Role of upward leaders in modifying the induced currents in solitary down-conductors during a nearby lightning strike to ground

Electromagnetic field produced by a lightning strike to ground causes significant induction to tall objects in the vicinity. The frequency of occurrence of such nearby ground strikes can be higher than the number of direct strikes. Therefore, a complete knowledge on these induced currents is of practical relevance. However, limited efforts towards the characterisation of such induced currents in tall down-conductors could be seen in the literature. Due to the intensification of the background field caused by the descending stepped leader, tall towers/down-conductors can launch upward leaders of significant length. The nonlinearity in the conductance of upward leader and the surrounding corona sheath can alter the characteristics of the induced currents. Preliminary aspects of this phenomenon have been studied by the author previously and the present work aims to perform a detailed investigation on the role of upward leaders in modifying the characteristics of the induced currents. A consistent model for the upward leader, which covers all the essential electrical aspects of the phenomena, is employed. A first order arc model for representing the conductance of upward leader and a field dependant quadratic conductivity model for the corona sheath is employed. The initial gradient in the upward leader and the field produced by the return stroke forms the excitation. The dynamic electromagnetic response is determined by solving the wave equation using thin-wire time-domain formulation. Simulations are carried out initially to ascertain the role of individual parameters, including the length of the upward leader. Based on the simulation results, it is shown that the upward leader enhances the induced current, and when significant in length, can alter the waveshape of induced current from bipolar oscillatory to unipolar. The duration of the induced current is governed by the length of upward leader, which in turn is dependant on the return stroke current and the effective length of the down-conductor. If the current during the upward leader developmental phase is considered along with that after the stroke termination to ground, it would present a bipolar current pulse. (C) 2015 Elsevier Ltd. All rights reserved.

Onset of plane layer magnetoconvection at low Ekman number

We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth's tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra-c and critical wavenumber a(c) are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number. (ratio of the Lorentz force to the Coriolis force). E is varied from 10(-9) to 10(-2) and. from 10(-3) to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E-one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E < 10(-6) and establish a map in the (E, Lambda) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal. (C) 2015 AIP Publishing LLC.

Upper bound on cubicity in terms of boxicity for graphs of low chromatic number

The boxicity (respectively cubicity) of a graph G is the least integer k such that G can be represented as an intersection graph of axis-parallel k-dimensional boxes (respectively k-dimensional unit cubes) and is denoted by box(G) (respectively cub(G)). It was shown by Adiga and Chandran (2010) that for any graph G, cub(G) <= box(G) log(2) alpha(G], where alpha(G) is the maximum size of an independent set in G. In this note we show that cub(G) <= 2 log(2) X (G)] box(G) + X (G) log(2) alpha(G)], where x (G) is the chromatic number of G. This result can provide a much better upper bound than that of Adiga and Chandran for graph classes with bounded chromatic number. For example, for bipartite graphs we obtain cub(G) <= 2(box(G) + log(2) alpha(G)] Moreover, we show that for every positive integer k, there exist graphs with chromatic number k such that for every epsilon > 0, the value given by our upper bound is at most (1 + epsilon) times their cubicity. Thus, our upper bound is almost tight. (c) 2015 Elsevier B.V. All rights reserved.

Clean localization super-resolution microscopy for 3D biological imaging

We propose clean localization microscopy (a variant of fPALM) using a molecule filtering technique. Localization imaging involves acquiring a large number of images containing single molecule signatures followed by one-to-one mapping to render a super-resolution image. In principle, this process can be repeated for other z-planes to construct a 3D image. But, single molecules observed from off-focal planes result in false representation of their presence in the focal plane, resulting in incorrect quantification and analysis. We overcome this with a single molecule filtering technique that imposes constraints on the diffraction limited spot size of single molecules in the image plane. Calibration with sub-diffraction size beads puts a natural cutoff on the actual diffraction-limited size of single molecules in the focal plane. This helps in distinguishing beads present in the focal plane from those in the off-focal planes thereby providing an estimate of the single molecules in the focal plane. We study the distribution of actin (labeled with a photoactivatable CAGE 552 dye) in NIH 3T3 mouse fibroblast cells. (C) 2016 Author(s).