Derivation of frequency-dependentX- andY-functions for a non-coherent scattering problem

The equation of transfer for the case of non-coherent scattering (Hummer, 1968; Ivanov, 1973; McCormick and Siewert, 1970) has been considered. The correspondingX- andY-functions have been derived by a combination of eigenfunction method developed by Case, and from the principle of invariance as developed by Chandrasekhar (1960).     

A stepwise method for determining the number of component distributions in a mixture

This paper considers the problem of estimatingm, the number of components in a finite mixture of distributions from a parametric family. A step-up procedure using the bootstrap method is proposed. Some properties of the procedure are illustrated with simulation studies. An example of the method, applied to orientation of beach clasts, is given.     

Effect of element size on the static finite element analysis of steep slopes

The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher‐order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd.     

Three-dimensional linear solution for wave propagation with slopingbottom

This paper presents a three-dimensional analytic linear wave solution for surface gravity wave propagation over a sloping bottom that is valid for small, but realistic, slopes. The sloping-bottom linear model is compared to published laboratory data and to predictions of two-dimensional, constant-bottom nonlinear theories. The model is shown to describe the measured wave-height growth in the wave transformation region up to a limiting local Ursell number U_r of 0.35-1.0, depending on the wave type, although, as a linear model, it does not predict the harmonics observed in that range. For U_r<0.35, the harmonics can generally be neglected and the sloping-bottom linear theory agrees closely with both the published wave-height data and third-order Stokes nonlinear theory. As a three-dimensional linear model, superposition can be invoked to synthesize and relate wave structure in the transformation region to complex incident ocean spectra with both wind wave and swell components that arrive with a range of incidence angles. As such, the sloping-bottom linear model presented here should be a convenient useful tool for ocean modeling through a significant portion of the wave transformation region     

Ambipolar diffusion in the solar atmosphere

The process of non-linear ambipolar diffusion in the region overlying the solar surface can be an effective mechanism for producing sharp magnetic structures and current sheets. These may be the sites responsible for the occurrence of connectivity of magnetic field lines, and the subsequent explosive input of energy for heating of some of the features in the atmosphere of the Sun..     

Emission-line outflows in PKS1549−79: the effects of the early stages of radio-source evolution?

We present new spectroscopic observations of the southern radio galaxy         . Despite the flat-spectrum character of the radio emission from this source, our optical spectra show no sign of the broad permitted lines and non-stellar continuum characteristic of quasar nuclei and broad-line radio galaxies. However, the high-ionization forbidden lines, including [O  iii ] λλ 5007, 4959, are unusually broad for a narrow-line radio galaxy     , and are blueshifted by 600 km s⁻¹ relative to the low-ionization lines such as [O  ii ] λλ 3726,3729. The [O  ii ] lines are also considerably narrower     than the [O  iii ] lines, and have a redshift consistent with that of the recently detected H  i 21-cm absorption-line system. Whereas the kinematics of the [O  iii ] emission lines are consistent with outflow in an inner narrow-line region, the properties of the [O  ii ] emission lines suggest that they are emitted by a more extended and quiescent gaseous component. We argue that, given the radio properties of the source, our line of sight is likely to be lying close to the direction of bulk outflow of the radio jets. In this case it is probable that the quasar nucleus is entirely obscured at optical wavelengths by the material responsible for the H  i absorption-line system. The unusually broad [O  iii ] emission lines suggest that the radio source is intrinsically compact. Overall, our data are consistent the idea that     is a radio source in an early stage of evolution.     

Gyldén Model: The Slowly Changing Equivalent Gravitational Parameter

In the Gyldén problem, the case of slowly changing equivalent gravitational parameter (e.g.p.) is studied. Assuming the following law for the variation of the e.g.p.: μ (t) = μ₀+ εμ (εt), ε< μ₀, we obtained a) a O(ε⁴ T⁴)-approximation of the solution, on a shortened time scale (0,T), with T of order o(ε^-1),for the general case (i.e. the support function μ is O(1)-valued and admits an expansion in power series of its argument), and b) a O(ε²)-approximation of the solution, on a natural timescale of order O(1/ε), for the case of a bounded variation rate (i.e. the support function μ and its derivative are both O(1)-valued). For the study of the first problem we introduced a type of Lissajous variables and used the Lie-Hori normalization scheme; for the second problem we used the Delaunay variables and applied the von Zeipel method for approximate integration. The physical interpretation of the results is in both cases the same: within the corresponding limits of approximation, the variation of e.g.p. (i) has no effect on the size of the osculating ellipse, (ii) it sets the pericenter in slow rotation and (iii) it introduces a secular variation in the longitudes. This revised version was published online in July 2006 with corrections to the Cover Date.