Shape Invariant Rational Extensions And Potentials Related to Exceptional Polynomials

In this paper, we show that an attempt to construct shape invariant extensions of a known shape invariant potential leads to, apart from a shift by a constant, the well known technique of isospectral shift deformation. Using this, we construct infinite sets of generalized potentials with $X_m$ exceptional polynomials as solutions. These potentials are rational extensions of the existing shape invariant potentials. The method is elucidated using the radial oscillator and the trigonometric P\"{o}schl-Teller potentials. For the case of radial oscillator, in addition to the known rational extensions, we construct two infinite sets of rational extensions, which seem to be less studied. For one of the potential, we show that its solutions involve a third type of exceptional Laguerre polynomials. Explicit expressions of this generalized infinite set of potentials and the corresponding solutions are presented. For the trigonometric P\"{o}schl-Teller potential, our analysis points to the possibility of several rational extensions beyond those known in literature.Comment: 18 pages, 1 figur

Lepton Masses in a Minimal Model with Triplet Higgs Bosons and S3S_3 Flavor Symmetry

Viable neutrino and charged lepton masses and mixings are obtained by imposing a $S_3 \times Z_4 \times Z_3$ flavor symmetry in a model with a few additional Higgs. We use two $SU(2)_L$ triplet Higgs which are arranged as a doublet of $S_3$, and standard model singlet Higgs which are also put as doublets of $S_3$. We break the $S_3$ symmetry in this minimal model by giving vacuum expectation values (VEV) to the additional Higgs fields. Dictated by the minimum condition for the scalar potential, we obtain certain VEV alignments which allow us to maintain $\mu-\tau$ symmetry in the neutrino sector, while breaking it maximally for the charged leptons. This helps us to simultaneously explain the hierarchical charged lepton masses, and the neutrino masses and mixings. In particular, we obtain maximal $\theta_{23}$ and zero $\theta_{13}$. We allow for a mild breaking of the $\mu-\tau$ symmetry for the neutrinos and study the phenomenology. We give predictions for $\theta_{13}$ and the CP violating Jarlskog invariant $J_{CP}$, as a function of the $\mu-\tau$ symmetry breaking parameter. We also discuss possible collider signatures and phenomenology associated with lepton flavor violating processes.Comment: 29 pages, 5 figures. Version to be appeared in PRD. Phenomenology of Lepton flavor violation and possible collider signatures of this model have been include

Magnetic interactions in the Martensitic phase of Mn rich Ni-Mn-In shape memory alloys

The magnetic properties of Mn$_{2}$Ni$_{(1+x)}$In$_{(1-x)}$ ($x$ = 0.5, 0.6, 0.7) and Mn$_{(2-y)}$Ni$_{(1.6+y)}$In$_{0.4}$ ($y$ = -0.08, -0.04, 0.04, 0.08) shape memory alloys have been studied. Magnetic interactions in the martensitic phase of these alloys are found to be quite similar to those in Ni$_2$Mn$_{(1+x)}$In$_{(1-x)}$ type alloys. Doping of Ni for In not only induces martensitic instability in Mn$_2$NiIn type alloys but also affects magnetic properties due to a site occupancy disorder. Excess Ni preferentially occupies X sites forcing Mn to the Z sites of X$_2$YZ Heusler composition resulting in a transition from ferromagnetic ground state to a state dominated by ferromagnetic Mn(Y) - Mn(Y) and antiferromagnetic Mn(Y)-Mn(Z) interactions. These changes in magnetic ground state manifest themselves in observation of exchange bias effect even in zero field cooled condition and virgin magnetization curve lying outside the hysteresis loop.Comment: Accepted in J. Appl. Phy

Resilience models for New Zealand's alpine skiers based on people's knowledge and experience: a mixed method and multi-step fuzzy cognitive mapping approach

Artificial Neural Networks (ANN) as a tool offers opportunities for modeling the inherent complexity and uncertainty associated with socio-environmental systems. This study draws on New Zealand ski fields (multiple locations) as socio- environmental systems while considering their perceived resilience to low probability but potential high consequences catastrophic natural events (specifically earthquakes). We gathered data at several ski fields using a mixed methodology including: geomorphic assessment, qualitative interviews, and an adaptation of Ozesmi and Ozesmi’s (2003) multi-step fuzzy cognitive mapping (FCM) approach. The data gathered from FCM are qualitatively condensed, and aggregated to three different participant social groups. The social groups include ski fields users, ski industry workers, and ski field managers. Both quantitative and qualitative indices are used to analyze social cognitive maps to identify critical nodes for ANN simulations. The simulations experiment with auto-associative neural networks for developing adaptive preparation, response and recovery strategies. Moreover, simulations attempt to identify key priorities for preparation, response, and recovery for improving resilience to earthquakes in these complex and dynamic environments. The novel mixed methodology is presented as a means of linking physical and social sciences in high complexity, high uncertainty socio-environmental systems. Simulation results indicate that participants perceived that increases in Social Preparation Action, Social Preparation Resources, Social Response Action and Social Response Resources have a positive benefit in improving the resilience to earthquakes of ski fields’ stakeholders

Non-classical photon pair generation in atomic vapours

A scheme for the generation of non-classical pairs of photons in atomic vapours is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows anti-bunching which has not been reported earlier and which is unlike the case of the three level cascade emission which shows bunching. The Cauchy-Schwarz inequality which is the ratio of cross-correlation to the auto correlation function in this case is estimated to be $10^3-10^6$ for controllable time delay, and is one to four orders of magnitude larger compared to previous experiments. The choice of Doppler free geometry in addition to the fact that at three photon resonance the excitation/deexcitation processes occur in a very narrow frequency band, ensures cleaner signals.Comment: 18 pages, 7 figure

Wave forecasting and monitoring during very severe cyclone Phailin in the Bay of Bengal

Wave fields, both measured and forecast during the very severe cyclone Phailin, are discussed in this communication. Waves having maximum height of 13.54 m were recorded at Gopalpur, the landfall point of the cyclone. The forecast and observed significant wave heights matched well at Gopalpur with correlation coefficient of 0.98, RMS error of 0.35 m and scatter index of 14%. Forecasts were also validated in the open ocean and found to be reliable (scatter index < 15%). The study also revealed the presence of Southern Ocean swells with a peak period of 20-22 sec hitting Gopalpur coast along with the cyclone-generated waves