Propagation of axi-symmetric relativistic shock waves

Solutions in series for the propagation of relativistic shock waves with axial symmetry are obtained in this paper. We assume that the gaseous elements move almost radially and that the disturbance moves through a cold gas at rest wherein the nucleon number density and the energy density obey an exponential law of distance from a given plane. The motion is sustained by continuous explosions in the central region liberating energy varying as the cube of time. Also, we assume the equation of state of the moving elements as that of photonic gas.     

Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Homogénéisation et validation des corrections de terrain gravimétriques jusqu'à la distance de 167 km sur l'ensemble de la FranceUpdating and validating the French gravity terrain corrections out to a distance of 167 km

For regional and national study purposes, there is a high need for updating the terrain corrections (TC) in the French gravity database. We have recomputed the TC for all the French gravity stations from 50 m out to a distance of 167 km. We compute the TC with a flat-top-prism algorithm and three DEM with grid spacing of 50, 250 and 1000 m, used in the zones 53 m/3 km, 3 km/10 km et 10 km/167 km, respectively. Analysing the DEM/station Δz and comparing our results to the ones previously obtained in the Alps area, we estimate the accuracy of our TC to be better than 1 mGal. To cite this article: G. Martelet et al., C. R. Geoscience 334 (2002) 449–454.     

Solution of the equation of transfer for interlocked multiplets by the method of discrete ordinates with the planck function as a nonlinear function of optical depth

The equation of transfer for interlocked multiplets has been solved by the method of discrete ordinates, originally due to Chandrasekhar, considering nonlinear form of the Planck function to be

Proterozoic Rifting in the Pranhita-Godavari Valley: Implication on India-Antarctica Linkage

The Pranhita-Godavari (PG) Valley, a major lineament within the South Indian cratonic province, that preserves sediment dominated deposits spanning from Mesoproterozoic to Mesozoic, appears to be a key element in supercontinent reconstruction. The sedimentary basins of the Valley include a thick succession of Early Mesoproterozoic to Late Neoproterozoic rocks, the Godavari Supergroup, which is unconformably overlain by the Late Palaeozoic-Mesozoic Gondwana sequence. The Godavari Supergroup is internally punctuated by several regional and interregional unconformities into a number of unconformity-bound sequences having group level and subgroup level status. The lithostratigraphic attributes of the succession indicate multiple events of fault controlled sedimentation marked by transgression and regression, as well as uneven rates of uplift and subsidence of the basin floor in an extensional tectonic regime. The amplitude of translation of the unconformity surfaces across the base level attests to collective role of tectonic movement and sea level changes in building the stratigraphic framework of the Valley. The stratigraphic framework and depositional systems, such as fan and fan-deltas, together with local outburst of felsic volcanism further indicate repeated rifting of the craton.Geochronologic data indicate that the rift basin started to open in Early Mesoproterozoic, concomitantly with the breakup of the Mesoproterozoic supercontinent during which the India and East Gondwana fragments were separated. The spatial variation in the declivity of the unconformity surfaces, and the trend of thickness variation of the unconformity-bound sequences point that the basin deepened and opened towards southeast to join an ocean that developed between the South Indian craton and East Antarctica. The contractional deformation structures preserved in several lithounits were produced under NE-SW directed regional compression during Late Neoproterozoic basin inversion.     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

An exact solution of the equation of transfer for coherent scattering in an exponential atmosphere

An exact solution of the transfer equation for coherent scattering in stellar atmospheres with Planck's function as a nonlinear function of optical depth, of the form $$B_v (T) = b_0 + b_1 {\text{ }}e^{ - \beta \tau } $$ is obtained by the method of the Laplace transform and Wiener-Hopf technique.     

Modeling of granular bed‐stone column‐improved soft soil

The present study pertains to the development of a mechanical model for predicting the behavior of granular bed‐stone column‐reinforced soft ground. The granular layer that has been placed over the stone column‐reinforced soft soil has been idealized by the Pasternak shear layer. The saturated soft soil has been idealized by the Kelvin–Voigt model to represent its time‐dependent behavior and the stone columns are idealized by stiffer Winkler springs. The nonlinear behavior of the granular fill has been incorporated in this study by assuming a hyperbolic variation of shear stress with shear strain as in one reported literature. Similarly, for soft soil it has also been assumed that load‐settlement variation is hyperbolic in nature. The effect of consolidation of the soft soil due to inclusion of the stone columns has also been included in the model. Plane‐strain conditions are considered for the loading and foundation soil system. The numerical solutions are obtained by a finite difference scheme and the results are presented in a non‐dimensional form. Parametric studies for a uniformly loaded strip footing have been carried out to show the effects of various parameters on the total as well as differential settlement and stress concentration ratio. It has been observed that the presence of granular bed on the top of the stone columns helps to transfer stress from soil to stone columns and reduces maximum as well as differential settlement. Copyright © 2007 John Wiley & Sons, Ltd.     

Reconnaissance report on geotechnical effects and structural damage caused by the 3 January 2017 Tripura earthquake,India

Natural Hazards - An earthquake of moment magnitude Mw 5.7 shook the northeastern region of India on 3 January 2017 at 14 h:39 min:0.5 s local time. The duration of the...