Search NASA⌕ Search

SEARCH · Search NASA

Results for “generalized gradient approximations”

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

Effects of gravity-gradient torque on the rotational motion of a triaxial satellite in a precessing elliptic orbit.

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗

The Galileo Probe: How it Has Changed Our Understanding of Jupiter

The Galileo Mission to Jupiter, which arrived in December of 1995, provided the first study by an orbiter, and the first in-situ sampling via an entry probe, of an outer planet atmosphere. The rationale for an entry probe is that, even from an orbiter, remote sensing of the jovian atmosphere could not adequately retrieve the information desired. This paper provides a current summary of the most significant aspects of the data returned from the Galileo entry probe. As a result of the probe measurements, there has been a reassessment of our understanding of outer planet formation and evolution of the solar system. The primary scientific objective of the Galileo probe was to determine the composition of the jovian atmosphere, which from remote sensing remained either very uncertain, or completely unknown, with respect to several key elements. The probe found that the global He mass fraction is. significantly above the value reported from the Voyager Jupiter flybys but is slightly below the protosolar value, implying that there has been some settling of He to the deep jovian interior. The probe He measurements have also led to a reevaluation of the Voyager He mass fraction for Saturn, which is now determined to be much closer to that of Jupiter. The elements C, N, S, Ar, Kr, Xe were all found to have global abundances approximately 3 times their respective solar abundances. This result has raised a number of fundamental issues with regard to properties of planetesimals and the solar nebula at the time of giant planet formation. Ne, on the other hand, was found to be highly depleted, probably as the result of it being carried along with helium as helium settles towards the deep interior. The global abundance of O was not obtained by the probe because of the influence of local processes at the probe entry site (PES), processes which depleted condensible species, in this case H2O, well below condensation levels. Other condensible species, namely NH3 and H2S, were similarly affected but attained their deep equilibrium mixing ratios before the maximum depth sampled by the probe. Processes that might be capable of producing such effects on the condensibles are still under investigation. Measured isotopic ratios of noble gases and other heavy elements are solar, and (D + (Sup 3)He)/H is the same to within measurement uncertainties as in the local interstellar medium. No thick clouds were detected, and in particular no significant water cloud, but the PES location clearly affected the probe measurements of clouds. In fact, the probe data must be understood in the context of the location of the PES, which was within what is termed a 5 micron hot spot, a local clearing in the clouds that is bright near the 5 microns spectral region. The thermal structure at the PES was determined from approximately 1000 km above the 1 bar pressure level (10(exp -9 bars)) to 132 km 1 bar (22bars). The probe showed the atmosphere to have a generally sub-adiabatic temperature gradient (static stability) of = 0.1 K/km to as deep as the probe made measurements. In the upper atmosphere the probe derived a maximum positive vertical temperature gradient of approximately 5 K/km, and maximum temperature of = 900 K. The energy sources producing the warm upper atmosphere have yet to be completely identified. At first glance, Doppler tracking of the probe indicates that the long observed cloud level zonal winds extend to levels at least as deep as the probe made measurements. Zonal wind increases from = 80 m/s at pressures less than a bar to about 180 m/s near 5 bars, and remains approximately constant with depth thereafter. However, there is a question as to whether the winds measured from probe tracking are representative of the general wind field, or are considerably influenced by localized winds associated with the PES.

Young, Richard E.↗

Planar turbulent wakes under pressure gradient: Integral and self-similarity analyses

By using a combination of integral and self-similarity analyses, the generalized analytical solutions for the mean transverse velocity and Reynolds shear stress are rigorously derived for the first time for the far field of planar turbulent wakes under arbitrary pressure gradients. Specifically, by assuming self-similarity for the mean axial velocity, the analytical formulation for the mean transverse velocity is obtained from the integral of the mean continuity equation, and the analytical formulation for the Reynolds shear stress is obtained from the integral of the momentum equation. The generalized analytical formulations for the mean transverse velocity and Reynolds shear stress consist of multiple components, each with its unique scale and physical mechanism. In the zero pressure gradient limit, the generalized formulations recover the single-scale equations reported by Wei, Liu, and Livescu. Furthermore, simpler approximate formulations for the mean transverse velocity and Reynolds shear stress are also obtained, and show excellent agreement with the experimental measurements. Here, the findings provide new insights into the properties of planar turbulent wakes under pressure gradients, filling some long-standing gaps in the existing literature.

