Volume 58, Issue 3
March 2002, pages 443-574
pp 443-448 March 2002 Research Articles
Korteweg-de Vries hierarchy using the method of base equations
Subhendu Chakrabarti J Pal B Talukdar
A base-equation method is implemented to realize the hereditary algebra of the Korteweg-de Vries (KdV) hierarchy and the N-soliton manifold is reconstructed. The novelty of our approach is that, it can in a rather natural way, predict other nonlinear evolution equations which admit local conservation laws. Significantly enough, base functions themselves are found to provide a basis to regard the KdV-like equations as higher order degenerate bi-Lagrangian systems.
pp 449-456 March 2002 Research Articles
On the generation techniques of axially symmetric stationary metrics
In the present paper, a relationship between the method of Gutsunaev-Manko and the soliton technique (for two-soliton solutions) of Belinskii-Zakharov, for generating solutions of axially symmetric stationary space-times in general relativity is discussed.
pp 457-463 March 2002 Research Articles
Tilted Bianchi type I dust fluid cosmological model in general relativity
In this paper, we have investigated a tilted Bianchi type I cosmological model filled with dust of perfect fluid in general relativity. To get a determinate solution, we have assumed a condition A = B^{n} between metric potentials. The physical and geometrical aspects of the model together with singularity in the model are also discussed.
pp 465-475 March 2002 Research Articles
One-soliton solutions from Laplace’s seed
One-soliton solutions of axially symmetric vacuum Einstein field equations are presented in this paper. Two sets of Laplace’s solutions are used as seed and it is shown that the derived solutions reduce to some already known solutions when the constants are properly adjusted. An analysis of the solutions in terms of the Ernst potential is also presented. It is found that the solutions do not reduce to the Euclidean form at spatial infinity. However, in the static limit, Weyl solutions are obtained for half integral ∂-values.
pp 477-488 March 2002 Research Articles
Invariant metric for nonlinear symplectic maps
Govindan Rangarajan Minita Sachidanand
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we demonstrate that the performance of a nonlinear Hamiltonian system is enhanced.
pp 489-498 March 2002 Research Articles
High spin properties of ^{124}Ba
The ^{124}Ba nucleus is investigated on the basis of the method of statistical mechanics by assuming the nucleons to move in triaxially deformed Nilsson potential. The variation in the Fermi energies of protons and neutrons is studied as a function of spin and temperature. The Fermi energies determined as a function of angular momentum is used to study the dependence of shell correction on angular momentum using the Strutinsky smoothing procedure. The most important observation is that the shell correction is almost the same for all spins for ^{124}Ba. The spin cutoff parameter and the single particle level density parameter are studied as a function of spin and temperature. Constant entropy lines drawn by plotting the excitation energy against angular momentum are found to be roughly at constant energy above the yrast line and are almost equally spaced. It is observed that no yrast traps are present for ^{124}Ba.
pp 499-519 March 2002 Research Articles
RK Singh RK Mohanta R Hippler R Shanker
Development of a new lectron-recoil ion/photon coincidence setup for investigating some of the electron induced collision processes, such as electron bremsstrahlung, electron backscattering, innershell excitation and multiple ionization of target atoms/molecules in bombardment of electrons having energies from 2.0 keV to 30.0 keV with solid and gaseous targets is described. The new features include the use of a compact multipurpose scattering chamber, a time-of-flight spectrometer for detection of multiply charged target ions, a 45°-parallel plate electrostatic analyzer for measuring energy and angle of the ejected electrons, a room temperature high resolution Si-PIN photo diode X-ray detector for counting the collisionally induced photons, a coincidence data acquisition system consisting of a 200 MHz Pentium based 8K-multichannel analyzer and a standard network of a fast/slow coincidence electronics. In particular, the details of design, fabrication and assembly of indigenous components employed in the setup are presented. Selected experiments planned with the setup are mentioned and briefly discussed. A report on performance, optimization, efficiency, time resolution etc. of the time-of-flight (TOF) spectrometer and that of the 45°-parallel plate electrostatic analyzer (PPEA) is presented. Test spectra of electron-recoil ion coincidences, energy distribution of ejected electrons and characteristic plus non-characteristic X-ray spectrum are illustrated to exhibit the satisfactory performance of the developed setup.
pp 521-528 March 2002 Research Articles
Molar extinction coefficients of some carbohydrates in aqueous solutions
K Singh GK Sandhu BS Lark SP Sud
Molar extinction coefficients of some carbohydrates viz. l-arabinose (C_{5}H_{10}O_{5}), d-glucose (C_{6}H_{12}O_{6}), d-mannose (C_{6}H_{12}O_{6}), d-galactose (C_{6}H_{12}O_{6}), d(-) fructose (C_{6}H_{12}O_{6}) and maltose (C_{12}H_{24}O_{12}) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well.
pp 529-536 March 2002 Research Articles
Schwinger variational calculation of ionization of hydrogen atoms for large momentum transfers
Schwinger variational principle is used here to study large momentum transfer cases of electron and positron impact ionization of atomic hydrogen from the ground state at intermediate and moderately high energies. The results appear somewhat better compared to other theories.
pp 537-544 March 2002 Research Articles
Scaling in the bombay stock exchange index
In this paper we study Bombay stock exchange (BSE) index financial time series for fractal and multifractal behaviour. We show that BSE index time series is monofractal and can be represented by a fractional Brownian motion.
pp 545-550 March 2002 Research Articles
Rajesh C Shah S R Tripathi M V Bhat
The squeeze film behaviour between rotating annular plates was analysed theoretically when the curved upper plate with a uniform porous facing approached the impermeable and flat lower plate, considering a magnetic fluid lubricant in the presence of an external magnetic field oblique to the plates. Expressions were obtained for pressure and load capacity; and response time is given by a differential equation. The increases in pressure and load capacity depended only on the magnetization. However, the increase in response time depended on magnetization, fluid inertia and speed of rotation of the plates.
pp 551-561 March 2002 Brief Reports
Semileptonic (Λ_{b} → Λcev) decay in a field theoretic quark model
RK Das AR Panda RK Sahoo MR Swain
The semileptonic decay width of heavy baryons such as (Λ_{b} → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.
pp 563-567 March 2002 Brief Reports
Theoretical study of relative width of photonic band gap for the 3-D dielectric structure
GK Johri Akhilesh Tiwari Saumya Saxena Rajesh Sharma Kuldeep Srivastava Manoj Johri
Calculations for the relative width (Δω/ω_{0}) as a function of refractive index and relative radius of the photonic band gap for the fcc closed packed 3-D dielectric microstructure are reported and comparison of experimental observations and theoretical predictions are given. This work is useful for the understanding of photonic crystals and occurrence of the photonic band gap.
pp 569-574 March 2002 Brief Reports
Photodissociation of NaH using time-dependent fourier grid method
Anindita Bhattacharjee Krishna Rai Dastidar
We have solved the time dependent Schrödinger equation by using the Chebyshev polynomial scheme and Fourier grid Hamiltonian method to calculate the dissociation cross section of NaH molecule by 1-photon absorption from the X^{1}Σ^{+} state to the B^{1}Π state. We have found that the results differ significantly from an earlier calculation [1] although we have used the same set of potential energy curves [2].
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