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At least 73 records · Page 4

A simple method of calculating power-law velocity profile exponents from experimental data

Analytical expressions for the effects of compressibility and heat transfer on laminar and turbulent shape factors H have been developed. Solving the turbulent equation for the power law velocity profile exponent N has resulted in a simple technique by which the N values of experimental turbulent profiles can be calculated directly from the integral parameters. Thus the data plotting, curve fitting, and slope measuring, which is the normal technique of obtaining experimental N values, is eliminated. The N values obtained by this method should be within the accuracy with which they could be measured.

Allen, J. M.↗

Radiatively driven winds for different power law spectra

The analytic solutions for radiatively driven winds are given for the case in which the winds are driven by absorption of line and continuum radiation. The wind solutions are analytically estimated for different parameters of the central source and for different power law spectra. For flat spectra, three sonic points can exist; it is shown, however, that only one of these sonic points is physically realistic. Parameters of the central source are given which generate winds of further interest for explaining the narrow and broad absorption lines in quasars. For the quasar model presented here, winds which could give rise to the narrow absorption lines are generated by central sources with parameters which are not realistic for quasars.

Beltrametti, M.↗

Can the cosmic x ray and gamma ray background be due to reflection of a steep power law spectrum and Compton scattering by relativistic electrons?

We reconsider the recent model for the origin in the cosmic X-ray and gamma-ray background by Rogers and Field. The background in the model is due to an unresolved population of AGNs. An individual AGN spectrum contains three components: a power law with the energy index of alpha = 1.1, an enhanced reflection component, and a component from Compton scattering by relativistic electrons with a low energy cutoff at some minimum Lorentz factor, gamma(sub min) much greater than 1. The MeV bump seen in the gamma-ray background is then explained by inverse Compton emission by the electrons. We show that the model does not reproduce the shape of the observed X-ray and gamma-ray background below 10 MeV and that it overproduces the background at larger energies. Furthermore, we find the assumptions made for the Compton component to be physically inconsistent. Relaxing the inconsistent assumptions leads to model spectra even more different from that of the observed cosmic background. Thus, we can reject the hypothesis that the high-energy cosmic background is due to the described model.

Zycki, Piotr T.↗

Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development

The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

Pines, V.↗

Determining the power-law wind-profile exponent under near-neutral stability conditions at sea

On the basis of 30 samples from near-simultaneous overwater measurements by pairs of anemometers located at different heights in the Gulf of Mexico and off the Chesapeake Bay, Virginia, the mean and standard deviation for the exponent of the power-law wind profile over the ocean under near-neutral atmospheric stability conditions were determined to be 0.11 +/- 0.03. Because this mean value is obtained from both deep and shallow water environments, it is recommended for use at sea to adjust the wind speed measurements at different heights to the standard height of 10 m above the mean sea surface. An example to apply this P value to estimate the momentum flux or wind stress is provided.

Hsu, S. A.↗

Deviations from uniform power law scaling in nonstationary time series

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

Non-NASA Center↗

Spectral Power-law Formation by Sequential Particle Acceleration in Multiple Flare Magnetic Islands

We present a first-principles model of pitch-angle and energy distribution function evolution as particles are sequentially accelerated by multiple flare magnetic islands. Data from magnetohydrodynamic (MHD) simulations of an eruptive flare/coronal mass ejection provide ambient conditions for the evolving particle distributions. Magnetic islands, which are created by sporadic reconnection at the self-consistently formed flare current sheet, contract and accelerate the particles. The particle distributions are evolved using rules derived in our previous work. In this investigation, we assume that a prescribed fraction of particles sequentially "hops" to another accelerator and receives an additional boost in energy and anisotropy. This sequential process generates particle number spectra that obey an approximate power law at mid-range energies and presents low- and high-energy breaks. We analyze these spectral regions as functions of the model parameters. We also present a fully analytic method for forming and interpreting such spectra, independent of the sequential acceleration model. The method requires only a few constrained physical parameters, such as the percentage of particles transferred between accelerators, the energy gain in each accelerator, and the number of accelerators visited. Our investigation seeks to bridge the gap between MHD and kinetic regimes by combining global simulations and analytic kinetic theory. The model reproduces and explains key characteristics of observed flare hard X-ray spectra as well as the underlying properties of the accelerated particles. Our analytic model provides tools to interpret high-energy observations for missions and telescopes, such as RHESSI, FOXSI, NuSTAR, Solar Orbiter, EOVSA, and future high-energy missions.

magnetic reconnection↗

HMI Data Driven Magnetohydrodynamic Model Predicted Active Region Photospheric Heating Rates: Their Scale Invariant, Flare Like Power Law Distributions, and Their Possible Association With Flares

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model pre- dicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q−s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E−S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.

