Pashan, India


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Mishra R.,IISER Pune | Raundal H.,IISER Pune
Journal of Knot Theory and its Ramifications | Year: 2015

We show that all knots up to six crossings can be represented by polynomial knots of degree at most 7, among which except for 52, 52 6 1, 61 - 6 2, 62 and 63 all are in their minimal degree representation. We provide concrete polynomial representation of all these knots. Durfee and O'Shea had asked a question: Is there any 5-crossing knot in degree 6? In this paper we try to partially answer this question. For an integer d 2, we define a set d to be the set of all polynomial knots given by t(f(t), g(t), h(t)) such that deg(f) = d - 2, deg(g) = d - 1 and deg(h) = d. This set can be identified with a subset of 3d and thus it is equipped with the natural topology which comes from the usual topology 3d. In this paper we determine a lower bound on the number of path components of d for d 7. We define a path equivalence for polynomial knots in the space abd and show that it is stronger than the topological equivalence. © 2015 World Scientific Publishing Company.

Hristov K.,Bulgarian Academy of Science | Katmadas S.,University of Milan Bicocca | Katmadas S.,National Institute of Nuclear Physics, Italy | Lodato I.,IISER Pune
Journal of High Energy Physics | Year: 2016

We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS2×S2(or other Riemann surface) preserves half of the supercharges in N = 2 supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending on the model, the attractors are part of full black hole solutions with different asymptotics, such as Minkowski, AdS4, and hvLif4. We give explicit examples for each of the asymptotic cases and comment on the implications. Among other results, we find that the Weyl-squared terms spoil the exact two-derivative relation to non-BPS asymptotically flat black holes in ungauged supergravity. © 2016, The Author(s).

Saha R.,Jadavpur University | Joarder B.,IISER Pune | Roy A.S.,Kalyani University | Manirul Islam S.,Kalyani University | Kumar S.,Jadavpur University
Chemistry - A European Journal | Year: 2013

Assimilation of open metal sites (OMSs) and free functional organic sites (FOSs) with a framework strut has opened up a new route for the fabrication of novel metal-organic materials, thereby providing a unique opportunity to explore their multiple functionalities. A new metal-organic framework (MOF), {[Cu(ina)2(H2O)][Cu(ina)2(bipy)]·2 H2O}n (1) (ina=isonicotinate, bipy=4,4′-bipyridine), has been synthesized and characterized. Complex 1 is crystallized in the orthorhombic noncentrosymmetric space group Aba2 and consists of two different 2D coordination polymers, [Cu(ina)2(H2O)]n and [Cu(ina)2(bipy)]n, with entrapped solvent water molecules. Hydrogen-bonding interactions assemble these two different 2D coordination layers in a single-crystal structure with interdigitation of pendant 4,4′-bipy from one layer into the groove of another. Upon removal of guest molecules, 1 undergoes a structural transformation in single-crystal-to-single- crystal fashion with expansion of the effective void space. Each metal center is five-coordinated and thus can potentially behave as an OMS, and the free pyridyl groups of pendant 4,4′-bipy moieties and free -C=O groups can act as free FOSs. Thus, owing to presence of both OMSs and free FOSs, the framework exhibits multifunctional properties. Owing to the presence of OMSs, the framework can act as a Lewis acid catalyst as well as a small-molecule sensor material, and in a similar way, owing to the presence of free FOSs, it performs as a Lewis base catalyst and a cation sensor material. Furthermore, owing to noncentrosymmetry with large polarity along a particular direction, it shows strong second-harmonic generation/nonlinear optical (SHG-NLO) activity. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Banerjee N.,IISER Pune | Bansal S.,IISER Pune | Bansal S.,University of Padua | Lodato I.,IISER Pune
Journal of High Energy Physics | Year: 2016

We show the equality between macroscopic and microscopic (statistical) black hole entropy for a class of four dimensional non-supersymmetric black holes in N = 2 supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of [1], connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term. © 2016, The Author(s).

