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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.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.

Adamiak, Daniel [Thomas Jefferson National Acceler↗
NASA NTRS1984

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Connor, J. N. L.↗
DOE OSTI2024

Geometric Interpretation of a Non-Linear Extension of Quantum Mechanics

We recently introduced a particular non-linear generalization of quantum mechanics that has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. In this paper, we suggest that the two components of the wave function represent the system described by the Hamiltonian H in two different asymptotic regions of spacetime and we show that the non-linear terms can be viewed as giving rise to gravitational effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Thermal conductance of pressed aluminum and stainless steel contacts at liquid helium temperatures

The thermal conductance of aluminum and stainless steel 304 sample pairs with surface finishes ranging from 0.1 to 1.6 microns rms roughness was investigated over a temperature range from 1.6 to 6.0 k. The thermal conductance follows a simple power law function of temperature, with the exponent ranging from 0.5 to 2.25, increases asymptotically with increasing applied force, and exhibits an anomaly for surface finishes in the 0.4 micron region.

Salerno, L. J.↗
NASA NTRS1988

Thermal conductance of pressed aluminum and stainless steel contacts at liquid helium temperatures

The thermal conductance of aluminum and stainless steel 304 sample pairs with surface finishes ranging from 0.1 to 1.6 microns rms roughness was investigated over a temperature range from 1.6 to 6.0 K. The thermal conductance follows a simple power law function of temperature, with the exponent ranging from 0.5 to 2.25, increases asymptotically with increasing applied force, and exhibits an anomaly for surface finishes in the 0.4 micron region.

Salerno, L. J.↗
NASA NTRS1991

A k-epsilon modeling of near wall turbulence

A k-epsilon model is proposed for turbulent bounded flows. In this model, the turbulent velocity scale and turbulent time scale are used to define the eddy viscosity. The time scale is shown to be bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using the time scale, removing the need to introduce the pseudo-dissipation. A damping function is chosen such that the shear stress satisfies the near wall asymptotic behavior. The model constants used are the same as the model constants in the commonly used high turbulent Reynolds number k-epsilon model. Fully developed turbulent channel flows and turbulent boundary layer flows over a flat plate at various Reynolds numbers are used to validate the model. The model predictions were found to be in good agreement with the direct numerical simulation data.

Yang, Z.↗
NASA NTRS1999

Magnetic Photon Splitting: The S-Matrix Formulation in the Landau Representation

Calculations of reaction rates for the third-order QED process of photon splitting gamma yields gamma.gamma in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner [1] presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant, advances beyond the work of [1] by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper- time formulations is demonstrated.

Baring, Matthew G.↗
NASA NTRS2008

Mapping Snow Grain Size over Greenland from MODIS

This paper presents a new automatic algorithm to derive optical snow grain size (SGS) at 1 km resolution using Moderate Resolution Imaging Spectroradiometer (MODIS) measurements. Differently from previous approaches, snow grains are not assumed to be spherical but a fractal approach is used to account for their irregular shape. The retrieval is conceptually based on an analytical asymptotic radiative transfer model which predicts spectral bidirectional snow reflectance as a function of the grain size and ice absorption. The analytical form of solution leads to an explicit and fast retrieval algorithm. The time series analysis of derived SGS shows a good sensitivity to snow metamorphism, including melting and snow precipitation events. Preprocessing is performed by a Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm, which includes gridding MODIS data to 1 km resolution, water vapor retrieval, cloud masking and an atmospheric correction. MAIAC cloud mask (CM) is a new algorithm based on a time series of gridded MODIS measurements and an image-based rather than pixel-based processing. Extensive processing of MODIS TERRA data over Greenland shows a robust performance of CM algorithm in discrimination of clouds over bright snow and ice. As part of the validation analysis, SGS derived from MODIS over selected sites in 2004 was compared to the microwave brightness temperature measurements of SSM\I radiometer, which is sensitive to the amount of liquid water in the snowpack. The comparison showed a good qualitative agreement, with both datasets detecting two main periods of snowmelt. Additionally, MODIS SGS was compared with predictions of the snow model CROCUS driven by measurements of the automatic whether stations of the Greenland Climate Network. We found that CROCUS grain size is on average a factor of two larger than MODIS-derived SGS. Overall, the agreement between CROCUS and MODIS results was satisfactory, in particular before and during the first melting period in mid-June. Following detailed time series analysis of SGS for four permanent sites, the paper presents SGS maps over the Greenland ice sheet for the March-September period of 2004.

Lyapustin, Alexei↗
DOE OSTI2024

Assessment of effective elastic constants of U-10Mo fuel: A multiscale modeling and homogenization study

The significant microstructural changes that U-Mo fuel undergoes during operation degrades its mechanical properties and structural integrity. Microstructural evolution entails the formation, evolution, and redistribution of porosity in conjunction with grain refinement. In the present paper, we employ numerical approaches to assess the impact of the various microstructural features—grains, nanoscale intragranular fission gas bubbles, and mesoscale intergranular voids—on the degradation of elastic constants. Phase-field microstructure models are combined with the asymptotic expansion homogenization technique in order to derive the effective elastic constants as a function of porosity and fission density. Here the results are verified and compared against theoretical bounds. Using this approach, elastic degradation in operating nuclear fuels can be quantified when the distributions of microstructural features are known.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1993

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Degani, A. T.↗
NASA NTRS1992

A near-wall two-equation model for turbulent heat fluxes

A near-wall two-equation model for turbulent heat fluxes is derived from the temperature variance and its dissipation-rate equations and the assumption of gradient transport. Only incompressible flows with non-buoyant heat transfer are considered. The near-wall asymptotics of each term in the exact equations are examined and used to derive near-wall correction functions that render the modeled equations consistent with these behavior. Thus modeled, the equations are used to calculate fully-developed pipe and channel flows with heat transfer. It is found that the proposed two-equation model yields asymptotically correct near-wall behavior for the normal heat flux, the temperature variance and its near-wall budget and correct limiting wall values for these properties compared to direct simulation data and measurements obtained under different wall boundary conditions.

