A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs

Characteristic polynomial coefficients of three classes of graph, namely L_n + n(p), C_n + n(p) and K _1,n-1 + n(p), which are known to have reciprocal pairs of eigenvalues, have been shown to be generated by simple manipulation of the Pascal's triangle.     

A comparative study on dual colour soft aperture cascaded second-order mode-locking with different nonlinear optical crystals

A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.     

Elastic scattering and fusion cross-sections in 7Li + 27Al reaction

With an aim to understand the effects of breakup and transfer channels on elastic scattering and fusion cross-sections in the ⁷Li + ²⁷Al reaction, simultaneous measurement of elastic scattering angular distributions and fusion cross-sections have been carried out at various energies (E _lab?=?8.0–16.0 MeV) around the Coulomb barrier. Optical model (OM) analysis of the elastic scattering data does not show any threshold anomaly or breakup threshold anomaly behaviour in the energy dependence of the real and imaginary parts of the OM potential. Fusion cross-section at each bombarding energy is extracted from the measured α-particle evaporation energy spectra at backward angles by comparing with the statistical model prediction. Results on fusion cross-sections from the present measurements along with data from the literature have been compared with the coupled-channels predictions. Detailed coupled-channels calculations have been carried out to study the effect of coupling of breakup, inelastic and transfer, channels on elastic scattering and fusion. The effect of 1n-stripping transfer coupling was found to be significant compared to that of the projectile breakup couplings in the present system.     

Plasma response to transient high voltage pulses

This review reports on plasma response to transient high voltage pulses in a low pressure unmagnetized plasma. Mainly, the experiments are reviewed, when a disc electrode (metallic and dielectric) is biased pulsed negative or positive. The main aim is to review the electron loss in plasmas and particle balance during the negative pulse electrode biasing, when the applied pulse width is less than the ion plasma period. Though the applied pulse width is less than the ion plasma period, ion rarefaction waves are excited. The solitary electron holes are reviewed for positive pulsed bias to the electrode. Also the excitation of waves (solitary electron and ion holes) is reviewed for a metallic electrode covered by a dielectric material. The wave excitation during and after the pulse withdrawal, excitation and propagation characteristics of various electrostatic plasma waves are reviewed here.     

Nuclear structure of 216 Ra at high spin

High-spin states of ²¹⁶Ra ( $\emph{Z}=88$ , $\emph{N}=128$ ) have been investigated through ²⁰⁹Bi(¹⁰B, 3n) reaction at an incident beam energy of 55?MeV and ²⁰⁹Bi(¹¹B, 4n) reaction at incident beam energies ranging from 65 to 78?MeV. Based on ??? coincidence data, the level scheme for ²¹⁶Ra has been considerably extended up to ~ 33 $\hbar$ spin and 7.2 MeV excitation energy in the present experiment with placement of 28 new ??-transitions over what has been reported earlier. Tentative spin-parity assignments are done for the newly proposed levels on the basis of the DCO ratios corresponding to strong gates. Empirical shell model calculations were carried out to provide an understanding of the underlying nuclear structure.     

Statistical analysis of the road network of India

In this paper we study the Indian highway network as a complex network where the junction points are considered as nodes, and the links are formed by an existing connection. We explore the topological properties and community structure of the network. We observe that the Indian highway network displays small-world properties and is assortative in nature. We also identify the most important road-junctions (or cities) in the highway network based on the betweenness centrality of the node. This could help in identifying the potential congestion points in the network. Our study is of practical importance and could provide a novel approach to reduce congestion and improve the performance of the highway network.     

Decay of Hoyle state

The prediction of Hoyle state was necessitated to explain the abundance of carbon, which is crucial for the existence of life on Earth and is the stepping stone for understanding the abundance of other heavier elements. After the experimental confirmation of its existence, soon it was realized that the Hoyle state was ‘different’ from other excited states of carbon, led to intense theoretical and experimental activities over the past few decades to understand its structure. In recent times, precision, high statistics experiments on the decay of Hoyle state have been performed at the Variable Energy Cyclotron Centre, to determine the quantitative contributions of various direct 3 α decay mechanisms of the Hoyle state. The present results have been critically compared with those obtained in other recent experiments and their implications have been discussed.