• Volume 69, Issue 3

September 2007,   pages  317-490

• Ray space `Riccati' evolution and geometric phases for 𝑁-level quantum systems

We present a simple derivation of the matrix Riccati equations governing the reduced dynamics as one descends from the group $\mathbb{U}(N)$ describing the Schrõdinger evolution of an 𝑁-level quantum system to the various coset spaces and Grassmanian manifolds associated with it. The special case pertaining to the geometric phase in 𝑁-level systems is described in detail. Further, we show how the matrix Riccati equation thus obtained can be reformulated as an equation describing Hamiltonian evolution in a classical phase space and establish correspondences between the two descriptions.

• Quality of potential harmonics expansion method for dilute Bose–Einstein condensate

We present and examine an approximate but ab initio many-body approach, viz., potential harmonics expansion method (PHEM), which includes two-body correlations for dilute Bose–Einstein condensates. Comparing the total ground state energy for three trapped interacting bosons calculated in PHEM with the exact energy, the new method is shown to be very good in the low density limit which is necessary for achieving Bose–Einstein condensation experimentally.

• Generalization of quasi-exactly solvable and isospectral potentials

A uniﬁed approach in the light of supersymmetric quantum mechanics (SSQM) has been suggested for generating multidimensional quasi-exactly solvable (QES) potentials. This method provides a convenient means to construct isospectral potentials of derived potentials.

• Beta-transition properties for neutron-rich Sn and Te isotopes by Pyatov method

Based on Pyatov's method, the low-lying Gamow–Teller (GT) 1+ state energies and log($f_{t}$) values for 128,130,132Sb and 132,134,136I isotopes have been calculated. In this method, the strength parameter of the effective spin–isospin interaction is found by providing the commutativity of the GT operator with the central part of the nuclear Hamiltonian. The problem has been solved within the framework of RPA. The calculation results have been compared with the corresponding experimental data.

• Background neutron in the endcap and barrel regions of resistive plate chamber for compact muon solenoid/large hadron collider using GEANT4

In this study the performance of double gap RPC has been tested by GEANT4 Monte Carlo simulation code. The detector response calculations taken as a function of the neutron energy in the range of 0.01 eV–1 GeV have been simulated through RPC set-up. In order to evaluate the response of detector in the LHC background environment, the neutron spectrum expected in the CMS muon endcap and barrel region were taken into account. A hit rate of about 165.5 Hz cm-2, 34 Hz cm-2, 33.6 Hz cm-2, and 27.0 Hz cm-2 due to an isotropic neutron source is calculated using GEANT4 standard electromagnetic package for a $20 \times 20$ cm2 RPC in the ME1, ME2, ME3 and ME4, respectively. While for the same neutron source and using GEANT4 package a hit rate of about 0.42 Hz cm-2, 0.7182 Hz cm-2 was measured for the MB1 and MB4 stations respectively. Similar characteristics of hit rates have been observed for GEANT4 low electromagnetic package.

• Computation of triple differential cross-sections with the inclusion of exchange effects in atomic K-shell ionization by relativistic electrons for symmetric geometry

The triple differential cross-section for K-shell ionization of silver and copper atoms by relativistic electrons have been computed in the coplanar symmetric geometry with the inclusion of exchange effects following the multiple scattering theory of Das and Seal [1] multiplied by suitable spinors. Present computed results are marginally improved in some cases from the previous computed results [2]. Present results are compared with measured values [3] and with previous computation results [2]. Some other theoretical computational results are also presented here for comparison.

• Optical parametric amplification beyond the slowly varying amplitude approximation

The coupled-wave equations describing optical parametric amplification (OPA) are usually solved in the slowly varying amplitude (SVA) approximation regime, in which the second-order derivatives of the signal and idler amplitudes are ignored and in fact the electromagnetic effects due to exit face of the medium is not involved. Here, an analytical plane-wave solution of these coupled-wave equations in a non-absorbing medium is presented. The solutions are derived beyond the SVA approximation up to order of $\kappa = k$ (coupling constant over the wave number). The intensity distributions of the signal and the idler waves show a periodic behavior about their corresponding distributions of SVA-adapted solution. This behavior can be explained by the interference of the forward propagating signal (idler) wave and the corresponding backward one resulted from the reflection by the end face of the medium. Furthermore, this interference pattern in the medium can in turn serve as a periodic source for the next generations of the signal and idler waves. Therefore, the superposition of the waves, generated from different points of this periodic source, at the exit face of the medium shows an oscillatory behavior of the transmitted signal (idler) wave in terms of normalized coupling constant, $\kappa L$. This study also shows that this effect is more considerable for high intensity pump beam, high relative refractive index and short length of the nonlinear medium.

