AR_final file_2018-19

Dharam Vir Ahluwalia Magnetic-field creation by solar-mass neutrino jets Parity violation and its effects for neutrinos in as- trophysical contexts have been considered earlier in pioneering papers of Hawking and Vilenkin. But because even the largest magnetic moments pre- dicted by physics beyond the Standard Model are some twelve orders of magnitude smaller than the Bohr magneton, their implications for magnetic- field generation and neutrino oscillations are gen- erally considered insignificant. Here, we show that since in astrophysical scenarios, a huge number of neutrinos may be emitted, the smallness of the magnetic moment, when coupled with parity viola- tion, is compensated by the sheer number of neu- trinos. The merger of neutron stars would leave be- hind a short pulse of electromagnetic synchrotron radiation even if the neutrino jet in the merger points away from the neutrino detectors. We show that the magnetic field can be as large as 10 6 Gauss and comment on the possibility of direct detection. Observation of such a pulse would lend strong sup- port for neutrino magnetic moments and resolve the missing neutrino problem in neutron star merg-ers. This work has been done in collaboration with Cheng-Yang Lee. Elko under spatial rotations Under a rotation by an angle θ , both the right-and left-handed Weyl spinors pick up a phase fac-tor exp ( ± iθ/ 2). The upper sign holds for the posi-tive helicity spinors, while the lower sign holds for the negative helicity spinors. For θ = 2 π radians, this produces the famous minus sign. However, the four- component spinors are built from a direct sum of the indicated two-component spinors. The effect of the rotation by 2 π radians on the eigenspinors of the parity - that is, the Dirac spinors - is the same as on Weyl spinors. It is because, for these spinors the right- and left-transforming components have the same helicity. And the rotation-induced phases, being the same, factor out. But for the eigenspinors of the charge conjugation operator, i.e., Elko, the left- and right-transforming components have op- posite helicities, and, therefore, they pick up op- posite phases. As a consequence, the behaviour of the eigenspinors of the charge conjugation op- erator (Elko) is more subtle: for θ < θ < 2 π a self-conjugate spinor becomes a linear combina- tion of the self - and antiself-conjugate spinors with θ − dependent superposition coefficients - and yet the rotation preserves the self-/antiself-conjugacy of these spinors! This apparently paradoxical situ- ation is fully resolved. This new effect, to the best of our knowledge, has never been reported before. The purpose of this communication is to present this result and to correct an interpretational error of a previous version. This work has been done in collaboration with Sweta Sarmah. G. Ambika Degree weighted recurrence networks for the analy- sis of time series data Recurrence networks (RNs) have become very pop- ular tools for the non-linear analysis of time-series data. They are unweighted and undirected com- plex networks constructed with specific criteria from time series. In this work, we propose a method to construct a ’weighted recurrence network’ from a time series and show that it can reveal useful information regarding the structure of a chaotic attractor, which the usual unweighted RN can- not provide. Especially, a network measure, the node strength distribution, from every chaotic at- tractor follows a power law (with exponential cut off at the tail) with an index characteristic to the fractal structure of the attractor. This provides a new class among complex networks to which networks from all standard chaotic attractors are found to belong. Two other prominent network measures, clustering coefficient and characteristic path length, are generalized and their utility in dis- criminating chaotic dynamics from noise is high- lighted. As an application of the proposed mea- sure, we present an analysis of variable star light curves whose behaviour has been reported to be strange non-chaotic in a recent study. Our numer- ical results indicate that the weighted recurrence network and the associated measures can become potentially important tools for the analysis of short and noisy time series from the real world. This work has been done in collaboration with Rinku Jacob, H. P. Harikrishnan, and Ranjeev Misra. ( 174 )