Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Contents of Volume 2 (2003)

Volume Contents

Contents of Volume 2 (2003)     

Ply-by-Ply Failure Analysis of Laminates Under Dynamic Loading

Ply-by-ply failure analysis of symmetric and anti-symmetric laminates under uniform sinusoidal transverse dynamic loading is performed for a specified duration. The study investigates the first ply failure load, followed by the detection of successive ply failures along with their failure modes using various failure theories. Some of the well-established failure theories, mostly used by the researchers, are considered for the failure prediction in laminates. The finite element computational model based on higher order shear deformation displacement field is used for the failure analysis and the complete methodology is computer coded using FORTRAN. The ply-discount stiffness reduction scheme is employed to modify the material properties of the failed lamina. The failure theories used in the analysis are compared according to their ability to predict failure load, failed ply, failure mode and progression of failure. The failure analysis is performed for both the cross-ply and angle-ply laminates with all edges simply supported and clamped. The significance of fibre orientation and stacking sequence in terms of the strength of a laminate and failure progression is also highlighted.     

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated(cigar shaped)confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.     

One-body nuclear friction

We have calculated the velocity dependent forces acting between two nuclei that arise due to one-body mechanism of nuclear excitation when they are dragged against one another with constant velocity. The nuclear friction coefficients are then extracted from the velocity dependence of these forces which is found to be strongly linear. The one-body force is calculated by solving the time-dependent Schrödinger equation for all the occupied single-particle states of a nuclear system in a central collision. Each nucleus in this model is assumed to be described by a single-particle Woods-Saxon potential filled with 40 nucleons each. The magnitude of the resulting one-body friction is found to be in between the proximity and surface frictions. The proximity-friction is too small by about an order of magnitude. To check this result, we calculated the one-sided flux from one nucleus to the other. The friction force connected to this flux (i.e. the one-body exchange friction) turns out to be about half or less than the one body friction. We conclude that theproximity-friction grossly underestimates the one-body exchange friction. Furthermore,inelastic excitations are at least as important for one-body dissipation at distances beyond the touching point as is particle exchange.     

0+ analogue state in 118Sb from 117Sn(p,nγ) reaction

The analogue of the 0⁺ ground state in ¹¹⁸Sn has been observed in the compound nucleus ¹¹⁸Sb through ¹¹⁷Sn(p,n γ) ¹¹⁷Sb reaction. The neutron decays of this analogue resonance have been studied from the deexciting γ-rays of the residual nucleus ¹¹⁷Sb. From off resonance excitation functions, spin assignments have been made to states in ¹¹⁷Sb, on the basis of Hauser-Feshbach formalism. The resonance parameters of the isobaric analogue resonance have been determined, including the total, proton and neutron decay widths.     

Order–disorder transition in nanocrystalline Ni3Al prepared by a chemical route

Ni₃Al alloys of nanometer dimensions in the range 10–38 nm could be synthesized by reaction sintering of sol–gel-derived Ni/SiO₂ nanocomposite and commercially available micrometer-sized aluminum powder. The sintering was carried out at a temperature of 923 K and a pressure of 2.4 MPa. By a suitable choice of sintering conditions a disordered phase of Ni₃Al was stabilized. The disordered phase could be converted to an ordered one by an increase of heat treatment temperature.     

Ionic composition of a humid air plasma under ionizing radiation

A kinetic model is proposed for ion–molecular processes involving charged particles of a humid air plasma produced by a fast electron beam. The model includes more than 600 processes involving electrons and 41 positive and 14 negative ions, including hydrated ions H₃O⁺ (H₂O) _n and O ₂ ^? (H₂O) _n with n = 1, 2, …, 12. The energy costs of production of electron–ion pairs and electronic and vibrational (for water molecules, also rotational) excitation of molecules are calculated in nitrogen, oxygen, water vapor, air, and humid air. A method is proposed for calculating the energy costs in mixtures by the calculation data in pure gases. The evolution of the plasma composition is studied by the numerical solution of a system of 56 time-dependent balance equations for the number of charged particles of plasma by the fourth-order Runge–Kutta method. The steady-state composition of plasma is determined by solving nonlinear steady-state balance equations for the ionization rates of humid air from 10 to 10¹⁶ cm^–3/s and the fraction of water molecules from 10^–3% to 1.5%. It is established that, for water vapor content (the ratio of the number density of water molecules to the total number density of air molecules) of 0.015–1.5% in air at atmospheric pressure and room temperature, the main ion species are two types of positive ions H₃O⁺ (H₂O) _n with the number of water molecules n = 5, 6 and three species of negative ions O ₂ ^? (H₂O) _n with n = 5, 8, 9.     

Derivation of muon spectrum at high energies from the recent JACEE primary cosmic-ray spectrum using Fermilab data on meson production

Summary The energy spectrum of sea level muons in the range (10²÷10⁴) GeV has been calculated from the latest directly measured JACEE primary spectrum using Fermilab results on pp→π^± X and pp→K^± X inclusive reactions. The conventional pion atmospheric diffusion equation after Bugaevet al. has been used in this analysis to account the flux of muons emerged from the multiple generation of mesons in air. The derived muon spectrum has been compared with the earlier magnetic spectrograph data of Durham and Kiel groups. The latest BAKSAN scintillator telescope data is well in agreement with the calculated integral spectrum originated from the meson decays in the range (1÷10⁴) GeV.     

Design of a highly sensitive photonic crystal waveguide platform for refractive index based biosensing

In this paper, a photonic crystal waveguide platform on silicon-on-insulator substrate is proposed in order to realize a highly sensitive refractive index based biosensor. Following the design, the analysis of the sensor structure are made by using the three dimensional Finite Difference Time Domain method. The principle of sensing is based on the change in refractive index, which in turn changes the output spectrum of the waveguide. Results show that the sensitivity of the sensor depends mainly on the geometrical properties of the defect region of the photonic crystal structure. The phenomenon is verified for various samples having refractive index ranging from 1 (air) to 1.57 (Bovine serum albumin). Further, the structure is compared with few other conventional photonic crystal waveguide designs to analyze the sensing performance. The estimated value of sensitivity of the sensor is found to be 260 nm/RIU with a detection limit of 0.001 RIU. This high sensitivity can enhance the performance of low-concentration analytes detection.