Study of self-similar and steady flows near singularities

One-dimensional steady state flow or a self-similar flow is represented by an integral curve of the system of ordinary differential equations and, in many important cases, the integral curve passes through a singular point. Kulikovskii & Slobodkina (1967) have shown that the stability of a steady flow near the singularity can be studied with the help of a simple first-order partial differential equation. In section 2 of this paper we have used their method to study steady transonic flows in radiation-gas-dynamics in the neighbourhood of the sonic point. We find that all possible one-dimensional steady flows in radiation-gas-dynamics are locally stable in the neighbourhood of the sonic point. A continuous disturbance on a steady flow, while decaying and propagating, may develop a surface of discontinuity within it. We have determined the conditions for the appearance of such a discontinuity and also the exact position where it appears. In section 3 we have shown that their method can be easily generalized to study the stability of self-similar flows. As an example we have considered the stability of the self-similar flow behind a strong imploding shock. In this case we find that the flow is stable with respect to radially symmetric disturbances

Study of self-similar and steady flows near singularities. II. A case of multiple characteristic velocity

We consider here a system of first-order quasilinear partial differential equations in two independent variables: t, time and x, spatial coordinate. In many physically realistic problems in fluid mechanics, a singularity of the system of ordinary differential equations representing the steady solutions represents a critical state where one of the characteristic velocities vanishes (e.g. sonic point in fluid mechanics). Kulikovskii & Slobodkina (1967) have shown that the stability of all the steady solutions near a singularity can be studied with the help of a simple first-order quasi-linear partial differential equation. The simplicity of their method lies in the fact that all the results can be deduced from the phase-plane of the steady equations. The analysis of Kulikovskii & Slobodkina is valid for any system of equations, totally hyperbolic or mixed type with the only assumption that the characteristic velocity under consideration is real and not multiple. We have earlier (1970, to be referred to as part I) extended their treatment to self-similar flows. In this paper we have shown that in the case of a characteristic velocity of multiplicity s (s > 1), it is still possible to approximate the system provided there exists exactly s linearly independent eigenvectors corresponding to this characteristic velocity. The approximate system consists of s quasi-linear equations and we have to consider the s + 1 dimensional phase-space of the steady equations. In the end we have also discussed two illustrative examples

Radio and near-infrared observations of the steep spectrum Galactic plane radio source WKB 0314+57.8

Radio and near-infared observations towards the steep spectrum Galactic plane radio source WKB 0314+57.8 are presented, in order to clarify the nature of this source. The radio observations include archival and survey data, together with new Giant Metrewave Radio Telescope observations at 617 MHz. The near-infrared observations are in the J and K bands, from the Gemini instrument on the Shane 3-m telescope. The radio observations show that WKB 0314+57.8 is extended, with an very steep spectrum (with flux density proportional to frequency to -2.5 power between 40 MHz and 1.5 GHz). The colour--magnitude diagram constructed from near-infrared observations of the field suggests the presence of a z approx 0.08 galaxy cluster behind the Galactic plane, reddened by about 6 magnitudes of visual extinction. Although the steep spectrum source has no obvious identification, two other radio sources in the field covered by the near-infrared observations have tentative identifications with galaxies. These observations indicate that WKB 0314+57.8 is a relic source in a cluster of galaxies, not a pulsar.Comment: 6 pages, to appear in MNRAS, typos correcte

The S0_0(0) structure in highly compressed hydrogen and the orientational transition

A calculation of the rotational S$_0$(0) frequencies in high pressure solid para-hydrogen is performed. Convergence of the perturbative series at high density is demonstrated by the calculation of second and third order terms. The results of the theory are compared with the available experimental data to derive the density behaviour of structural parameters. In particular, a strong increase of the value of the lattice constant ratio $c/a$ and of the internuclear distance is determined. Also a decrease of the anisotropic intermolecular potential is observed which is attributed to charge transfer effects. The structural parameters determined at the phase transition may be used to calculate quantum properties of the rotationally ordered phase.Comment: accepted Europhysics Letter

Stability of plasma in helical field

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Oscillations of a three-component assembly in the presence of a magnetic field using the generalized BGK collision model

The BGK collision model for one-component assembly of neutral particles has been extended to two-component assembly of charged particles by Gross and Krook (1956) and later on modified by Bhatnagar (1962). Following the lines of the latter, the model has been generalized to N-component assembly of both charged and neutral particles. This model is further applied to the study of small amplitude plasma oscillations in an assembly consisting of ions, electrons and neutral particles in the direction perpendicular to a uniform magnetic field. The dispersion relation splits up into two, one determining the transverse oscillations and the other longitudinal oscillations. In the transverse oscillations for small wave numbers k, it has been shown that apart from the Gross-gaps occurring at the multiples of gyro-frequencies of electrons and ions, if the magnetic energy density M is greater than one-third the kinetic energy density K of charged particles, and terms only up to k2 are retained, five more forbidden ranges of frequencies occur. If M < ± ½ K, the number of additional gaps reduces to three. When M = 0, Oster's (1960) result is obtained as a particular case. The oscillations of neutral particles excited by collisions are strong at low frequencies, whereas for high frequencies they are mostly damped out. Exact analytical and graphical discussion of the transverse dispersion relations is given. Longitudinal propagation has been studied under very restricted circumstance numerically and it is shown that, unless the magnetic field is very high, propagation is possible for all frequencies. For a sufficiently high magnetic field, when the Alfven velocity is comparable with the velocity of light, there is one forbidden range but, for the discussion of such high velocities, one should work with the relativistic equations