42 ENGINEERING↗

Comparative In Situ Measurements of Plasma Instabilities in the Equatorial and Auroral Electrojets

This presentation provides a comparison of in situ measurements of plasma instabilities gathered by rocket-borne probes in the equatorial and auroral electrojets. Specifically, using detailed measurements of the DC electric fields, current density, and plasma number density within the unstable daytime equatorial electrojet from Brazil (Guara Campaign) and in the auroral electrojet from Sweden (ERRIS Campaign), we present comparative observations and general conclusions regarding the observed physical properties of Farley-Buneman two-stream waves and large scale, gradient drift waves. The two stream observations reveal coherent-like waves propagating near the E x B direction but at reduced speeds (nearer to the presumed acoustic velocity) with wavelengths of approximately 5-10m in both the equatorial and auroral electrojet, as measured using the spaced-receiver technique. The auroral electrojet data generally shows extensions to shorter wavelengths, in concert with the fact that these waves are driven harder. With respect to gradient-drift driven waves, observations of this instability are much more pronounced in the equatorial electrojet, given the more favorable geometry for growth provided by the vertical gradient and horizontal magnetic field lines. We present new analysis of Guara rocket observations of electric field and plasma density data that reveal considerable structuring in the middle and lower portion of the electrojet (90-105 km) where the ambient plasma density gradient is unstable. Although the electric field amplitudes are largest (approximately 10-15 mV/m) in the zonal direction, considerable structure (approximately 5-10 mV/m) is also observed in the vertical electric field component as well, implying that the dominant large scale waves involve significant vertical interaction and coupling within the narrow altitude range where they are observed. Furthermore, a detailed examination of the phase of the waveforms show that on some, but not all occasions, locally enhanced eastward fields are associated with locally enhanced upwards (polarization) electric fields. The measurements are discussed in terms of theories involving the non-linear evolution and structuring of plasma waves.

Pfaff, Robert F.↗

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate are considered. These equations, suggest certain successive-approximations iterative procedures for obtaining maximum-likelihood estimates. These are generalized steepest ascent (deflected gradient) procedures. It is shown that, with probability 1 as N sub 0 approaches infinity (regardless of the relative sizes of N sub 0 and N sub 1, i=1,...,m), these procedures converge locally to the strongly consistent maximum-likelihood estimates whenever the step size is between 0 and 2. Furthermore, the value of the step size which yields optimal local convergence rates is bounded from below by a number which always lies between 1 and 2.

Walker, H. F.↗

Inelastic strain analogy for piecewise linear computation of creep residues in built-up structures

An analogy between inelastic strains caused by temperature and those caused by creep is presented in terms of isotropic elasticity. It is shown how the theoretical aspects can be blended with existing finite-element computer programs to exact a piecewise linear solution. The creep effect is determined by using the thermal stress computational approach, if appropriate alterations are made to the thermal expansion of the individual elements. The overall transient solution is achieved by consecutive piecewise linear iterations. The total residue caused by creep is obtained by accumulating creep residues for each iteration and then resubmitting the total residues for each element as an equivalent input. A typical creep law is tested for incremental time convergence. The results indicate that the approach is practical, with a valid indication of the extent of creep after approximately 20 hr of incremental time. The general analogy between body forces and inelastic strain gradients is discussed with respect to how an inelastic problem can be worked as an elastic problem.

Jenkins, Jerald M.↗

Static Subspace Approximation for Random Phase Approximation Correlation Energies: Applications to Materials for Catalysis and Electrochemistry

Modeling complex materials using high-fidelity, ab initio methods at low cost is a fundamental goal for quantum chemical software packages. The GW approximation and random phase approximation (RPA) provide a unified description of both electronic structure and total energies using the same physics in a many-body perturbative approach that can be more accurate than generalized-gradient density functional theory (DFT) methods. However, GW/RPA implementations have historically been limited to either specific materials classes or application toward small chemical systems. Here, the static subspace approximation allows for reduced cost full-frequency GW/RPA calculations and has previously been benchmarked thoroughly for GW calculations. Here, we describe our approach to including partial occupations of electronic orbitals in full-frequency GW and RPA calculations for the study of electrocatalysts. We benchmarked RPA total energy calculations using the subspace approximation across a diverse test suite of materials for a variety of computational parameters. The benchmarking quantifies the impact of different extrapolation procedures for representing the static polarizability at infinite screened cutoff, and shows that using screened cutoffs above 20-25 Ryd result in diminishing accuracy returns for predicting RPA total energies. Additionally, for moderately sized electrocatalytic models, 2-3 times fewer computational resources are used to compute RPA total energies by representing the static polarizability with 20-30% of the static subspace basis, with an error of approximately 0.01 eV or better in RPA adsorption energy calculations. Finally, we show that for these electrochemical models RPA can shift DFT adsorption energy shifts by up to 0.5 eV and that GW can frequently shift DFT eigenvalues of surface and adsorbate states by approximately 0.5-1 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The numerical evaluation of maximum-likelihood estimates of the parameters for a mixture of normal distributions from partially identified samples

Likelihood equations determined by the two types of samples which are necessary conditions for a maximum-likelihood estimate were considered. These equations suggest certain successive approximations iterative procedures for obtaining maximum likelihood estimates. The procedures, which are generalized steepest ascent (deflected gradient) procedures, contain those of Hosmer as a special case.