• Analytical prediction of forced convective heat transfer of ﬂuids embedded with nanostructured materials (nanoﬂuids)

Nanoﬂuids are a new class of heat transfer ﬂuids developed by suspending nanosized solid particles in liquids. Larger thermal conductivity of solid particles compared to the base ﬂuid such as water, ethylene glycol, engine oil etc. signiﬁcantly enhances their thermal properties. Several phenomenological models have been proposed to explain the anomalous heat transfer enhancement in nanoﬂuids. This paper presents a systematic literature survey to exploit the characteristics of nanoﬂuids, viz., thermal conductivity, speciﬁc heat and other thermal properties. An empirical correlation for the thermal conductivity of Al2O3 + water and Cu + water nanoﬂuids, considering the effects of temperature, volume fraction and size of the nanoparticle is developed and presented. A correlation for the evaluation of Nusselt number is also developed and presented and compared in graphical form. This enhanced thermophysical and heat transfer characteristics make ﬂuids embedded with nanomaterials as excellent candidates for future applications.

• Gauss law constraints on Debye–Hückel screening

We demand that the Gauss law at the edge must be obeyed by the electric potential $\phi(r)$ generated within a neutral plasma/electrolyte of strictly ﬁnite size by the introduction of a test charge $q_{b}$. Our proposal has the nice features that total ionic numbers are conserved, the point-Coulomb behaviour of $\phi(r)$ is guaranteed at short-distance, and accumulation of induced charges near the centre and the surface can be demonstrated rigorously. In contrast, the standard Debye–Hückel potential $\phi_{D}(r)$ applicable to unbounded plasma has the strange features that the Gauss law cannot be obeyed at the plasma's edge, total ionic numbers themselves are altered, the short-distance Coulomb behaviour has to be imposed by hand, and induced charge appearance at the surface cannot be built-in.

• Variation of long periodicity in blends of styrene butadiene, styrene copolymer/polyaniline using small angle X-ray scattering data

Small angle X-ray scattering data have been recorded for the blends of styrene butadiene, styrene copolymer/polyaniline using the beamline of the LNLS (Laboratorio Nacional de Luz sincroton-Campinas, Brazil). Employing one-dimensional Hosemann's paracrystalline model, we have simulated the meridional reﬂections of these blends in order to compute the long periodicity and hence to ﬁnd the variation with concentrations of the blends. Within the region of available experimental data we observe that there is a linear relationship between long periodicity and concentration of blends. These parameters are compared with physical measurements like tensile strength to ﬁnd the structure–property relation in these blends.

• Temperature variation of higher-order elastic constants of MgO

An effort has been made for obtaining higher-order elastic constants for MgO starting from basic parameters, viz. nearest-neighbor distance and hardness parameter using Coulomb and Börn–Mayer potentials. These are calculated in a wide temperature range (100–1000 K) and compared with available theoretical and experimental results.

• Electron paramagnetic resonance parameters and local structure for Gd3+ in KY3F10

The electron paramagnetic resonance parameters, zero-ﬁeld splittings (ZFSs) b$_{2}^{0}$, b$_{4}^{0}$, b$_{4}^{4}$, b$_{6}^{0}$, b$_{6}^{4}$ and the 𝑔 factors for Gd3+ on the tetragonal Y3+ site in KY3F10 are theoretically studied from the superposition model for the ZFSs and the approximation formula for the 𝑔 factor containing the admixture of the ground 8S$_{7/2}$ and the excited 6L$_{7/2}$ (L=P, D, F, G) states via the spin–orbit coupling interactions, respectively. By analysing the above ZFSs, the local structure information for the impurity Gd3+ is obtained, i.e., the impurity–ligand bonding angles related to the four-fold (C4) axis for the impurity Gd3+ center are found to be about $0.6^{\circ}$ larger than those for the host Y3+ site in KY3F10. The calculated ZFSs based on the above angular distortion as well as the 𝑔 factors are in reasonable agreement with the observed values. The present studies on the ZFSs and the local structure would be helpful to understand the optical and magnetic properties of this material with Gd dopants.

