A possible connection between neutrino mass generation and the lightness of a NMSSM pseudoscalar

One of the interesting properties of the NMSSM is that it can accommodate a light pseudoscalar of order 10 GeV. However, such scenarios are challenged by several experimental constraints, especially those related to the fermionic decays of the pseudoscalar. In this Letter, we extend the NMSSM field content by two gauge singlets, with lepton numbers +1 and −1. This serves the twin purpose of generating neutrino masses via the inverse seesaw mechanism and keeping the option of a very light pseudoscalar experimentally viable by opening dominant invisible decay channels of the pseudoscalar which help it evade the existing bounds.     

Coexistence of competing predators in a coral reef ecosystem

An analysis is made using a four-dimensional mathematical model where there is a constant rate of flow of input nutrient. An organism is introduced in the model which is growing by taking in that nutrient. Two other predators on that organism are also introduced. The predators at the second and third trophic levels belong to the same species, though of different age groups. The predator at the third trophic level exhibits a distinct cannibalistic attitude to the predator of the second trophic level. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the species associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained when one or more of the predators go extinct. Under appropriate circumstances a positive rest point of the system is obtained. Computer simulations have been carried out to illustrate different analytical results.     

On the calculation of second order properties: An equation of motion approach

In the light of the equation of motion method a general expression for polarisability calculation has been derived. From this general expression, different approximation methods can be deduced for different choices of ground state and excitation manifold. Among these the coupled Hartree-Fock theory is the most extensively used one for polarisability calculations. It has also been shown that this theory has a simple relationship with random phase approximation.     

Robust Hurwitz stability via sign-definite decomposition

In this paper, we first consider the problem of determining the robust positivity of a real function f(x) as the real vector x varies over a box X∈R^l. We show that, it is sufficient to check a finite number of specially constructed points. This is accomplished by using some results on sign-definite decomposition. We then apply this result to determine the robust Hurwitz stability of a family of complex polynomials whose coefficients are polynomial functions of the parameters of interest. We develop an eight polynomial vertex stability test that is a sufficient condition of Hurwitz stability of the family. This test reduces to Kharitonov’s well known result for the special case where the parameters are just the polynomial coefficients. In this case, the result is tight. This test can be recursively and modularly used to construct an approximation of arbitrary accuracy to the actual stabilizing set. The result is illustrated by examples.     

Beyond the standard model: Working group report

This report summarises the work done in the ‘Beyond the Standard Model’ working group of the Sixth Workshop on High Energy Physics Phenomenology (WHEPP-6) held at the Institute of Mathematical Sciences, Chennai, Jan 3–15, 2000. The participants in this working group were: R Adhikari, B Ananthanarayan, K P S Balaji, Gour Bhattacharya, Gautam Bhattacharyya, Chao-Hsi Chang (Zhang). D Choudhury, Amitava Datta, Anindya Datta, Asesh K Datta, A Dighe, N Gaur, D Ghosh, A Goyal, K Kar, S F King, Anirban Kundu, U Mahanta, R N Mohapatra, B Mukhopadhyaya, S Pakvasa, P N Pandita, M K Parida, P Poulose, G Raffelt, G Rajasekaran, S Rakshit, Asim K Ray, A Raychaudhuri, S Raychaudhuri, D P Roy, P Roy, S Roy, K Sridhar and S Vempati.     

Use of zirconium phosphate as ion exchanger in some parent-daughter radioisotope separations

Zirconium phosphate as ion exchanger suitable for column operation has been prepared by mixing hot metaphosphoric acid solution with a solution of zirconium oxychloride when the white insoluble phosphate separated out which was dried and purified. The ratio of zirconium: phosphate was found to be 1:2. Separation of parent-daughter systems like¹¹⁵Cd-^115mIn,¹⁴⁴Ce-¹⁴⁴Pr and²¹⁰Pb-²¹⁰Bi were carried out with this exchanger. γ-ray spectrum of the separated^115mIn and the β-decay curve of¹⁴⁴Pr and²¹⁰Bi showed that all the daughter activities are radiochemically pure. The separation process in each case takes less than half an hour and the yield is quantitative.     

Sommerfeld effect in a gyroscopic overhung rotor-disk system

Deflection of a rotor-disk at the free end of a flexible overhung rotor-shaft causes rotation about diametral axis and consequently leads to a strong gyroscopic coupling in a spinning overhung rotor system. When the rotor is spun up about its axis, the unbalance in the rotor-disk causes transverse and rotational vibrations to increase as the spin speed approaches the critical speed of the rotor. These transverse and rotational vibrations dissipate a lot of energy, and if the rotor is driven through a non-ideal drive, i.e., a motor which can supply a limited amount of power, then the entire motor power may be spent to account for the energy dissipation. As a result, the rotor speed may get stuck in resonance at the critical speed or jump through the critical speed to a much higher speed with lower transverse and rotational vibration levels. These symptoms, normally referred to as the Sommerfeld effect, occur due to the intrinsic energetic coupling between the drive and the driven systems and are important design considerations for development of various rotating machinery with flexible rotor-shafts or supports (bearings). Sommerfeld effect in a strongly gyroscopic rotor dynamic system is studied in this article. The dynamics of an overhung rotor system near the regimes of Sommerfeld effect is studied by using a discrete and a continuous shaft-rotor model coupled with the model of the non-ideal motor drive. The models are developed using multi-energy domain modeling approach in bond graph model form. A steady-state analysis of power transfer mechanism is used to postulate the ideal characteristics of Sommerfeld effect in the neighborhood of the critical speed, and thereafter, full transient analysis is performed with aid of the bond graph model-generated coupled equations of motion to validate the postulated characteristics of the Sommerfeld effect.