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.     

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.     

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.     

Nonplanar ion-acoustic Gardner solitons in a pair-ion plasma with nonextensive electrons and positrons

The properties of nonplanar (cylindrical and spherical) ion-acoustic solitary waves (IA SWs) in an unmagnetized, collisionless electron-positron-ion (e-p-i) plasma, whose constituents are q-distributed electrons and positrons and inertial ions, are investigated by deriving the modified Gardner (MG) equation. The well known reductive perturbation method is employed to derive the MG equation. The basic features of nonplanar IA Gardner solitons (GSs) are discussed. It is found that the properties of nonplanar IA GSs (rarefactive and compressive) are significantly affected by the particle nonextensivity.     

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.     

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

In this paper we obtain similarity solutions for the propagation of plane relativistic shock waves in the presence of a transverse magnetic field for the medium, where the nucleon number density obeys a power law of distance from the plane of explosion. 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.     

Trends in major and minor meteorological variables and their influence on reference evapotranspiration for mid Himalayan region at east Sikkim,India

Estimation of evapotranspiration(ET) for mountain ecosystem is of absolute importance since it serves as an important component in balancing the hydrologic cycle.The present study evaluates the performance of original and location specific calibrated Hargreaves equation(HARG) with the estimates of Food and Agricultural Organization(FAO)Penman Monteith(PM) method for higher altitudes in East Sikkim,India.The results show that the uncalibrated HARG model underestimates ET_0 by 0.35 mm day~(-1) whereas the results are significantly improved by regional calibration of the model.In addition,this paper also presents the variability in the trajectory associated with the climatic variables with the changing climate in the study site.Nonparametric Mann-Kendall(MK) test was used to investigate and understand the mean monthly trendof eight climatic parameters including reference evapotranspiration(ET_0) for the period of 1985-2009.Trend of ET_0 was estimated for the calculations done by FAO PM equation.The outcomes of the trend analysis show significant increasing(p ≤ 0.05) trend represented by higher Z-values,through MK test,for net radiation(Rn),maximum temperature(Tmax) and minimum temperature(Tmin),especially in the first months of the year.Whereas,significant(0.01 ≥ p ≤0.05) decreasing trend in vapor pressure deficit(VPD)and precipitation(P) is observed throughout the year.Declining trend in sunshine duration,VPD and ET_0 is found in spring(March- May) and monsoon(June –November) season.The result displays significant(0.01≤ p ≤ 0.05) decreasing ET_0 trend between(June- December) except in July,exhibiting the positive relation with VPD followed by sunshine duration at the station.Overall,the study emphasizes the importance of trend analysis of ET_0 and other climaticvariables for efficient planning and managing the agricultural practices,in identifying the changes in the meteorological parameters and to accurately assess the hydrologic water balance of the hilly regions.     

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).     

Numerical simulation by a stretched-coordinate Ocean General Circulation Model: A preliminary results

Summary ?A three-dimensional Ocean General Circulation Model has been developed in stretched coordinate from scratch. The same model has been used to perform some numerical experiments to simulate the basic circulation pattern and the model variability to atmospheric forcing. For numerical simulations 72 × 25 grid points in the horizontal directions and nine (10, 30, 75, 250, 500, 1000, 1500, 2000 and 3000 m) vertical levels are considered. The lateral boundaries are set at 60° N and 60° S. The basic focus of the paper is on the demonstration of the performance of the model and its assessment by employing appropriate forcing from the outputs of an atmospheric general circulation model. Hence, the model was forced with the forcing (wind and thermodynamic) derived from the ECMWF runs from the AMIP archives. The preliminary results show the realistic simulation of basic pattern of different fields. The model simulations show that the model is able to reproduce some of the general features of the ocean, such as surface currents, surface temperature and salinity, mass transport and meridional heat transport. It is also to be noted that the model is capable to capture the El-Ni?o and La-Ni?a type events. Received April 3, 2002; revised June 6, 2002; accepted July 24, 2002 Published online: February 20, 2003