Department of Mathematics

&ldquo;IIT Jodhpur is committed to impart quality education to facilitate the creation of qualified, competent and responsible human resources to meet the emerging technological challenges of the world. It is working towards creating an equitable learning platform that is positive, accessible and effective in the face of the modern societal and scientific advancements.

Flexibility in curriculum, in all its academic programs, encompassing elements of teaching, research, creativity, innovation and entrepreneurship is the most unique feature of IIT Jodhpur. The Department of Science and Technology (DST), under the National Mission on Cyber Physical Systems, has identified IIT Jodhpur as a Technology &amp; Innovation Hub in the area of Augmented Reality and Virtual Reality. The institute has also been nominated as the coordinator for the Jodhpur City and Knowledge Cluster by the Office of Principal Scientific Adviser, Government of India.

The sprawling 852-acre IIT Jodhpur campus is a majestic tribute to the deep-rooted diverse cultural heritage of the region. The campus is an architectural masterpiece, which is slated to become an international exemplar of sustainability with net-zero energy, and advanced water and waste management strategies.&rdquo;

IIT Jodhpur

In this paper, we use adaptive wavelet collocation method (AWCM) to solve the 2D time domain Maxwell's equations. Our motivation of choosing AWCM is because it effectively adapts numerical grid points along moving signals according to the requirements of resolution levels of them. In the region where moving signals are intensive, there will be assigned more grid points; and in the region where signals are sparse, there will be arranged less grid points. Since signals are moving during time stepping, the grid changes dynamically at each time step. We verified that AWCM is an efficient method especially for problems in which signals are highly concentrated inside and guided through optical waveguides such as micro-ring resonators. © 2016 Elsevier GmbH

World University root node

Optik

Adaptive wavelet collocation method for simulation of a 2D micro-ring resonator

In this paper, we consider the Galerkin method to approximate the solution of Volterra-Urysohn integral equations of second kind with a smooth kernel, using piecewise polynomial bases. We show that the exact solution is approximated with the order of convergence O(hr) for the Galerkin method, whereas the iterated Galerkin solutions converge with the order O(h2r) in uniform norm, where h is the norm of the partition and r is the smoothness of the kernel. For improving the accuracy of the approximate solution of the integral equation, the multiGalerkin method is also discussed here and we prove that the exact solution is approximated with the order of convergence O(h3r) in uniform norm for iterated multi-Galerkin method. Numerical examples are given to illustrate the theoretical results. © Springer Nature Singapore Pte Ltd. 2017.

Communications in Computer and Information Science

Superconvergence results for volterra-urysohn integral equations of second kind

In this article, we study the following non-linear Choquard equation with singular non-linearity (Formula presented.) where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, n &gt; 2, λ &gt;0, 0 &lt; q &lt; 1, 0 &lt; μ &lt; n and 2*μ = 2n-μ/n-2. Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positive weak solutions of the above problem, if λ is less than some positive constant. We also study the regularity of these weak solutions. © 2017 Informa UK Limited, trading as Taylor & Francis Group.

Fulltext

Complex Variables and Elliptic Equations

Positive solutions for nonlinear Choquard equation with singular nonlinearity

In this paper, a novel logo watermarking framework is proposed using non-linear chaotic map. The essence of proposed technique is to use chaotic map to generate keys to be used in the embedding process. Therefore, a method for generating keys is first proposed followed by the embedding process. A robust extraction process is then proposed to verify the presence of watermark from the possibly attacked watermarked image. Experimental results and attack analysis reveal the efficiency and robustness of the proposed framework. © Springer Science+Business Media Singapore 2017.

Advances in Intelligent Systems and Computing

A novel chaos based robust watermarking framework

In this paper, a robust image hashing framework is proposed using image normalization, discrete wavelet transform and singular value decomposition. The stressed motive of the proposed scheme is to obtain a randomize hash sequence which can be used for image authentication and database search. For this purpose, the image is first normalized followed by hash generation in the wavelet domain utilizing the properties of singular value decomposition (SVD). Experimental evaluations demonstrate that the proposed scheme is providing the better robustness and security. © 2017 IEEE.

