Propagation of a Three-dimensional Weak Shock Front Using Kinematical Conservation Laws

In this paper we present a mathematical theory and a numerical method to study the propagation of a three-dimensional (3-D) weak shock front into a polytropic gas in a uniform state and at rest, though the method can be extended to shocks moving into nonuniform flows. The theory is based on the use of 3-D kinematical conservation laws (KCL), which govern the evolution of a surface in general and a shock front in particular. The 3-D KCL, derived purely on geometrical considerations, form an under-determined system of conservation laws. In the present paper the 3-D KCL system is closed by using two appropriately truncated transport equations from an infinite hierarchy of compatibility conditions along shock rays. The resulting governing equations of this KCL based 3-D shock ray theory, leads to a weakly hyperbolic system of eight conservation laws with three divergence-free constraints. The conservation laws are solved using a Godunov-type central finite volume scheme, with a constrained transport technique to enforce the constraints. The results of extensive numerical simulations reveal several physically realistic geometrical features of shock fronts and the complex structures of kink lines formed on them. A comparison of the results with those of a weakly nonlinear wavefront shows that a weak shock front and a weakly nonlinear wavefront are topologically same. The major important differences between the two are highlighted in the contexts of corrugational stability and converging shock fronts

Minimum Dominating Set for a Point Set in \IR^2

In this article, we consider the problem of computing minimum dominating set for a given set $S$ of $n$ points in \IR^2. Here the objective is to find a minimum cardinality subset $S'$ of $S$ such that the union of the unit radius disks centered at the points in $S'$ covers all the points in $S$. We first propose a simple 4-factor and 3-factor approximation algorithms in $O(n^6 \log n)$ and $O(n^{11} \log n)$ time respectively improving time complexities by a factor of $O(n^2)$ and $O(n^4)$ respectively over the best known result available in the literature [M. De, G.K. Das, P. Carmi and S.C. Nandy, {\it Approximation algorithms for a variant of discrete piercing set problem for unit disk}, Int. J. of Comp. Geom. and Appl., to appear]. Finally, we propose a very important shifting lemma, which is of independent interest and using this lemma we propose a $\frac{5}{2}$-factor approximation algorithm and a PTAS for the minimum dominating set problem.Comment: 14 pages, 8 figure

Einstein energy-momentum complex for a phantom black hole metric

In this paper we calculate the energy distribution E(r) associated with a static spherically symmetric non-singular phantom black hole metric in Einstein's prescription in general relativity. As required for Einstein energy-momentum complex, we perform calculations in quasi-Cartesian coordinates. We also calculate momentum components and get zero values as expected from the geometry of the metric.Comment: 5 pages, 2 figure

Thermo-optic coefficient measurement of liquids using silicon photonic microring resonators

On-chip measurement of thermo-optic coefficient (TOC) of samples along with on-chip temperature measurements can be used to compensate for thermal fluctuation induced noise in refractometry using integrated photonic sensors. In this article we demonstrate a device design and describe the method to extract TOCs of liquid samples using resonant wavelength shifts of a silicon microring resonator. The TOCs of three standard fluids; De-ionized water, Ethanol and Isopropanol, were determined using our sensor and show a good agreement with values reported in literature. A mechanism for tracking of on-chip temperature variations is also included for ensuring accuracy of TOC measurements. Potential applications of the demonstrated on-chip TOC sensor include improvements in accuracy of refractive index measurements and multiparametric analysis of biochemical analytes

Energy Efficiency in Massive MIMO-Based 5G Networks: Opportunities and Challenges

As we make progress towards the era of fifth generation (5G) communication networks, energy efficiency (EE) becomes an important design criterion because it guarantees sustainable evolution. In this regard, the massive multiple-input multiple-output (MIMO) technology, where the base stations (BSs) are equipped with a large number of antennas so as to achieve multiple orders of spectral and energy efficiency gains, will be a key technology enabler for 5G. In this article, we present a comprehensive discussion on state-of-the-art techniques which further enhance the EE gains offered by massive MIMO (MM). We begin with an overview of MM systems and discuss how realistic power consumption models can be developed for these systems. Thereby, we discuss and identify few shortcomings of some of the most prominent EE-maximization techniques present in the current literature. Then, we discuss "hybrid MM systems" operating in a 5G architecture, where MM operates in conjunction with other potential technology enablers, such as millimetre wave, heterogenous networks, and energy harvesting networks. Multiple opportunities and challenges arise in such a 5G architecture because these technologies benefit mutually from each other and their coexistence introduces several new constraints on the design of energy-efficient systems. Despite clear evidence that hybrid MM systems can achieve significantly higher EE gains than conventional MM systems, several open research problems continue to roadblock system designers from fully harnessing the EE gains offered by hybrid MM systems. Our discussions lead to the conclusion that hybrid MM systems offer a sustainable evolution towards 5G networks and are therefore an important research topic for future work.Comment: IEEE Wireless Communications, under revie

