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.

46 records · Page 3
All sourcesNASA NTRSDOE OSTI
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 OSTI2014

Understanding the Cu-Zn brass alloys using a short-range-order cluster model: Significance of specific compositions of industrial alloys

Metallic alloys show complex chemistries that are not yet understood so far. It has been widely accepted that behind the composition selection lies a short-range-order mechanism for solid solutions. The present paper addresses this fundamental question by examining the face-centered-cubic Cu-Zn a-brasses. A new structural approach, the cluster-plus-glue-atom model, is introduced, which suits specifically for the description of short-range-order structures in disordered systems. Two types of formulas are pointed out, [Zn-Cu 12 ]Zn 1,6 and [Zn-Cu 12 ](Zn,Cu) 6 , which explain the a-brasses listed in the American Society for Testing and Materials (ASTM) specifications. In these formulas, the bracketed parts represent the 1 st -neighbor cluster, and each cluster is matched with one to six 2 nd -neighbor Zn atoms or with six mixed (Zn,Cu) atoms. Such a cluster-based formulism describes the 1 st - and 2 nd -neighbor local atomic units where the solute and solvent interactions are ideally satisfied. The Cu-Ni industrial alloys are also explained, thus proving the universality of the cluster-formula approach in understanding the alloy selections. The revelation of the composition formulas for the Cu-(Zn,Ni) industrial alloys points to the common existence of simple composition rules behind seemingly complex chemistries of industrial alloys, therefore offering a fundamental and practical method towards composition interpretations of all kinds of alloys.

36 MATERIALS SCIENCE↗
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↗
NASA NTRS2007

Electromechanically Actuated Valve for Controlling Flow Rate

A proposed valve for controlling the rate of flow of a fluid would include an electric-motor-driven ball-screw mechanism for adjusting the seating element of the valve to any position between fully closed and fully open. The motor would be of a type that can be electronically controlled to rotate to a specified angular position and to rotate at a specified rate, and the ball screw would enable accurate linear positioning of the seating element as a function of angular position of the motor. Hence, the proposed valve would enable fine electronic control of the rate of flow and the rate of change of flow. The uniqueness of this valve lies in a high degree of integration of the actuation mechanism with the flow-control components into a single, relatively compact unit. A notable feature of this integration is that in addition to being a major part of the actuation mechanism, the ball screw would also be a flow-control component: the ball screw would be hollow so as to contain part of the main flow passage, and one end of the ball screw would be the main seating valve element. The relationships among the components of the valve are best understood by reference to the figure, which presents meridional cross sections of the valve in the fully closed and fully open positions. The motor would be supported by a bracket bolted to the valve body. By means of gears or pulleys and a timing belt, motor drive would be transmitted to a sleeve that would rotate on bearings in the valve body. A ball nut inside the sleeve would be made to rotate with the sleeve by use of a key. The ball screw would pass through and engage the ball nut. A key would prevent rotation of the ball screw in the valve body while allowing the ball screw to translate axially when driven by the ball nut. The outer surface of the ball screw would be threaded only in a mid-length region: the end regions of the outer surface of the ball screw would be polished so that they could act as dynamic sealing surfaces. The inlet end (the right end as depicted in the figure) of the ball screw would be the main seating valve element: in the fully closed position, it would be pressed against the valve seat, as depicted in the upper part of the figure. A retainer would hold the valve seat in an inlet fitting. In addition, the retainer would be contoured to obtain a specified flow rate as a function of axial position of the ball screw. In the fully closed position, little force would be needed to press the ball screw against the seat because the push bore area upon which the upstream pressure would act would be small. The motor would position and hold the ball screw against the seat, providing the force necessary for sealing. To open the valve to a particular position, the motor would be commanded to rotate to a particular angular position (equivalently, a particular number of revolutions) at a particular rate of rotation within its torque limitations. Once the valve was open, fluid would flow through the inlet fitting and the chamber in the inlet housing, past the seat and its retainer, along the hollow core of the ball screw, and through the outlet housing and outlet fitting. The net force generated from fluid pressure in the open position would be small because the pressure exposed to the push bore areas at the inlet and outlet are nearly equal and the forces generated would be in opposing directions.

Patterson, Paul↗
DOE OSTI2025

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling↗
DOE OSTI2022

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