREO A/B. Specifically, Ulysses will be within 5 degrees of the limb from December 2006 to May 2007 and within 10 degrees of the limb from December 2007 to May 2008. These long-lasting quadratures and bracketing STEREO A/B observations overcome the limitations inherent in the short observation intervals of typical quadratures. Furthermore, ionization and charge state measurements like those on Ulysses will also be made on STEREO and these will be essential for identification of CME ejecta - one of the prime objectives for STEREO.

Suess, Steven↗
NASA NTRS2000

Structure of Protoplanetary Environments

Our research focused on the structure and composition of the disks in the T Tau and Haro 6-10 multiple star systems and on the nature of the 'infrared companions' that these systems contain. This work has resulted in two papers, one on T Tau, presently under review at the Astrophysical Journal, and the other, on Haro 6-10, about to be submitted to Astronomy and Astrophysics. In the paper 'Evidence for Extinction and Accretion Variability in T Tau S' by Tracy L. Beck, L. Prato, and M. Simon, we present angularly resolved spectra of T Tau N (the visible star) and T Tau S (the infrared companion, IRC) in the three micrometer water ice-feature and the K-band. Most of the water ice absorption lies along the line of sight to T Tau S, confirming it is seen through stronger obscuration. A decrease in the ice-band absorption toward T Tau S between 12/98 and 1/00, significant, at the two-sigma level, was associated with an increase in its near IR flux. Bracket gamma emission is detected in T Tau N and S, and H2 (2.12 micrometer) emission only toward T Tau S, consistent with previous studies of IRCs. Our results suggest that the near IR variability of T Tau S is probably caused by both variations in accretion rate and extinction. Our paper on Haro 6-10, 'The Near IR and Ice Band Variability of Haro, 6-10' by Ch. Leinert, T.L. Beck, S. Ligori, M. Simon, J. Woitas, and R.R. Howell, represents a fusion of originally independent efforts at the Max Planck Institut fur Astronomie (Heidelberg) and Stony Brook. Our combined observations demonstrate that both Haro 6-10 S (the visible star) and Haro 6-10 N (the IRC) vary significantly in near IR flux on time scales as short as a month. The substantial decrease of Haro 6-10 S in the last four years carries the photometric signature of increased extinction. However, a comparable K-band flux increase of the IRC is associated with a dimming at H so cannot be explained by lower extinction. Absorption in the 3.1 micrometer ice band was always greater toward the IRC during our observations indicating a large amount of obscuring material. We detect variable extinction in the ice-band toward Haro 6-10 S and the IRC, significant at the 3.5-sigma and 2.0-sigma levels, respectively.

Simon, Michal↗
DOE OSTI2025

Algebra of invariants for the Vlasov–Maxwell system

The algebra of invariants for both the relativistic and nonrelativistic multispecies Vlasov–Maxwell system is examined, including the case with a fixed ion background. Invariants and their associated fluxes are obtained directly from the Vlasov–Maxwell system. The invariants are shown to Poisson commute with the Hamiltonian and the rest of the Poisson bracket algebra of invariants is identified. Special attention is given to the role played by the monopole condition, ∇ · B.

Fundamental invariants↗
NASA NTRS1978

User's guide to computer programs JET 5A and CIVM-JET 5B to calculate the large elastic-plastic dynamically-induced deformations of multilayer partial and/or complete structural rings

These structural ring deflections lie essentially in one plane and, hence, are called two-dimensional (2-d). The structural rings may be complete or partial; the former may be regarded as representing a fragment containment ring while the latter may be viewed as a 2-d fragment-deflector structure. These two types of rings may be either free or supported in various ways (pinned-fixed, locally clamped, elastic-foundation supported, mounting-bracket supported, etc.). The initial geometry of each ring may be circular or arbitrarily curved; uniform-thickness or variable-thickness rings may be analyzed. Strain-hardening and strain-rate effects of initially-isotropic material are taken into account. An approximate analysis utilizing kinetic energy and momentum conservation relations is used to predict the after-impact velocities of each fragment and of the impact-affected region of the ring; this procedure is termed the collision-imparted velocity method (CIVM) and is used in the CIVM-JET 5 B program. This imparted-velocity information is used in conjunction with a finite-element structural response computation code to predict the transient, large-deflection, elastic-plastic responses of the ring. Similarly, the equations of motion of each fragment are solved in small steps in time. Provisions are made in the CIVM-JET 5B code to analyze structural ring response to impact attack by from 1 to 3 fragments, each with its own size, mass, translational velocity components, and rotational velocity. The effects of friction between each fragment and the impacted ring are included.