Sommer, T. P.↗
NASA NTRS1988

Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model

An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.

Heller, Urs M.↗
NASA NTRS1994

Magnetocentrifugally driven flows from young stars and disks. 2: Formulation of the dynamical problem

We formulate the dynamical problem of a cool wind centrifugally driven from the magnetic interface of a young star and an adjoining Keplerian disk. We examine the situation for mildly accreting T Tauri stars that rotate slowly as well as rapidly accreting protostars that rotate near break-up. In both cases a wind can be driven from a small X-region just outside the stellar magnetopause, where the field lines assume an open geometry and are rooted to material that rotates at an angular speed equal both to the local Keplerian value and to the stellar angular speed. Assuming axial symmetry for the ideal magnetohydrodynamic flow, which requires us to postpone asking how the (lightly ionized) gas is loaded onto field lines, we can formally integrate all the governing equations analytically except for a partial equation that describes how streamlines spread in the meridional plane. Apart from the difficulty of dealing with PDEs of mixed type, finding the functional forms of the conserved quantities along streamlines - the ratio beta of magnetic field to mass flux, the specific energy H of the fluid in the rotating frame, and the total specific angular momentum J carried in the matter and the field - constitutes a standard difficulty in this kind of (Grad-Shafranov) formalism. Fortunately, because the ratio of the thermal speed of the mass-loss regions to the Keplerian speed of rotation of the interface constitutes a small parameter epsilon, we can attack the overall problem by the method of matched asymptotic expansions. This procedure leads to a natural and systematic technique for obtaining the relevant functional dependences of beta, H, and J. Moreover, we are able to solve analytically for the properties of the flow emergent from the small transsonic region driven by gas pressure without having to specify the detailed form of any of the conserved functions, beta, H, and J. This analytical solution provides inner boundary conditions for the numerical computation in a companion paper by Najita & Shu of the larger region where the main acceleration to terminal speeds occurs.

Shu, Frank H.↗
NASA NTRS1977

Plasma oscillations and Landau damping

The Fourier-Hermite expansion is used to follow the time development of a non-analytic initial perturbation of the linearized Vlasov-Poisson system. The calculations differ from some previous applications of the Fourier-Hermite expansion in that they relax certain symmetry conditions on the distribution functions and in that many coefficients are required to describe the initial conditions. The results confirm Weitzner's prediction of the asymptotic t to the -3rd time dependence for this problem, and exhibit the way in which this behavior develops. An appendix outlines the way in which the initial conditions are expanded in Hermite functions.

Crownfield, F. R., Jr.↗
NASA NTRS1976

The use of dispersion to eliminate multipath in planetary radio occultations

Occultation geometry is analyzed with a view toward eliminating all multipath resulting from layer effects. It is assumed that the spacecraft moves behind the planet with a constant velocity perpendicular to the direction from the spacecraft to the earth, and that for radio frequencies of 1 to 2 GHz the angle of refraction of a radio ray passing through the ionosphere is so small as to be imperceptible if drawn to scale. It is shown that if a particular amount of dispersion is inserted into the process at any stage prior to signal detection, the frequency vs time curve will be converted to a frequency vs ray asymptote height curve. Because there can be only one mode from any one ray asymptote height in a layered medium, frequency must be a single-valued function of this parameter. The introduction of an appropriate dispersion will therefore eliminate all multipath insofar as it is caused by spherically symmetric planetary layers. The degree of accuracy to be provided in flight and during postflight analysis is discussed.

Croft, T. A.↗
NASA NTRS1977

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Volland, H.↗
NASA NTRS1984

The dissolution or growth of a sphere

The problem of the dissolution or growth of an isolated stationary sphere in a large fluid body is analyzed. The motion of the boundary as well as the the resulting motion in the liquid are properly taken into account. The governing equations are solved using a recently developed technique (Subramanian and Weinberg, 1981) which employs an asymptotic expansion in time. Results for the radius of the sphere as a function of time are calculated. The range of utility of the present solution is established by comparison with a numerical solution of the governing equations obtained by the method of finite differences.

Shankar, N.↗
NASA NTRS1993

Random interactions in higher order neural networks

Recurrent networks of polynomial threshold elements with random symmetric interactions are studied. Precise asymptotic estimates are derived for the expected number of fixed points as a function of the margin of stability. In particular, it is shown that there is a critical range of margins of stability (depending on the degree of polynomial interaction) such that the expected number of fixed points with margins below the critical range grows exponentially with the number of nodes in the network, while the expected number of fixed points with margins above the critical range decreases exponentially with the number of nodes in the network. The random energy model is also briefly examined and links with higher order neural networks and higher order spin glass models made explicit.

Baldi, Pierre↗