Goodman, Michael L.↗

HMI Data Driven Magnetohydrodynamic Model Predicted Active Region Photospheric Heating Rates: Their Scale Invariant, Flare Like Power Law Distributions, and Their Possible Association With Flares

A data driven, near photospheric, 3 D, non-force free magnetohydrodynamic model predicts time series of the complete current density, and the resistive heating rate Q at the photosphere in neutral line regions (NLRs) of 14 active regions (ARs). The model is driven by time series of the magnetic field B observed by the Helioseismic and Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. Errors in B due to these periods can be significant. The number of occurrences N(q) of values of Q > or = q for each AR time series is found to be a scale invariant power law distribution, N(Q) / Q−s, above an AR dependent threshold value of Q, where 0.3952 < or = s < or = 0.5298 with mean and standard deviation of 0.4678 and 0.0454, indicating little variation between ARs. Observations show that the number of occurrences N(E) of coronal flares with a total energy released > or = E obeys the same type of distribution, N(E) / E−S, above an AR dependent threshold value of E, with 0.38 < or approx. S < or approx. 0.60, also with little variation among ARs. Within error margins the ranges of s and S are nearly identical. This strong similarity between N(Q) and N(E) suggests a fundamental connection between the process that drives coronal flares and the process that drives photospheric NLR heating rates in ARs. In addition, results suggest it is plausible that spikes in Q, several orders of magnitude above background values, are correlated with times of the subsequent occurrence of M or X flares.

Goodman, Michael L.↗

Power Law Versus Exponential Form of Slow Crack Growth of Advanced Structural Ceramics: Dynamic Fatigue

The life prediction analysis based on an exponential crack velocity formulation was examined using a variety of experimental data on glass and advanced structural ceramics in constant stress-rate ("dynamic fatigue") and preload testing at ambient and elevated temperatures. The data fit to the strength versus In (stress rate) relation was found to be very reasonable for most of the materials. It was also found that preloading technique was equally applicable for the case of slow crack growth (SCG) parameter n > 30. The major limitation in the exponential crack velocity formulation, however, was that an inert strength of a material must be known priori to evaluate the important SCG parameter n, a significant drawback as compared to the conventional power-law crack velocity formulation.

Choi, Sung R.↗

Evidence for a continuous, power law, electron density irregularity spectrum

The spectral form of the irregularities in electron density that cause interplanetary scintillation (IPS) of small angular diameter radio sources is discussed. The intensity scintillation technique always yields an irregularity scale size, which is of the order of the first Fresnel zone for the wavelength at which the observations are taken. This includes not only the radio wavelength measurements of the structure of the interplanetary medium, but also radio wavelength measurements of the irregularity structure of the ionosphere and interstellar medium, and optical wavelength measurements of the irregularity structure of the atmosphere.

Cronyn, W. M.↗

Power law rheology of ice and the relaxation style and retention of craters on Ganymede

A numerical finite element model of viscous relaxation of craters in ice is presented which incorporates rheological data for ice at temperatures and pressures appropriated to the near-surface regions of Ganymede. For temperature gradients in reasonable agreement with those obtained from thermal and structural models of Ganymede, relaxation times greater than 10 to the 7th years were obtained for craters with diameters less than 100 km. For all craters with diameters greater than 10 km, the dependence of viscosity on stress was found to significantly shorten the relaxation time. The rheological laws which dominate crater relaxation are discussed for craters of various sizes. The results are compared with imagery from Voyager.

Thomas, Paul J.↗

The kink instability in infinite cylindrical flux tubes - Eigenvalues for power-law twist profiles

Simple, accurate methods of calculating ideal MHD instability eigenvalues for infinitely long cylindrical tubes with twist function T(r) are developed. The results show that the most rapidly growing and energetic instabilities occur in the Gold-Hoyle v = 0 field, with the instability progressively weakening with increasing v. However, the maximum force eigenvalue is always small, so that even in the Gold-Hoyle case only a small proportion of the available magnetic energy can be released in the linear phase. The results also confirm that the linear pinch is remarkably weak yet relatively resistant to line-tying. It is shown that the weakness of the force eigenvalue implies that the influence of uniform gas pressure on stability is negligible. Implications for the energy-release mechanism in solar flares are discussed.

Craig, I. J. D.↗