Viability of Noether symmetry of F(R) theory of gravity

Canonization of F(R) theory of gravity to explore Noether symmetry is performed treating R - 6(\frac{\ddot a}{a} + \frac{\dot a^2}{a^2} + \frac{k}{a^2}) = 0 as a constraint of the theory in Robertson-Walker space-time, which implies that R is taken as an auxiliary variable. Although it yields correct field equations, Noether symmetry does not allow linear term in the action, and as such does not produce a viable cosmological model. Here, we show that this technique of exploring Noether symmetry does not allow even a non-linear form of F(R), if the configuration space is enlarged by including a scalar field in addition, or taking anisotropic models into account. Surprisingly enough, it does not reproduce the symmetry that already exists in the literature (A. K. Sanyal, B. Modak, C. Rubano and E. Piedipalumbo, Gen.Relativ.Grav.37, 407 (2005), arXiv:astro-ph/0310610) for scalar tensor theory of gravity in the presence of R^2 term. Thus, R can not be treated as an auxiliary variable and hence Noether symmetry of arbitrary form of F(R) theory of gravity remains obscure. However, there exists in general, a conserved current for F(R) theory of gravity in the presence of a non-minimally coupled scalar-tensor theory (A. K. Sanyal, Phys.Lett.B624, 81 (2005), arXiv:hep-th/0504021 and Mod.Phys.Lett.A25, 2667 (2010), arXiv:0910.2385 [astro-ph.CO]). Here, we briefly expatiate the non-Noether conserved current and cite an example to reveal its importance in finding cosmological solution for such an action, taking F(R) \propto R^{3/2}.Comment: 16 pages, 1 figure. appears in Int J Theoretical Phys (2012

First-principles calculations of exchange interactions, spin waves, and temperature dependence of magnetization in inverse-Heusler-based spin gapless semiconductors

Employing first principles electronic structure calculations in conjunction with the frozen-magnon method we calculate exchange interactions, spin-wave dispersion, and spin-wave stiffness constants in inverse-Heusler-based spin gapless semiconductor (SGS) compounds Mn$_2$CoAl, Ti$_2$MnAl, Cr$_2$ZnSi, Ti$_2$CoSi and Ti$_2$VAs. We find that their magnetic behavior is similar to the half-metallic ferromagnetic full-Heusler alloys, i.e., the intersublattice exchange interactions play an essential role in the formation of the magnetic ground state and in determining the Curie temperature, $T_\mathrm{c}$. All compounds, except Ti$_2$CoSi possess a ferrimagnetic ground state. Due to the finite energy gap in one spin channel, the exchange interactions decay sharply with the distance, and hence magnetism of these SGSs can be described considering only nearest and next-nearest neighbor exchange interactions. The calculated spin-wave dispersion curves are typical for ferrimagnets and ferromagnets. The spin-wave stiffness constants turn out to be larger than those of the elementary 3$d$-ferromagnets. Calculated exchange parameters are used as input to determine the temperature dependence of the magnetization and $T_\mathrm{c}$ of the SGSs. We find that the $T_\mathrm{c}$ of all compounds is much above the room temperature. The calculated magnetization curve for Mn$_2$CoAl as well as the Curie temperature are in very good agreement with available experimental data. The present study is expected to pave the way for a deeper understanding of the magnetic properties of the inverse-Heusler-based SGSs and enhance the interest in these materials for application in spintronic and magnetoelectronic devices.Comment: Accepted for publ;ication in Physical Review

Enteropathogenicity of Plesiomonas Shigelloides

Plesiomonas Shigelloides has been implicated as an aetiological agent in sporadic cases and outbreaks of diarrhoea, and in food poisoning, in various parts of the world. (Schmid, Velaudapillai and Niles, 1954; Osada and Shibata, 1956; Vandepitte et al., 1957; Ueda, Yamasaki and Hori, 1963; Aldova, Rakovsky and Chovanova, 1966; Geizer, Kopecky and Aldova, 1966; Hori et al., 1966; Cooper and Brown, 1968; Pauova and Fukalova, 1968; von Graevenitz and Mensch, 1968; Winton, 1968; Sakazaki et al., 1971; Chatterjee and Neogy, 1972; Sanyal et al., 1972a and b; Zajc-Satler, Dragas and Kumelj, 1972; Bhat, Shantha Kumari and Rajan, 1974; Vandepitte, Makulu and Gatti, 1974; Sanyal, Singh and Sen, 1975; Jandl and Linke, 1976; Tsukamoto et al., 1978). P. shigelloides was isolated in pure culture from stools of patients with diarrhoea of otherwise unexplained origin, and more often from patients than from symptomless persons. Experimental evidence has not, however, been reported in support of its enteropathogenicity, except our preliminary communication on the activity of a few strains in the rabbit ileal-loop model (Saraswathi, Sharma and Sanyal, 1978). The present investigation was undertaken to examine its enterotoxicity and invasiveness

Structure, bonding and magnetism in cobalt clusters

The structural, electronic and magnetic properties of Co$_n$ clusters ($n=2-$20) have been investigated using density functional theory within the pseudopotential plane wave method. An unusual hexagonal growth pattern has been observed in the intermediate size range, $n=15-$20. The cobalt atoms are ferromagnetically ordered and the calculated magnetic moments are found to be higher than that of corresponding hcp bulk value, which are in good agreement with the recent Stern-Gerlach experiments. The average coordination number is found to dominate over the average bond length to determine the effective hybridization and consequently the cluster magnetic moment.Comment: 12 pages and 9 figure