• Energy resolution methods efficiency depending on beam source position of potassium clusters in time-of-ﬂight mass spectrometer

Energy resolution of the time-of-ﬂight mass spectrometer was considered. The estimations indicate that the time-lag energy focusing method provides better resolution for the parallel case while the turnaround time is more convenient for the perpendicular position. Hence the applicability of the methods used for the energy resolution depends on beam source arrangement.

• Role of polyvinyl alcohol in the conductivity behaviour of polyethylene glycol-based composite gel electrolytes

An attempt has been made in the present work to combine gel and composite polymer electrolyte routes together to form a composite polymeric gel electrolyte that is expected to possess high ionic conductivity with good mechanical integrity. Polyethylene glycol (PEG) based composite gel electrolytes using polyvinyl alcohol (PVA) as guest polymer have been synthesized with 1 molar solution of ammonium thiocyanate (NH4SCN) in dimethyl sulphoxide (DMSO) and electrically characterized. The ionic conductivity measurements indicate that PEG : PVA : NH4SCN-based composite gel electrolytes are superior ($\sigma_{\text{max}} = 5.7 \times 10^{−2}$ S cm-1) to pristine electrolytes (PEG : NH4SCN system) and conductivity variation with ﬁller concentration remains within an order of magnitude. The observed conductivity maxima have been correlated to PEG : PVA : NH4SCN- and PVA : NH4SCN-type complexes. Temperature dependence of conductivity proﬁles exhibits Arrhenius behaviour in low temperature regime followed by VTF character at higher temperature.

• Lifetime measurement of some excited states belonging to the 3p4nd ($n = 4–6$) conﬁgurationof ArII

The radiative lifetimes of eight levels belonging to the 3p4nd ($n = 4–6$) conﬁguration of ArII have been measured using high frequency deﬂection technique together with a delayed coincidence single photon counting arrangement. Lifetimes of some of the levels have been measured for the ﬁrst time. The results have been compared with other experimental and theoretical values.

• Photoacoustic spectroscopy of thin ﬁlms of As2S3, As2Se3 and GeSe2

Photoacoustic spectroscopy (PAS) is one of the important branches of spectroscopy, which enables one to detect light-induced heat production following the absorption of pulsed radiation by the sample. As2S3, As2Se3 and GeSe2 exhibit a wide variety of photo-induced phenomena that enable them to be used as optical imaging or storage medium and various electronic devices, including electro-optic information storage devices and optical mass memories. Therefore, accurate measurement of thermal properties of semiconducting ﬁlms is necessary to study the memory density. The thermal conductivity of thin ﬁlms of As2S3 (thickness 100 𝜇m and 80 𝜇m), As2Se3 (thickness 100 𝜇m and 80 𝜇m) and GeSe2 (thickness 120 𝜇m and 100 𝜇m) has been measured using PAS technique. Our result shows that the thermal conductivity of thicker ﬁlms is larger than the thinner ﬁlms. This can be explained by the thermal resistance effect between the ﬁlm and the surface of the substrate.

• Electrical conduction mechanism of polyvinyl chloride (PVC)–polymethyl methacrylate (PMMA) blend ﬁlm

The electrical conduction mechanism in polyvinyl chloride (PVC)–polymethyl methacrylate (PMMA) blend ﬁlm has been studied at various temperatures in the range 313 K to 353 K. The results are presented in the form of $I–V$ characteristics. Analysis has been made in the light of Poole–Frenkel, Fowler–Nordheim, Schottky, log(𝐽) vs. 𝑇 plots and Arrhenius plots. It is observed that, Schottky–Richardson mechanism is primarily responsible for the observed conduction.

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