Low-Dimensionality of Noise-Free RSS and its Application in Distributed Massive MIMO

We examine the dimensionality of noise-free uplink received signal strength (RSS) data in a distributed multiuser massive multiple-input multiple-output system. Specifically, we apply principal component analysis to the noise-free uplink RSS and observe that it has a low-dimensional principal subspace. We make use of this unique property to propose RecGP - a reconstruction-based Gaussian process regression (GP) method which predicts user locations from uplink RSS data. Considering noise-free RSS for training and noisy test RSS for location prediction, RecGP reconstructs the noisy test RSS from a low- dimensional principal subspace of the noise-free training RSS. The reconstructed RSS is input to a trained GP model for location prediction. Noise reduction facilitated by the reconstruction step allows RecGP to achieve lower prediction error than standard GP methods which directly use the test RSS for location prediction.Comment: submitted to IEEE Wireless Communication Letters, July 201

A Deep Learning Approach for Similar Languages, Varieties and Dialects

Deep learning mechanisms are prevailing approaches in recent days for the various tasks in natural language processing, speech recognition, image processing and many others. To leverage this we use deep learning based mechanism specifically Bidirectional- Long Short-Term Memory (B-LSTM) for the task of dialectic identification in Arabic and German broadcast speech and Long Short-Term Memory (LSTM) for discriminating between similar Languages. Two unique B-LSTM models are created using the Large-vocabulary Continuous Speech Recognition (LVCSR) based lexical features and a fixed length of 400 per utterance bottleneck features generated by i-vector framework. These models were evaluated on the VarDial 2017 datasets for the tasks Arabic, German dialect identification with dialects of Egyptian, Gulf, Levantine, North African, and MSA for Arabic and Basel, Bern, Lucerne, and Zurich for German. Also for the task of Discriminating between Similar Languages like Bosnian, Croatian and Serbian. The B-LSTM model showed accuracy of 0.246 on lexical features and accuracy of 0.577 bottleneck features of i-Vector framework.Comment: 17 page

Dissipation scale lengths of density turbulence in the inner solar wind

Knowing the lengthscales at which turbulent fluctuations dissipate is key to understanding the nature of weakly compressible magnetohydrodynamic turbulence. We use radio wavelength interferometric imaging observations which measure the extent to which distant cosmic sources observed against the inner solar wind are scatter-broadened. We interpret these observations to determine that the dissipation scales of solar wind density turbulence at heliocentric distances of 2.5 -- 20.27 $R_{\odot}$ range from $\approx$ 13500 to 520 m. Our estimates from $\approx$ 10--20 $R_{\odot}$ suggest that the dissipation scale corresponds to the proton gyroradius. They are relevant to in-situ observations to be made by the Parker Solar Probe, and are expected to enhance our understanding of solar wind acceleration.Comment: Accepted for publication in The Astrophysical Journal (8 pages, 4 figures, 1 table

LASCO Measurements of the Energetics of Coronal Mass Ejections

We examine the energetics of Coronal Mass Ejections (CMEs) with data from the LASCO coronagraphs on SOHO. The LASCO observations provide fairly direct measurements of the mass, velocity and dimensions of CMEs. Using these basic measurements, we determine the potential and kinetic energies and their evolution for several CMEs that exhibit a flux-rope morphology. Assuming flux conservation, we use observations of the magnetic flux in a variety of magnetic clouds near the Earth to determine the magnetic flux and magnetic energy in CMEs near the Sun. We find that the potential and kinetic energies increase at the expense of the magnetic energy as the CME moves out, keeping the total energy roughly constant. This demonstrates that flux rope CMEs are magnetically driven. Furthermore, since their total energy is constant, the flux rope parts of the CMEs can be considered to be a closed system above $\sim$ 2 R_{\sun}.Comment: Accepted for publication, Astrophysical Journal. Uses AASTeX 5.

The Receiver System for the Ooty Wide Field Array

The legacy Ooty Radio Telescope (ORT) is being reconfigured as a 264-element synthesis telescope, called the Ooty Wide Field Array (OWFA). Its antenna elements are the contiguous 1.92 m sections of the parabolic cylinder. It will operate in a 38-MHz frequency band centred at 326.5 MHz and will be equipped with a digital receiver including a 264-element spectral correlator with a spectral resolution of 48 kHz. OWFA is designed to retain the benefits of equatorial mount, continuous 9-hour tracking ability and large collecting area of the legacy telescope and use modern digital techniques to enhance the instantaneous field of view by more than an order of magnitude. OWFA has unique advantages for contemporary investigations related to large scale structure, transient events and space weather watch. In this paper, we describe the RF subsystems, digitizers and fibre optic communication of OWFA and highlight some specific aspects of the system relevant for the observations planned during the initial operation.Comment: 10 pages, 5 figures, 1 table, (Accepted for publication in J. Astrophysics and Astronomy