Wu, R. W. H.↗
NASA NTRS1988

Locking hinge

The space station configuration currently studied utilizes structures which require struts to be hinged in the middle in the stowed mode and locked into place in the deployed mode. Since there are hundreds of hinges involved, it is necessary that they have simple, positive locking features with a minimum of joint looseness or slack. This invention comprises two similar housings hinged together with a spring loaded locking member which assists in making as well as breaking the lock. This invention comprises a bracket hinge and bracket members with a spring biased and movable locking member. The locking or latch member has ear parts received in locking openings where wedging surfaces on the ear parts cooperate with complimentary surfaces on the bracket members for bringing the bracket members into a tight end-to-end alignment when the bracket members are in an extended position. When the locking member is moved to an unlocking position, pivoting of the hinge about a pivot pin automatically places the locking member to retain the locking member in an unlocked position. In pivoting the hinge from an extended position to a folded position, longitudinal spring members are placed under tension over annular rollers so that the spring tension in a folded position assists in return of the hinge from a folded to an extended position. Novelty lies in the creation of a locking hinge which allows compact storage and easy assembly of structural members having a minimal number of parts.

Wesselski, Clarence J.↗
DOE OSTI2022

Linear stability analysis via simulated annealing and accelerated relaxation

Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Warming-Induced Biome Change at the Temperate-Boreal Ecotone: An Experimental Test of Key Regeneration Processes (Final Technical Report)

This project advanced our understanding of plants’ key physiological and ecological processes that are essential to the survival, success, and carbon cycling of plants from the boreal-temperate forest ecotone in the future climate. A primary goal of the project was to test the effect of warming and water limitation on plants from the Boreal-Temperate Ecotone using a realistic outdoor long-term experiment. Plant at this ecotone is predicted to be particularly sensitive to future climate since the ecotone represents a relatively sharp boundary between many temperate species to the south and boreal species to the north. This work was important, as there was and still is a significant uncertainty surrounding the mechanisms of future climate effects on vegetation compositional and carbon cycling change, especially in forests mostly due to lack of experimental examination of response to warming and limited water availability. Consequently, we tested our central objective, that was to assess the potential for projected climate to alter tree species composition and carbon cycling at the southern boreal-temperate forest ecotone by experimentally warming forest plots and documenting effects on establishment and juvenile performance for tree species near their warmer (boreal species) and colder (temperate species) range limits in northern Minnesota. To accomplish our goals, we designed and built a successful highly manipulative experiment that implemented vegetation-soil warming and rainfall removal in both understory and open habitats at two sites in northern Minnesota (MN). The sites lie at different distances to the north of the ecotone between the southern boreal and northern temperate forest biomes. We focused on ten target species, all of which are near their warmer (Pinus banksiana, Picea glauca, Abies balsamea, Populus tremuloides, Betula papyrifera) or colder (Pinus strobus, Quercus macrocarpa, Quercus rubra, Acer rubrum, Acer saccharum) range edge in northern MN; we also studied other species such as a woody invader and native herbs and shrubs. Three temperature treatments (ambient, +1.7°C, +3.4°C) were imposed using infra-red heating lamps augmented with soil heating cables to simultaneously control soil and vegetation temperatures, enabling assessment of non-linear responses. These temperatures bracket the range of anticipated warming in the region during the next 75-100 years. In addition, we implemented summer rain removal treatment mimicking predicted distribution in precipitation patterns by future climate where we actively removed ~40% of rainfall. Measurements included germinant establishment, plant growth, phenology, physiology and survival, soil, plant and air temperature, soil moisture and nutrient status. These measures enabled us to assess how germination, growth and survival at the establishment stage are influenced by direct climate effects and/or indirect effects of warming, soil resources such as water and nutrients availability or other environmental variables that either directly or indirectly influence plant performance.

60 APPLIED LIFE SCIENCES↗