Department of Mathematics

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In this paper, we study the dynamics induced by finite commutative relation. We prove that the dynamics generated by such a non-trivial collection cannot be transitive/super-transitive and hence cannot exhibit higher degrees of mixing. As a consequence we establish that the dynamics induced by such a collection on the hyperspace endowed with any admissible hit and miss topology cannot be transitive and hence cannot exhibit any form of mixing. We also prove that if the system is generated by such a commutative collection, under suitable conditions the induced system cannot have dense set of periodic points. In the end we give example to show that the induced dynamics in this case may or may not be sensitive. © AGT, UPV, 2016.

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Applied General Topology

Induced dynamics on the hyperspaces

We consider a reaction-diffusion system where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We establish local well-posedness and global existence of solutions for these systems using classical potential theory and linear estimates for initial boundary value problems. © 2016 Society for Industrial and Applied Mathematics.

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SIAM Journal on Mathematical Analysis

Global existence of solutions to reaction-diffusion systems with mass transport type boundary conditions

In this article, we study the fractional Laplacian equation with critical growth and singular nonlinearity (Formula Presented) where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, n &gt; 2s, s ∈ (0,1), λ &gt; 0, 0 &lt; q ≤ 1, θ ≤ a(x) ∈ L∞ for some θ &gt; 0 and (Formula Presented). We use variational methods to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter λ. © Texas State University 2016.

Electronic Journal of Differential Equations

Fractional elliptic equations with critical growth and singular nonlinearities

The properties of a coherent system with a single general standby component is investigated. Here three different switch over viz. perfect switching, imperfect switching and random warm up period of the standby component are considered with some numerical examples. © 2015 Elsevier B.V.

Statistics and Probability Letters

Reliability study of a coherent system with single general standby component

The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Physics of Fluids

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

In this article, randomly distributed wire based metamaterial absorber is designed and analyzed numerically in microwave frequency region. The metamaterial absorber is composed of randomly distributed metallic wire on lossy FR4 substrate backed with metallic plate. Twenty random coordinates are generated within a unit cell of absorber. Total forty wire elements are distributed, including twenty wires horizontally and twenty wires vertically, at these random coordinate in unit cell. The numerical result shows the bandwidth of absorber is 1.2 GHz and 2 GHz for 10 dB and 5 dB return loss respectively. The wire elements dimensions (width and thickness) are of 14 μm and 35 μm respectively. Observed multiple absorption peaks expected to correspond to the absorption modes excited by varied effective lengths of shortened randomly distributed metallic wires. © 2015 IEEE.

2015 International Conference on Microwave, Optical and Communication Engineering, ICMOCE 2015

Numerical study of randomly distributed wire based metamaterial absorber

We present the design and fabrication of a bandwidth enhanced metamaterial absorber, based on multiple wires printed on metal backed lossy dielectric substrate. The proposed structure is fabricated using screen printing technique. In the proposed structure, broadband absorption is achieved by overlapping the absorption peaks of individual wires. Results show that bandwidth of proposed absorber corresponding to 10dB return loss, is 0.5 GHz. The simulated bandwidth of proposed absorber is independent of the variation in incidence angle from 0 to 30°. © 2015 IEEE.

Proceedings of the 2015 International Conference on Microwave and Photonics, ICMAP 2015

Design and fabrication of wire based bandwidth enhanced metamaterial absorber

In the literature, stochastic orders are used to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system made out of independent components, which have been used for some units of time, performs better (worse) than a used coherent system (i.e., a system is formed by some new independent components and then the system has been used for sometime) with respect to different stochastic orders. Some results on stochastic comparisons between a coherent system of inactive components and an inactive coherent system are also discussed. © 2016 IEEE.

IEEE Transactions on Reliability

Stochastic Comparisons between Used Systems and Systems Made by Used Components

The thin-film structures of DC/FR magnetron-sputtered ZrOx/ZrC–ZrN/Zr tandem solar-selective coatings are investigated using X-ray diffraction and room-temperature Raman spectroscopic measurements. These studies suggest that the major contribution is coming from h-ZrN0.28, c-ZrC, h-Zr3C2 crystallographic phases in ZrN–ZrC absorber layer, in conjunction with mixed ZrOx crystallographic phases. The change in structure for thermally annealed samples has been examined and observed that cubic and hexagonal ZrOx phase converted partially into tetragonal and monoclinic ZrOx phases, whereas hexagonal and cubic ZrN phases, from absorber layer, have not been observed for these thermally treated samples in air. These studies suggest that thermal treatment may lead to the loss of ZrN phase in absorber, degrading the thermal response for the desired wavelength range in open ambient conditions in contrast to vacuum conditions. © 2016, Springer-Verlag Berlin Heidelberg.