Volume 54, Issue 2
February 2000, pages 215-330 and L331-L336
pp 215-225 February 2000 Research Articles
Static charged spheres with anisotropic pressure in general relativity
J Krishna Rao M Annapurna MM Trivedi
We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r^{2}, u=4πξr^{2}, v_{r}=4πp_{r}r^{2}, v_{⊥}=4πp_{⊥}r^{2}[ρ, ξ(=−(1/2)F_{14}F^{14}), p_{r}, p_{⊥} being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v_{r}=(a^{2}/2κ)r^{n+2}, v_{⊥}=k_{1}v_{r}, w=k_{2}v_{r}; a^{2}, n(>0), k_{1}, k_{2} being constants with κ=((k_{1}+2)/3+k_{2}) and (ii) w+u=(b^{2}/2)r^{n+2}, u=v_{r}, v_{⊥}−v_{r}=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r^{2} since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary.
pp 227-234 February 2000 Research Articles
Λ_{b}→Λ_{c}+a_{1} decay in the heavy quark effective theory
Using the heavy quark approximation, we have studied the nonleptonic decay mode Λ_{b}→Λ_{c}a_{1}. We have included nonfactorizable contributions as well as factorizable ones in our analysis. The estimated branching ratio for this process is (1.4±0.1)% and the asymmetry parameter α found to be −0.8.
pp 235-246 February 2000 Research Articles
Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets
N Nimai Singh S Biramani Singh
Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefficients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD-QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the unification of top-b-τ Yukawa couplings at the scale M_{1}=0.59×10^{8} GeV for a fixed value of tan β=58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of M_{1}=0.59×10^{11} GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.
pp 247-253 February 2000 Research Articles
Skyrme-Hartree-Fock approach to the change of level occupancy of low mass halo nuclei
With a new parameterization of potential parameters which reproduces the ground state properties of shell closed nuclei fairly accurately, the role of occupancy of 2s_{1/2} level in determining the halo structures of ^{17}O, ^{16}N, ^{15}C, ^{14}B, ^{13}Be have been investigated. The results show interesting cross over of level occupancies which may explain the increase in interaction radii.
pp 255-267 February 2000 Research Articles
Estimation of light transport parameters in biological media using coherent backscattering
S Anantha Ramakrishna K Divakara Rao
The suitability of using the angular peak shape of the coherent backscattered light for estimating the light transport parameters of biological media has been investigated. Milk and methylene blue doped milk were used as tissue phantoms for the measurements carried out with a He-Ne laser (632.8 nm). Results indicate that while the technique accurately estimates the transport length, it can determine the absorption coefficient only when the absorption is moderately high (α>1 cm^{−1}) for the long transport lengths typical of tissues. Further, the possibility of determining the anisotropy factor by estimating the single scattering contribution to the diffuse background is examined.
pp 269-274 February 2000 Research Articles
A comparison between spatial burning in the semiclassical theory of laser and the intensity contours of the fringes due to multiple reflections in a Fabry-Perot cavity is presented. The concept of spatial hole burning is also used in a quantum well system.
pp 275-285 February 2000 Research Articles
Nonlinear wave propagation through a ferromagnet with damping in (2+1) dimensions
We investigate how dissipation and nonlinearity can affect the electromagnetic wave propagating through a saturated ferromagnet in the presence of an external magnetic field in (2+1) dimensions. The propagation of electromagnetic waves through a ferromagnet under an external magnetic field in the presence of dissipative effect has been studied using reductive perturbation method. It is found that to the lowest order of perturbation the system of equations for the electromagnetic waves in a ferromagnet can be reduced to an integro-differential equation.
pp 287-303 February 2000 Research Articles
Correlation between deformation bleaching and mechanoluminescence in coloured alkali halide crystals
B P Chandra M Ramrakhiani P Sahu A M Rastogi
The present paper reports the correlation between deformation bleaching of coloration and mechanoluminescence (ML) in coloured alkali halide crystals. When the F-centre electrons captured by moving dislocations are picked up by holes, deep traps and other compatible traps, then deformation bleaching occurs. At the same time, radiative recombination of dislocation captured electrons with the holes gives rise to the mechanoluminescence. Expressions are derived for the strain dependence of the density of colour centres in deformed crystals and also for the number of colour centres bleached. So far as strain, temperature, density of colour centres, E_{a} and volume dependence are concerned, there exists a correlation between the deformation bleaching and ML in coloured alkali halide crystals. From the strain dependence of the density of colour centres in deformed crystals, the value of coefficient of deformation bleaching D is determined and it is found to be 1.93 and 2.00 for KCl and KBr crystals, respectively. The value of (D+χ) is determined from the strain dependence of the ML intensity and it is found to be 2.6 and 3.7 for KCl and KBr crystals, respectively. This gives the value of coefficient of deformation generated compatible traps χ to be 0.67 and 1.7 for KCl and KBr crystals, respectively.
pp 305-315 February 2000 Research Articles
The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.
pp 317-330 February 2000 Research Articles
Role of vanadium in Bi-2223 ceramics
D R Mishra S V Sharma R G Sharma
The effect of substitution of vanadium in Bi_{1.6}Pb_{0.4}Sr_{2}Ca_{2}Cu_{3} O_{δ} ceramic at Bi and Cu sites has been investigated for the resistivity, a.c. susceptibility, XRD and a.c. magnetization studies. Enhancement in T_{c} for the smaller concentrations of V at either of the two sites was observed which followed an expected lattice distortion and decrease in T_{c} for higher V concentrations. V plays a role of substituting element more than just a sintering agent as reflected in the more rapid decrease in T_{c} at Cu-site and further in the magnetization values that are higher compared to the values at the Bi-site. It indicates higher magnetization scattering at the Cu site. The results were explained keeping in mind the liquid phase mechanism behind the formation of the 2223 phase and the possibility of magnetic scattering.
pp L331-L336 February 2000 Rapid Communication
A simpler and elegant algorithm for computing fractal dimension in higher dimensional state space
S Ghorui A K Das N Venkatramani
Chaotic systems are now frequently encountered in almost all branches of sciences. Dimension of such systems provides an important measure for easy characterization of dynamics of the systems. Conventional algorithms for computing dimension of such systems in higher dimensional state space face an unavoidable problem of enormous storage requirement. Here we present an algorithm, which uses a simple but very powerful technique and faces no problem in computing dimension in higher dimensional state space. The unique indexing technique of hypercubes, used in this algorithm, provides a clever means to drastically reduce the requirement of storage. It is shown that theoretically this algorithm faces no problem in computing capacity dimension in any dimension of the embedding state space as far as the actual dimension of the attractor is ﬁnite. Unlike the existing algorithms, memory requirement offered by this algorithm depends only on the actual dimension of the attractor and has no explicit dependence on the number of data points considered.
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