Athale C.A.,IISER Pune | Dinarina A.,EMBL | Dinarina A.,Thermo Fisher Scientific | Nedelec F.,EMBL | Karsenti E.,EMBL
Physical Biology | Year: 2014

Microtubules (MTs) nucleated by centrosomes form star-shaped structures referred to as asters. Aster motility and dynamics is vital for genome stability, cell division, polarization and differentiation. Asters move either toward the cell center or away from it. Here, we focus on the centering mechanism in a membrane independent system of Xenopus cytoplasmic egg extracts. Using live microscopy and single particle tracking, we find that asters move toward chromatinized DNA structures. The velocity and directionality profiles suggest a random-walk with drift directed toward DNA. We have developed a theoretical model that can explain this movement as a result of a gradient of MT length dynamics and MT gliding on immobilized dynein motors. In simulations, the antagonistic action of the motor species on the radial array of MTs leads to a tug-of-war purely due to geometric considerations and aster motility resembles a directed random-walk. Additionally, our model predicts that aster velocities do not change greatly with varying initial distance from DNA. The movement of asymmetric asters becomes increasingly super-diffusive with increasing motor density, but for symmetric asters it becomes less super-diffusive. The transition of symmetric asters from superdiffusive to diffusive mobility is the result of number fluctuations in bound motors in the tug-of-war. Overall, our model is in good agreement with experimental data in Xenopus cytoplasmic extracts and predicts novel features of the collective effects of motor-MT interactions. © 2014 IOP Publishing Ltd.

Kiruthiga J.,Pondicherry University | Chatterji A.,IISER Pune
Journal of Chemical Physics | Year: 2013

We present a theoretical model, which elucidates the physical principles involved in the formation of very uniform CdS nanocylinders of different radii by combining the physics of flow, diffusion, self assembly, and aggregation of constituent particles. Very recent experiments report that when 0.1M solutions of CdCl2 and Na2S were allowed to mix through some anodised aluminium oxide (AAO) nanochannels, one observes the growth of an array of CdS nano-cylinders on only one end of the AAO template [A. Varghese and S. Datta, Phys. Rev. E 85, 056104 (2012)]. These cylinders have a pore along the center of the cylinder but closed at one end. The reaction happens only in the Na2S chamber, and growth of cylinders of uniform size and shape continues as long as the supply of the reactant molecules (CdCl2 and Na2S) is maintained. To try to understand the physics of the observed phenomenon, we propose a model where the Cd+2 ions exit the AAO-nanochannel to enter Na2S chamber with a finite velocity; these ions then react with the diffusing S-2 ions to form CdS, which then self assemble to form cylinders of uniform width and cross-section. The flow of Cd+2 out of the AAO nano-channel is the key symmetry breaking feature, which facilitates the formation of uniform cylindrical structures of CdS instead of a CdS precipitate. Since our model does not crucially depend on the chemical details of the reaction, this mechanism can be extended to self-assemble other structures of relevance. © 2013 American Institute of Physics.

Kiruthiga J.,Pondicherry University | Chatterji A.,IISER Pune
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2014

We present our conclusions of the investigation of the self-assembly and growth of an array of CdS nanotubes: a consequence of a fine balance of directed motion, diffusion, and aggregation of reacting Cd+2 and S-2 ions. In a previous communication [Kiruthiga and Chatterji, J. Chem. Phys. 138, 024905 (2013)JCPSA60021-960610.1063/1.4773279], we identified the mechanism of an unexpected growth of a CdS nanocylinder of uniform radial cross section from the end of a nanochannel. Furthermore, the cylinder had a pore along the axis but was closed at one end. This unique phenomenon of self-assembly of very monodisperse CdS nanocylinders had been observed in a rather simple experiment where two chambers containing 0.1M CdCl2 and 0.1M Na2S solutions were joined by an array of anodized aluminium oxide (AAO) nanochannels [Varghese and Datta, Phys. Rev. E 85, 056104 (2012)PLEEE81539-375510.1103/PhysRevE.85.056104]. Interestingly, the growth of CdS nanotubes was observed only in the Na2S chamber. The primary focus of our previous study was on identifying the principles governing the growth of a single nanotube at the exit point of a single AAO nanochannel. In this communication, we identify factors affecting the self-assembly of a nanotube in the presence of other similar neighboring nanotubes growing out from an array of closely spaced AAO nanochannel exit points, a scenario closer to the experimental situation. Our model is not Cd+2 or S-2 specific, thus our conclusions suggest that the experimental scheme can be extended to the self-assembly of a general class of reacting-diffusing A and B ions with A (in this case Cd+2 ions) selectively migrating out from a nanochannel. In particular, we note that after the initial growth of nanotubes for a period of time, there can arise a severe deficiency of B ions (S-2) near the AAO-nanochannel exits. The low concentration of B near the nanochannel exits impedes further growth of uniform CdS nanotubes. We further identify the parameters which can be tuned to obtain an improved crop of monodisperse nanotubes. Thereby we predict the necessary characteristics of reacting systems which can be self-assembled using suitable adaptations of experiments used to grow CdS cylinders. © 2014 American Physical Society.

