Tata Institute of Fundamental Research

About: Tata Institute of Fundamental Research is a education organization based out in Mumbai, Maharashtra, India. It is known for research contribution in the topics: Magnetization & Large Hadron Collider. The organization has 7786 authors who have published 21742 publications receiving 622368 citations. The organization is also known as: TIFR.

On orbits of unipotent flows on homogeneous spaces

Abstract: We show that if (ut) is a one-parameter subgroup of SL (n, ℝ) consisting of unipotent matrices, then for any e > 0 there exists a compact subset K of SL(n, ℝ)/SL(n, ℤ) such that the following holds: for any g ∈ SL(n, ℝ) either m({t ∈ [0, T] | utg SL (n, ℤ) ∈ K}) > (1 – e)T for all large T (m being the Lebesgue measure) or there exists a non-trivial (g−1utg)-invariant subspace defined by rational equations.Similar results are deduced for orbits of unipotent flows on other homogeneous spaces. We also conclude that if G is a connected semisimple Lie group and Γ is a lattice in G then there exists a compact subset D of G such that for any closed connected unipotent subgroup U, which is not contained in any proper closed subgroup of G, we have G = DΓ U. The decomposition is applied to get results on Diophantine approximation.

Interstellar CH absorption in the diffuse interstellar medium along the sight-lines to G10.6-0.4 (W31C), W49N, and W51

Abstract: We report the detection of the ground state N, J = 1, 3/2 → 1, 1/2 doublet of the methylidyne radical CH at ∼532 GHz and ∼536 GHz with the Herschel/HIFI instrument along the sight-line to the massive star-forming regions G10.6–0.4 (W31C), W49N, and W51. While the molecular cores associated with these massive star-forming regions show emission lines, clouds in the diffuse interstellar medium are detected in absorption against the strong submillimeter background. The combination of hyperfine structure with emission and absorption results in complex profiles, with overlap of the different hyperfine components. The opacities of most of the CH absorption features are linearly correlated with those of CCH, CN, and HCO + in the same velocity intervals. In specific narrow velocity intervals, the opacities of CN and HCO + deviate from the mean trends, giving rise to more opaque absorption features. We propose that CCH can be used as another tracer of the molecular gas in the absence of better tracers, with [CCH]/[H2] ∼3.2 ± 1.1 × 10 −8 . The observed [CN]/[CH], [CCH]/[CH] abundance ratios suggest that the bulk of the diffuse matter along the lines of sight has gas densities nH = n(H) + 2n(H2) ranging between 100 and 1000 cm −3 .

Fine structure of the sensory organs of Drosophila melanogaster Meigen larva (Diptera : Drosophilidae)

Abstract: Fine structure of the prominent external and internal sensory organs of Drosophila melaogaster Meigan (Diptera : Drosophilidae) larva was determined by transmission electron microscopy (TEM). The external sensory organs, namely, antennal, maxillary, ventral and labial organs, dorsal pits, sensory cones on the 8th and 9th abdominal segments, and the sensory hairs on the body of the larva, were studied. A new knob in pit (KIP) sensillum innervated by 3 dendrites was found on the dorsolateral surface on either side. Four tufts of hairs at the posterior end of each great lateral tracheal trunk were found to be sensory with a dendrite at the base of each tuft. Internally in the pharynx of the larva, 3 groups of symmetrically located sensory organs, namely, the anteroventral, dorsal, and posteroventral groups were found. In all they contain 10 pairs of sensilla. Amongst them, 2 pairs of sensilla were found to be of the compound type; one having 9 dendrites arranged in 3 groups of 4, 3 and 2; while the other had 6 dendrites grouped as 2 and 4. In addition, 2 groups of sensilla were found on the internal dorsal fold on either side. Similarities were observed in the dendritic organisation of sensilla in the internal mouthparts of the Drosophila larva and the adult. Unlike nerves of the adult, the larval nerves connected with the dorsal and maxillary organs have a significantly thick layer of glial cells ensheathing the bundle of axons.

Uniformly distributed orbits of certain flows on homogeneous spaces

Abstract: is non-compact. For a co-compact lattice, this result was strengthened by F/irstenberg [1 lJ proving that every orbit is uniformly distributed with respect to a G-invariant measure. For non-uniform lattices in SL(2, R), using a classification of invariant measures obtained by Dani in [21, Dani and Smillie [31 proved that every non-periodic orbit is uniformly distributed. There are also various results obtained on orbit closures and invariant measures etc. of larger subgroups consisting of unipotent elements, especially the horospherical subgroups. Recently, there was a spurt in the area initiated by Margulis' proof (cf. [151, see also [7]) of Oppenheim conjecture on values of quadratic forms at integral points using the study of unipotent flows. The reader is referred to the survey articles by Dani [41 and Margulis [14J for various related developments. We now note some conjectures expected to hold for orbits of a unipotent flow, namely the U-action on

Giant inverse magnetocaloric effect near room temperature in Co substituted NiMnSb Heusler alloys

Abstract: The effect of Co on the structural, magnetic and magnetocaloric effect (MCE) of Ni50−xCoxMn38Sb12 (x = 0, 2, 3, 4, 5) Heusler alloys was studied. Using x-ray diffraction, we show the evolution of the martensitic phase from the austenite phase. The martensitic transition temperature is found to decrease monotonically with Co concentration. Remarkable enhancement of MCE is observed near room temperature upon Co substitution. The maximum magnetic entropy change of 34Jkg −1 K −1 was achieved for x = 5 at 262K in a field of 50kOe and a value of 29Jkg −1 K −1 was found near room temperature. The significant increase in the magnetization with large magneto-structural coupling associated with the reverse martensitic transition is responsible for the giant MCE in these compounds. (Some figures in this article are in colour only in the electronic version)