Time as an independent variable for current ripples developing towards linguoid equilibrium morphology

Flume experiments show that current ripples on very fine sand surfaces always develop towards a linguoid shape with constant height and wavelength provided that sufficient time is allowed for their formation. Straight and sinuous current ripples only reflect intermediate stages in ripple development and may be regarded as non-equilibrium bedforms. The time period which current ripples require to reach linguoid equilibrium morphology is related to an inverse power of flow velocity. In the transitional stage from current ripples to upper stage plane bed (i.e. washed-out ripple stage) only the equilibrium wavelength remains constant, whereas equilibrium height rapidly decreases to zero. Our observations imply that bed-roughness parameters in sediment transport calculations can be simplified when equilibrium conditions are attained, and that inferences about flow energy from the dimensions of current ripples in very fine sand need to be regarded with caution.     

A New Magnitude-Frequency Relation for Earthquakes and a Classification of Relation Types

Summary. In this paper some aspects of the deviations of frequency distributions of earthquakes from a linear trend are considered. For recurrence curves with inflexions, the formula
is proposed as a magnitude-frequency relation, with critical magnitude M _cr. Comparison with actual data shows better agreement than other formulae. The slope of the frequency graph is considered in the most general case to be a function of M and some parameters p ₁, p ₂, …. A classification of the types of magnitude-frequency relation is given and all known types of relations N : M and N: K ( K = log E , E = seismic energy) are summarized.     

A comparison of solar EUV intensities and K-coronameter measurements

Characteristics of the emission observed above the solar limb in four EUV lines, Sixii 499, Mgx 625, Neviii 770, and Ovi 1032 are discussed. The mean temperature of the corona derived from the ratios of the intensities of Sixii 499 and Mgx 625 is 1.8 million K. There do not appear to be significant temperature differences in regions with low EUV intensities and those with high EUV intensities, suggesting that the EUV emission from the lithium-like ions depends primarily on the integral of n _e ² along the line of sight.The EUV data are compared with K-coronameter measurements in order to yield new estimates of the abundances of Si, Mg, Ne and O relative to hydrogen. Within the uncertainties of the analysis, these coronal abundances are in agreement with the corresponding photospheric values.     

Principles of quantitative absorbance measurements in anisotropic crystals

The accurate measurement of absorbance (A=-log T; T=I/I ₀) in anisotropic materials like crystals is highly important for the determination of the concentration and orientation of the oscillator (absorber) under investigation. The absorbance in isotropic material is linearly dependent on the concentration of the absorber and on the thickness of the sample (A=?·c·t). Measurement of absorbance in anisotropic media is more complicated, but it can be obtained from polarized spectra (i) on three random, but orthogonal sections of a crystal, or (ii) preferably on two orthogonal sections oriented parallel to each of two axes of the indicatrix ellipsoid. To compare among different crystal classes (including cubic symmetry) it is useful to convert measured absorbance values to one common basis (the total absorbance A _tot), wherein all absorbers are corrected as if they were aligned parallel to the E-vector of the incident light. The total absorption coefficient (a _tot=A _tot/t) is calculated by $$\left( {\text{i}} \right)a_{{\text{tot}}} = \sum\limits_{i = 1}^3 {(a_{\max ,i} + a_{\min ,i} )} /2, {\text{or}} {\text{by}} {\text{(ii) }}a_{{\text{tot}}} = a_x + a_y + a_z .$$ Only in special circumstances will unpolarized measurements of absorbance provide data useful for quantitative studies of anisotropic material. The orientation of the absorber with respect to the axes of the indicatrix ellipsoid is calculated according to A _x/A _tot=cos² (x < absorber), and analogously for A _yand A _z. In this way, correct angles are obtained for all cases of symmetry. The extinction ratio of the polarizer (Pe=I _crossed/I _parallel) has considerable influence on the measured amplitude of absorption bands, especially in cases of strong anisotropic absorbance. However, if Pe is known, the true absorbance values can be calculated even with polarizers of low extinction ratio, according to A _max=?log[(T _max,obs?0.5·Pe·T _min,obs)/(1?0.5·Pe)], and similar for A _min. The theoretical approach is confirmed by measurements on calcite and topaz.     

Compatible potentials and orbits in synodic systems

For a given family of orbits f(x,y) = c ^* which can be traced by a material point of unit in an inertial frame it is known that all potentials V(x,y) giving rise to this family satisfy a homogeneous, linear in V(x,y), second order partial differential equation (Bozis,1984). The present paper offers an analogous equation in a synodic system Oxy, rotating with angular velocity . The new equation, which relates the synodic potential function (x,y), = –V(x, y) + % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaaaa!3780!\[\tfrac{1}{2}\]²(x ² + y ²) to the given family f(x,y) = c ^*, is again of the second order in (x,y) but nonlinear.As an application, some simple compatible pairs of functions (x,y) and f(x, y) are found, for appropriate values of , by adequately determining coefficients both in and f.     

The Hard X-ray Imaging Spectrometer (HXIS)

The HXIS, a joint instrument of the Space Research Laboratory at Utrecht, The Netherlands, and the Department of Space Research of the University of Birmingham, U.K., images the Sun in hard X-rays: Six energy bands in energy range 3.5–30 keV, spatial resolution 8 over Ø 240 and 32 over Ø 624 field of view, and time resolution of 0.5–7 s depending on the mode of operation. By means of a flare flag it alerts all the other SMM instruments when a flare sets in and informs them about the location of the X-ray emission. The experiment should yield information about the position, extension and spectrum of the hard X-ray bursts in flares, their relation to the magnetic field structure and to the quasi-thermal soft X-rays, and about the characteristics and development of type IV electron clouds above flare regions.     

Space Telescope Astrometry from CCD images

The astrometric application of the Wide Field Camera and the Planetary Camera is reviewed. It is shown that the digital image centering algorithms can yield a positional accuracy of 0.1 milli-arcsecond. Deconvolution of CCD's sensitivity, non-flatness of the filters, and crinkling of the CCD surface may limit the positional accuracy to 1 milli-arcsecond.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.