Barua A.K.,IISER Pune | Goel P.,IISER Pune
Physica D: Nonlinear Phenomena | Year: 2016

The traditional computational model of the pancreatic islets of Langerhans is a lattice of β-cells connected with gap junctions. Numerous studies have investigated the behavior of networks of coupled β-cells and have shown that gap junctions synchronize bursting strongly. This simplistic architecture of islets, however, seems increasingly untenable at the face of recent experimental advances. In a microfluidics experiment on isolated islets, Rocheleau et al. (2004) showed a failure of penetration of excitation when one end received high glucose and other end was not excited sufficiently; this suggested that gap junctions may not be efficient at inducing synchrony throughout the islet. Recently, Stozer et al. (2013) have argued that the functional networks of β-cells in an islet are small world. Their results implicate the existence of a few long-range connections among cells in the network. The physiological reason underlying this claim is not well understood. These studies cast doubt on the original lattice model that largely predict an all-or-none synchrony among the cells. Here we have attempted to reconcile these observations in a unified framework. We assume that cells in the islet are coupled randomly to their nearest neighbors with some probability, p. We simulated detailed β-cell bursting in such islets. By varying p systematically we were led to network parameters similar to those obtained by Stozer et al. (2013). We find that the networks within islets break up into components giving rise to smaller isles within the super structure - isles-within-islets, as it were. This structure can also account for the partial excitation seen by Rocheleau et al. (2004). Our updated view of islet architecture thus explains the paradox how islets can have strongly synchronizing gap junctions, and be weakly coordinated at the same time. © 2015 Elsevier B.V.

Athale C.A.,IISER Pune | Chaudhari H.,IISER Pune
Bioinformatics | Year: 2011

Motivation: Cell sizes and shapes are a fundamental defining characteristic of all cellular life. In bacteria like Escherichia coli, the machinery that determines cell length is complex and interconnected, spanning extracellular cues, biosynthesis and cell division. Few tools exist to study cell lengths in a population. We have developed and tested three automated image analysis routines on growing E. coli cultures to simultaneously measure cell lengths and nucleoid numbers in populations of bacteria. We find population profiles changing with culture density-higher density of culture leads to fewer long cells. Additionally, lab strains mutant for recA show a correlation between the number of nucleoids and cell length. © The Author 2011. Published by Oxford University Press. All rights reserved.

Mubeena S.,IISER Pune | Chatterji A.,IISER Pune
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2015

We report many different nanostructures which are formed when model nanoparticles of different sizes (diameter σn) are allowed to aggregate in a background matrix of semiflexible self-assembled polymeric wormlike micellar chains. The different nanostructures are formed by the dynamical arrest of phase-separating mixtures of micellar monomers and nanoparticles. The different morphologies obtained are the result of an interplay of the available free volume, the elastic energy of deformation of polymers, the density (chemical potential) of the nanoparticles in the polymer matrix, and, of course, the ratio of the size of self-assembling nanoparticles and self-avoidance diameter of polymeric chains. We have used a hybrid semi-grand-canonical Monte Carlo simulation scheme to obtain the (nonequilibrium) phase diagram of the self-assembled nanostructures. We observe rodlike structures of nanoparticles which get self-assembled in the gaps between the nematically ordered chains, as well as percolating gel-like network of conjoined nanotubes. We also find a totally unexpected interlocked crystalline phase of nanoparticles and monomers, in which each crystal plane of nanoparticles is separated by planes of perfectly organized polymer chains. We identified the condition which leads to such interlocked crystal structure. We suggest experimental possibilities of how the results presented in this paper could be used to obtain different nanostructures in the laboratory. © 2015 American Physical Society.

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