Degeneracy in one dimension: Role of singular potentials

That the bound energy eigenstates of one-dimensional quantum systems can be degenerate in the presence of specific singular or supersingular potentials is demonstrated by choosing a family of bistable and other oscillators. Relevance of our study to spectroscopic observations is noted. Quasi-degeneracy is found even in the absence of any singularity in the potential and the importance of tunneling is highlighted in this context to analyze the general nature of such potentials leading to double degeneracy. Additionally, the case of spiked oscillators is discussed with particular reference to the “Klauder phenomenon,” revealing clearly that the mere presence of singularity in the potential is not a sufficient criterion for the occurrence of degeneracy. © 1996 John Wiley & Sons, Inc.     

Mössbauer Studies of Nanosize CuFe2O4 Particles

⁵⁷Fe Mössbauer spectra of pulsed-laser deposited (PLD) films of CoFe₂O₄ of 0.3 µm thickness is investigated using transmission geometry is reported. Mössbauer parameters were determined for the tetrahedral (A) and octahedral (B) sites. The PLD processed films gave measurable spectra with no visible evidence of clustering or multiple phases present. Results on the films agreed with those of the bulk material. The films exhibited magnetic hyperfine and quadruple splittings similar to that of bulk CoFe₂O₄. This work demonstrates that measurable transmission Mössbauer spectra may be obtained for PLD deposited CoFe₂O₄ thick films.     

Directly writing with nanoparticles at the nanoscale using dip-pen nanolithography

Well-defined nanostructures were written with quantum dots and magnetic nanoparticles on gold and mica surfaces using dip-pen nanolithography at room temperature. The structures with both the nanoparticles were characterised by in situ topography measurements, and the quantum dot structures were mapped by fluorescence mapping. It is demonstrated that structures of various kinds such as dots and lines can be prepared using such nanoparticles on suitably prepared surfaces.     

Entry distribution, fission barrier, and formation mechanism of 254102No

The entry distribution in angular momentum and excitation energy for the formation of 254No has been measured after the 208Pb(48Ca,2n) reaction at 215 and 219 MeV. This nucleus is populated up to spin 22Planck's over 2pi and excitation energy greater, similar6 MeV above the yrast line, with the half-maximum points of the energy distributions at approximately 5 MeV for spins between 12Planck's over 2pi and 22Planck's over 2pi. This suggests that the fission barrier is greater, similar5 MeV and that the shell-correction energy persists to high spin.     

Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

Phosphinine-Based Ligands in Gold-Catalyzed Reactions

A series of substituted phosphinines, 1-phosphabarrelenes and 5-phosphasemibullvalenes were synthesized and evaluated for their potential application as ligands in homogeneous catalytic reactions. While their buried volume (%V_bur) was calculated to get insight into the steric properties, [LNi(CO)₃] complexes were prepared in order to determine the corresponding Tolman electronic parameter. ETS-NOCV (extended-transition-state natural orbital for chemical valence) calculations on [LAuCl] complexes further allowed an estimation of the σ- and π-contributions to the L− M interaction. Au^I coordination compounds of selected examples were prepared and characterized by single crystal X-ray diffraction. Finally, the three classes of P^III compounds were successfully used in the Au^I-catalyzed cycloisomerization of N-2-propyn-1-ylbenzamide, showing very good activities and selectivities, which are comparable with the reported data of cationic phosphorus-based gold catalysts.     

Anti-resonant reflecting photonic crystal waveguide (ARRPCW): modeling and design

In this paper, we apply an antiresonant reflecting layer concept in photonic crystal based waveguides. We have proposed a thin core ARRPCW with linear waveguide carved in it and hence calculated the transmission spectra for various length of waveguide and have shown that the longer waveguides in ARRPCW yields transmission with significantly high quality factor. Comparison of the transmission characteristics of normal conventional planar ARROW-B waveguides & ARRPCW has also been reported. The 2D FDTD numerical modeling reveals improved transmission for various lengths of planar ARROW and ARRPCW with low losses in long waveguides. Transmittance and quality factor are also calculated to confirm superior performance of the proposed design of ARROW based photonic crystal waveguide.     

When almost Cohen–Macaulay algebras map into big Cohen–Macaulay modules

In this article, we show that almost Cohen–Macaulay algebras are solid. Moreover, we seek for the conditions when (a) an almost Cohen–Macaulay algebra is a phantom extension and (b) when it maps into a balanced big Cohen–Macaulay module.     

A wavelet cross-spectral analysis of solar–ENSO–rainfall connections in the Indian monsoons

The possible connections between the El Nino-Southern Oscillation (ENSO) phenomenon and Indian monsoon rainfall have been widely discussed in the meteorological literature. We show strong statistical evidence here for connections of ENSO with solar activity. This is particularly evident in a comparison between the two contrasting test periods of 1878–1913 and 1933–1964, representing three complete cycles of lowest and highest solar activity respectively since 1850. Wavelet statistical analysis reveals that the link between solar activity and ENSO is generally stronger than that between ENSO and rainfall but only slightly weaker than that between solar activity and rainfall. Over the two test periods an increase in solar activity is associated with a decrease in ENSO indices and an increase in the monsoon rainfall in the 8–16 y period band. In the 2–7 y period band the effects vary with region. The net effect of solar processes on rainfall thus appears to be the result of counteracting or cooperating influences on shorter (about 5–6 y) and longer (about 11–12 y) time scales, the latter on the whole dominating over the former. The present analysis thus suggests that the influence of solar processes on Indian rainfall operates in part indirectly through ENSO, but on more than one time scale.     

Heat transfer in boundary layer stagnation-point flow towards a shrinking sheet with non-uniform heat flux

In this paper, the effect of non-uniform heat flux on heat transfer in boundary layer stagnation-point flow over a shrinking sheet is studied. The variable boundary heat fluxes are considered of two types: direct power-law variation with the distance along the sheet and inverse power-law variation with the distance. The governing partial differential equations (PDEs) are transformed into non linear self-similar ordinary differential equations (ODEs) by similarity transformations, and then those are solved using very efficient shooting method. The direct variation and inverse variation of heat flux along the sheet have completely different effects on the temperature distribution. Moreover, the heat transfer characteristics in the presence of non-uniform heat flux for several values of physical parameters are also found to be interesting.