Proceedings of the 2017 IEEE International Conference on Signal and Image Processing Applications, ICSIPA 2017

A robust image hashing based on discrete wavelet transform

Thermal emittance is an important parameter for the solar thermal collectors as thermal radiative losses from the solar thermal collector increase to the fourth power of temperature. This should be minimized using infrared reflectors in designing spectrally selective absorber coatings for solar thermal applications. The thermal emittance of zirconium (Zr) film as an infrared reflector has been investigated for the use in the spectrally selective absorber. The Zr metallic films are deposited using DC magnetron sputtering process on stainless steel and glass substrates and the deposition process has been optimized to achieve the minimum thermal emittance. The effect of structural, microstructural and surface morphological properties of Zr films is investigated on the emittance of fabricated structures. The X-ray diffraction analysis revealed that the Zr film coatings consist of both cubic and hexagonal Zr crystallographic phase. The optimized deposition time and temperature showed 0.12 and 0.14 emittance values for Zr film coatings on stainless steel and glass substrates respectively. © 2017 Elsevier B.V.

Department of Mechanical Engineering

Department of Physics

Thin Solid Films

Optimization of sputtered zirconium thin films as an infrared reflector for use in spectrally-selective solar absorbers

In this paper, Galerkin method is applied to approximate the solution of Volterra integral equations of second kind with a smooth kernel, using piecewise polynomial bases. We prove that the approximate solutions of the Galerkin method converge to the exact solution with the order (Formula presented.) whereas the iterated Galerkin solutions converge with the order (Formula presented.) in infinity norm, where h is the norm of the partition and r is the smoothness of the kernel. We also consider the multi-Galerkin method and its iterated version, and we prove that the iterated multi-Galerkin solution converges with the order (Formula presented.) in infinity norm. Numerical examples are given to illustrate the theoretical results. © 2017 Korean Society for Computational and Applied Mathematics

Journal of Applied Mathematics and Computing

Superconvergence results for linear second-kind Volterra integral equations

We consider reaction-diffusion systems where some compo- i nents react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those 011 the boundary through mass transport. We establish criteria guaranteeing that solutions are uniformly bounded in time.

Differential and Integral Equations

Uniform bounds for solutions to volume-surface reaction diffusion systems

In this article, a wire based metamaterial absorber is capped with dielectric absorber to achieve bandwidth enhancement. The unit cell of the designed absorber consists of copper wires, placed on the metal back FR4 sheet and dielectric absorber is located on the top of wire elements. The simulated return loss shows two resonant modes, one due to the dielectric absorber and other due to wire based metamaterial absorber. By optimizing the design parameters, the resonant peaks are tailored to achieve a bandwidth of more than 6 GHz for 10 dB return loss in TE polarization. The electric field and power loss densities are plotted to present the origin of the absorption peaks. © 2017 IEEE.

2017 International Conference on Advances in Computing, Communications and Informatics, ICACCI 2017

Bandwidth enhancement of wire-based metamaterial absorber using dielectric cap

The effect of wall velocity slip on the stability of a pressure-driven two-dimensional asymmetric channel flow is examined by considering Navier slip condition on the channel walls. The two-parameter families of mean velocity profiles are considered to approximate the underlying asymmetric basic flow. Competing effects of skewness and maximum velocity on the stability of the flow are explored for a range of model parameters. The Orr-Sommerfeld system of the asymmetric flow is solved using a Chebyshev spectral collocation method for both symmetric and non-symmetric type slip boundary conditions. Numerical results indicate that moderate asymmetry in the basic flow has a significant role on the stability of the Poiseuille-kind parallel/nearly parallel flows. Wall slip shows a passive control on the instability of the asymmetric flow by increasing or decreasing the critical Reynolds number and the set of unstable wave numbers. The stabilizing/destabilizing effect of slip velocity on the flow instability is weak or strong depending on the presence of velocity slip at the upper or lower wall. Velocity slip has a profound grip on the flow behaviour by changing the shear rate inside the perturbed flow. © 2016 by the authors; licensee MDPI, Basel, Switzerland.