Walker, H. F.↗

Nucleon-pair approximation for nuclei from spherical to deformed regions

Here we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provide a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by S D G pairs) reproduce the nuclear shape evolution in the N = 26 isotones, Ca 46 , Ti 48 , Cr 50 , and Fe 52 , and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: Ti 44 – 48 , Cr 48 , Cr 50 , Fe 52 , Zn 60 – 64 , Ge 64 , 66 , Mo 84 , and Xe 108 – 112 . Finally, using the S D G I -pair approximation we describe low-lying states of Ba 112 , 114 , cases difficult to reach by conventional configuration-interaction methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

First results of a general circulation model applied to the SST-NOx problem

Results of model runs, one using two-dimensional distribution of NO2 in the unperturbed stratosphere and another including an additional localized source of NO2 to approximate the effect of SSTs, are reported. The general circulation model and chemical reactions are described, and corrections in the previous latitudinal and seasonal gradients of total columnar ozone and the diffusion coefficient in the neighborhood of the tropopause are noted. Excellent agreement with previous observations was obtained. Global distributions of ozone and NO2 are described and represented in graphs. Results indicate ozone reduction of approximately 16% in the Northern Hemisphere and approximately 8% in the Southern Hemisphere, with the mid-latitude source of NO2 apparently having a blocking effect on the horizontal transport of ozone, resulting in larger reductions of ozone at high latitudes than at low ones.

Cunnold, D. M.↗

Approximating Nash Equilibrium in Day-ahead Electricity Market Bidding with Multi-agent Deep Reinforcement Learning

In this paper, a day-ahead electricity market bidding problem with multiple strategic generation company (GEN-CO) bidders is studied. The problem is formulated as a Markov game model, where GENCO bidders interact with each other todevelop their optimal day-ahead bidding strategies. Considering unobservable information in the problem, a model-free and data-driven approach, known as multi-agent deep deterministic policy gradient (MADDPG), is applied for approximating the Nash equilibrium (NE) in the above Markov game. The MADDPG algorithm has the advantage of generalization due to the automatic feature extraction ability of the deep neural networks. The algorithm is tested on an IEEE 30-bus system with three competitive GENCO bidders in both an uncongested caseand a congested case. Comparisons with a truthful bidding strategy and state-of-the-art deep reinforcement learning methods including deep Q network and deep deterministic policy gradient (DDPG) demonstrate that the applied MADDPG algorithm can find a superior bidding strategy for all the market participants with increased profit gains. In addition, the comparison with a conventional model-based method shows that the MADDPG algorithm has higher computational efficiency, which is feasible for real-world applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

From the Blazar Sequence to the Blazar Envelope: Revisiting the Relativistic Jet Dichotomy in Radio-Loud AGN

We revisit the concept of a blazar sequence that relates the synchrotron peak frequency (Vpeak) in blazars with synchrotron peak luminosity (Lpeak, in vLv) using a large sample of radio-loud AGN. We present observational evidence that the blazar sequence is formed from two populations in the synchrotron Vpeak - Lpeak plane, each forming an upper edge to an envelope of progressively misaligned blazars, and connecting to an adjacent group of radio galaxies having jets viewed at much larger angles to the line of sight. When binned by jet kinetic power (Lkin; as measured through a scaling relationship with extended radio power), we find that radio core dominance decreases with decreasing synchrotron Lpeak, revealing that sources in the envelope are generally more misaligned. We find population-based evidence of velocity gradients in jets at low kinetic powers (approximately 10(exp 42) - 10(exp 44.5) erg s(exp -1)), corresponding to FR I radio galaxies and most BL Lacs. These low jet power 'weak jet' sources, thought to exhibit radiatively inefficient accretion, are distinguished from the population of non-decelerating, low synchrotron-peaking (LSP) blazars and FR II radio galaxies ('strong' jets) which are thought to exhibit radiatively efficient accretion. The two-population interpretation explains the apparent contradiction of the existence of highly core-dominated, low-power blazars at both low and high synchrotron peak frequencies, and further implies that most intermediate synchrotron peak (ISP) sources are not intermediate in intrinsic jet power between LSP and high synchrotron-peaking (HSP) sources, but are more misaligned versions of HSP sources with similar jet powers.

