A Sixth-order P-stable Symmetric Multistep Method for Periodic Initial-value Problems of Second-order Differential Equations

A sixth-order P-stable symmetric multistep method for periodicinitial-value problem y = f(x, y) is suggested. It requiresthree function evaluations per iteration. The method can beconsidered as a stabilized modification of Lambert and Watson'ssixth-order implicit method which has a finite interval of periodicity.The method is illustrated for three numerical examples.     

Effect of isospin-dependent cross-section on fragment production in the collision of charge asymmetric nuclei

To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin-dependent quantum molecular dynamics model. Here simulations have been carried out for $^{124}{\rm X}_{n}+^{124}{\rm X}_{n}$ , where n varies from 47 to 59 and for $^{40}{\rm Y}_{m}+^{40}{\rm Y}_{m}$ , where m varies from 14 to 23. Our study shows that isospin-dependent cross-section shows its influence on fragmentation in the collision of neutron-rich nuclei.     

Einstein A Coefficients,Oscillator Strengths,and Absolute Band Strengths for the First Negative System,and Franck-Condon Factors for the Second Negative System of

The Franck-Condon factors and r centroids for the first negative and the second negative band systems of the molecule, based on the Rydberg-Klein-Rees potential energy curves, have been computed. The variation of the electronic transition moment with the internuclear separation has been studied for the first negative bands and the Einstein A coefficients, the oscillator strengths, and the absolute band strengths for this system have been calculated by adopting the recent experimental data on the lifetimes of the various levels of the excited B state. On a calculé pour la molécule les facteurs de Franck-Condon et les r centroïds pour les deux premiers systèmes de bandes négatives avec des courbes de potential de Rydberg-Klein-Rees. On a étudié la variation du moment de transition éléctronique avec la séparation internucléaire pour les premières bandes négatives. Les constantes A d'Einstein, les forces d'oscillateur et les intensités absolues des bandes ont été calculé des données expérimentales récentes sur les durées de vie des niveaux différents de l'état excité B . Die Franck-Condon-Faktoren und die r-Zentroide der zwei ersten negativen Banden-systeme des -Moleküls, wurden mit den Rydberg-Klein-kees Potentialkurven berechnet. Die Variation des elektronischen Übergangsmoment mit dem Kernabstand würde für die ersten negativen Bänder studiert. Die Einsteinschen A-Koeffizienten, die Oszillatorstärken and die absoluten Bandenstärken wurden mit die neuen experimentellen Tatsachen über die Lebensdauern der verschiedenen Niveaus des angeregten B Zustands berechnet.     

Efficient delivery of 60 J pulse energy of long pulse Nd:YAG laser through 200 μm core diameter optical fibre

Most of today’s industrial Nd:YAG lasers use fibre-optic beam delivery. In such lasers, fibre core diameter is an important consideration in deploying a beam delivery system. Using a smaller core diameter fibre allows higher irradiances at focus position, less degradation of beam quality, and a larger stand-off distance. In this work, we have put efforts to efficiently deliver the laser output of ‘ceramic reflector’-based long pulse Nd:YAG laser through a 200 μm core diameter optical fibre and successfully delivered up to 60 J of pulse energy with 90% transmission efficiency, using a GRADIUM (axial gradient) plano-convex lens to sharply focus down the beam on the end face of the optical fibre and fibre end faces have been cleaved to achieve higher surface damage thresholds.     

Optimum Runge-Kutta-Fehlberg Methods for Second-order Differential Equations

^* Presently at Deparment of Mathematics, Indian Institute of Technology, Madras, India. The optimum Runge-Kutta method of a particular order is theone whose truncation error is minimum. In this paper, we havederived optimum Runge-Kutta mehtods of 0(h^m+4), 0(h^m+5) and0(h^m+6) for m = 0(1)8, which can be directly used for solvingthe second order differential equation yⁿ = f(x, y, y'). Thesemethods are based on a transformation similar to that of Fehlbergand require two, three and four evaluations of f(x, y, y') respectively,for each step. The numercial solutions of one example obtainedwith these methods are given. It has been assumed that f(x,y, y')is sufficiently differentiable in the entire region ofintegration.     

Solar diurnal anisotropy measured using muons in GRAPES-3 experiment in 2006

The GRAPES-3 experiment at Ooty contains a large-area (560 m²) tracking muon detector. This detector consists of 16 modules, each 35 m² in area, that are grouped into four supermodules of 140 m² each. The threshold energy of muons is sec(θ) GeV along a direction with zenith angle θ and the angular resolution of the muon detector is 6°. Typically, it records ~4×10⁹ muons every day. The muon detector has been operating uninterruptedly since 2001, thus providing a high statistics record of the cosmic ray flux as a function of time over one decade. However, prior to using these data, the muon rate has to be corrected for two important atmospheric effects, namely, variations in atmospheric pressure and temperature. Because of the near equatorial location of Ooty (11.4°N), the seasonal variations in the atmospheric temperature are relatively small and shall be ignored here. Due to proximity to the equator, the pressure changes at Ooty display a dominant 12 h periodic behaviour in addition to other seasonal changes. Here, we discuss various aspects of a novel method for accurate pressure measurement and subsequent corrections applied to the GRAPES-3 muon data to correct these pressure-induced variations. The pressure-corrected muon data are used to measure the profile of the solar diurnal anisotropy during 2006. The data, when divided into four segments, display significant variation both in the amplitude (~45%) and phase (~42 m) of the solar diurnal anisotropy during 2006, which was a period of relatively low solar activity.