Meyer, Eileen T.↗

L-BFGS Class Implementation in C++

This report presents a header-only C++ class implementation of the Limited-memory BroydenFletcher-Goldfarb-Shanno (L-BFGS) algorithm. The L-BFGS method is a general purpose quasi-Netwon optimization method that builds an approximation of the descent direction from consecutive iterate and gradient vectors. The limited-memory aspect stems from the replacement of the N × N approximation matrix of the original BFGS method with M vectors of length N. An example usage of the class is included along with the reference source code.

97 MATHEMATICS AND COMPUTING↗

A simple approximate result for the maximum growth rate of baroclinic instabilities

The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem has precluded extracting simple results of generality. It is shown that there exists very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. The result extends to substantially more general profiles than those in the Charney problem.

Lindzen, R. S.↗

Long-term motion in a restricted problem of rotational motion

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is constrained to precess and spin with constant rates. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/omega sub 0, where n is the orbital mean motion of the center of mass and omega sub 0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗

Identifying Controlling Variables for Mercury Vapors in Alpha-4 at Y-12: Two Year Data Collection Update

Multiple sensor packages were deployed at Alpha-4 by SRNL, in collaboration with United Cleanup Oak Ridge LLC (UCOR), to monitor mercury vapor concentrations and meteorological parameters. These sensors collected data, inside and outside of the legacy-use facility, for approximately two years. Though data gaps still exist, particularly in colder months, several controlling variables were identified that govern mercury vapor concentrations within Alpha-4. Temperature, barometric pressure gradients, humidity, and wind speed have been identified as controlling variables. A strong positive correlation was seen between mercury vapor concentrations and temperature which generally followed diurnal fluctuations. Temperatures below approximately 10 degrees Celsius did not show any spikes above the PEL, indicating more work can be performed at any time during the winter months – more data should be collected to confirm consistency in this finding. Additionally, spikes in mercury vapor concentrations above that of the permissible exposure limit (PEL; 100 µg/m 3 ) occurred primarily in late afternoon or evening/overnight hours (between 3 PM and 6 AM), which suggests D&D operations might be best scheduled during morning or daytime hours prior to the late afternoon. However, a limited number of spikes did occur outside of the identified window, although this may be attributed to disturbances in air flow and mercury vapor release from work activities performed inside of the Alpha-4 building. The analysis conducted allows for a strong predictive capability for estimating mercury vapor concentrations based upon accurate meteorological parameters. Still, additional data collection, particularly in the winter months, could help to strengthen the predictive power and validate the identified data trends. Further, increased temporal resolution could also help to better characterize the incipient stages of the increases and decreases in the mercury vapor concentration. Continued monitoring support by SRNL at Y-12 is underway at Alpha-4 to further close remaining data gaps and support deactivation and decommissioning work. Within a collaborative effort with UCOR, the SRNL team is collecting mercury vapor data to study the efficacy of a novel mercury suppressant, FerroBlack® which was recently deployed at Alpha-4. In addition, modifications to the current monitoring setup to increase measurement resolution is also being investigated.

54 ENVIRONMENTAL SCIENCES↗

Leptodermic corrections to the TOV equations and nuclear astrophysics within the effective surface approximation

The macroscopic model for a neutron star (NS) as a liquid drop at the equilibrium is used to extend the Tolman-Oppenheimer-Volkoff (TOV) equations taking into account the gradient terms responsible for the system surface. The parameters of the Schwarzschild metric in the spherical case are found with these surface corrections to the known leading (zero) order of the leptodermic approximation a/R << 1, where a is the NS effective-surface (ES) thickness, and R is the effective NS radius. The energy density $\mathscr{E}$ is considered in a general form including the functions of the particle number density and of its gradient terms. The macroscopic gravitational component $Φ$(ρ) of the energy density is taken into account in the simplest form as expansion in powers of $ρ$ – $\overline{ρ}$, where $\overline{ρ}$ is the saturation density, up to second order, in terms of its contributions to the separation particle energy and incompressibility. Density distributions ρ across the NS ES in the normal direction to the ES, which are derived in the simple analytical form at the same leading approximation, was used for the derivation of the modified TOV (MTOV) equations by accounting for their NS surface corrections. As a result, the MTOV equations are analytically solved at first order and the results are compared with the standard TOV approach of the zero order.

Magner, A. G. [Institute for Nuclear Research, Kyi↗