Department of Mathematics

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Cadmium telluride (CdTe) quantum dots are integrated with mesoporous titanium dioxide “TiO2” electrode using an in-situ sensitization approach for the first time, where water soluble N-Acetyl Cysteine capped CdTe quantum dots (diameter 4–5 nm) are grown hydrothermally inside mesoporous TiO2 electrode matrix. This in-situ sensitization approach has shown the effective sensitization over the conventional reported sensitization processes. The in-situ CdTe sensitized TiO2 electrodes are further unified with PbS counter electrode to realize the quantum dot sensitized solar cell (QDSSC). The fabricated CdTe QDSSC has shown the optimal short circuit current density 3.35 ± 0.21 mA/cm2 and open circuit voltage 0.58 ± 0.01 V. The observed current density is the highest among such cell configurations, reported till date. The in-situ sensitized CdTe QDs are further treated with zinc sulfide for surface passivation to realize the reduced back recombination, if any. These ZnS passivated CdTe QDs sensitized solar cells in similar device configurations resulted into the significant reduction in the short circuit current density (20%) with the minimal change in open circuit voltage (5%). The impedance spectroscopy measurements suggest that the transmission resistance “Rtr” has increased after ZnS treatment for these electrodes, however, the recombination resistance Rrec has not changed much. The observed high Rtr might be responsible for the observed current deterioration after ZnS surface passivation. These studies suggest that in-situ QD sensitization may provide a new method of integrating QDs into mesoporous TiO2 matrix for effective QDSSC device performance without any additional surface passivation. © 2018 Elsevier Ltd

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Department of Physics

Solar Energy

A novel process for sensitization and infiltration of quantum dots in mesoporous metal oxide matrix for efficient solar photovoltaics response

In this work, absorption properties of spatially disordered metamaterials are analysed using numerical simulations. For this purpose, position randomness is introduced in a supercell, which transforms a periodic metamaterial structure into a random metamaterial structure, where the constituent resonators are interacting with each other. It is demonstrated that the disorder can be used to enhance the absorption bandwidth. This enhancement is obtained due to the coupling among the nearby resonators, which results in broadening of collective resonance. The proposed disordered metamaterial absorbers also exhibit polarisation-insensitivity and have wide-band absorption for both normal and oblique incidences, which makes them a promising candidate for a variety of applications. © 2018 IEEE.

2018 IEEE Indian Conference on Antennas and Propagation, InCAP 2018

Effect of Position Randomness on Absorption Bandwidth of Disordered Metamaterial Absorbers

This article concerns about the existence and multiplicity of weak solutions for the following nonlinear doubly nonlocal problem with critical nonlinearity in the sense of Hardy–Littlewood–Sobolev inequality {(−Δ)su=λ|u|q−2u+(∫Ω[Formula presented]dy)|u|2μ ⁎−2uinΩ(−Δ)sv=δ|v|q−2v+(∫Ω[Formula presented]dy)|v|2μ ⁎−2vinΩu=v=0inRn∖Ω where Ω is a smooth bounded domain in Rn, n&gt;2s, s∈(0,1), (−Δ)s is the well known fractional Laplacian, μ∈(0,n), 2μ ⁎=[Formula presented] is the upper critical exponent in the Hardy–Littlewood–Sobolev inequality, 1&lt;q&lt;2 and λ,δ&gt;0 are real parameters. We study the fibering maps corresponding to the functional associated with (Pλ,δ) and show that minimization over suitable subsets of Nehari manifold renders the existence of at least two non trivial solutions of (Pλ,δ) for suitable range of λ and δ. © 2018 Elsevier Inc.}, author_keywords={Choquard equation; Fractional Laplacian; Hardy–Littlewood–Sobolev critical exponent; Nonlocal operator}, funding_details={Indo-French Centre for Applied MathematicsIndo-French Centre for Applied Mathematics, IFCAM, UMI CNRS 3494}, funding_text_1={The authors were funded by IFCAM (Indo-French Centre for Applied Mathematics) UMI CNRS 3494 under the project “Singular phenomena in reaction diffusion equations and in conservation laws”.}, references={Alves, C.O., Figueiredo, M.G., Yang, M., Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity (2016) Adv. Nonlinear Anal., 5 (4), pp. 331-345; Alves, C.O., Gao, F., Squassina, M., Yang, M., Singularly perturbed critical Choquard equations (2017) J. Differential Equations, 263, pp. 3943-3988; Applebaum, D., Lévy processes—from probability to finance and quantum groups (2004) Notices Amer. Math. Soc., 51 (11), pp. 1336-1347; Bonanno, C., D'Avenia, P., Ghimenti, M., Squassina, M., Soliton dynamics for the generalized Choquard equations (2014) J. Math. Anal. Appl., 417, pp. 180-199; Buffoni, B., Jeanjean, L., Stuart, C.A., Existence of a nontrivial solution to a strongly indefinite semilinear equation (1993) Proc. Amer. Math. Soc., 119 (1), pp. 179-186; Chen, Y.-H., Liu, C., Ground state solutions for non-autonomous fractional Choquard equations (2016) Nonlinearity, 29, pp. 1827-1842; Chen, W., Squassina, M., Critical nonlocal systems with concave-convex powers (2016) Adv. Nonlinear Stud., 16 (4), pp. 821-842; Choi, W., On strongly indefinite systems involving the fractional Laplacian (2015) Nonlinear Anal., 120, pp. 127-153; D'Avenia, P., Siciliano, G., Squassina, M., On fractional Choquard equations (2015) Math. Models Methods Appl. Sci., 25 (8), pp. 1447-1476; D'Avenia, P., Siciliano, G., Squassina, M., Existence results for a doubly nonlocal equation (2015) São Paulo J. Math. Sci., 9 (2), pp. 311-324; Fan, H., Multiple positive solutions for a fractional elliptic system with critical nonlinearities (2016) Bound. Value Probl., 2016, p. 196; Faria, L.F.O., Miyagaki, O.H., Pereira, F.R., Squassina, M., Zhang, C., The Brezis–Nirenberg problem for nonlocal systems (2015) Adv. Nonlinear Anal., 5 (1), pp. 85-103; Gao, F., Yang, M., On nonlocal Choquard equations with Hardy–Littlewood–Sobolev critical exponents (2017) J. Math. Anal. Appl., 448 (2), pp. 1006-1041; Gao, F., Yang, M., On the Brezis–Nirenberg type critical problem for nonlinear Choquard equation (2018) Sci. China Math., 61 (7), pp. 1219-1242; Ghimenti, M., Van Schaftingen, J., Nodal solutions for the Choquard equation (2016) J. Funct. Anal., 271, pp. 107-135; Ghimenti, M., Moroz, V., Schaftingen, J.V., Least action nodal solutions for the quadratic Choquard equation (2017) Proc. Amer. Math. Soc., 145 (2), pp. 737-747; Giacomoni, J., Mishra, P.K., Sreenadh, K., Critical growth fractional elliptic systems with exponential nonlinearity (2016) Nonlinear Anal., 136, pp. 117-135; Giacomoni, J., Mukherjee, T., Sreenadh, K., Positive solutions of fractional elliptic equation with critical and singular nonlinearity (2017) Adv. Nonlinear Anal., 6 (3), pp. 327-354; Guo, Z., Luo, S., Zou, W., On critical systems involving frcational Laplacian (2017) J. Math. Anal. Appl., 446 (1), pp. 681-706; He, X., Squassina, M., Zou, W., The Nehari manifold for fractional systems involving critical nonlinearities (2016) Commun. Pure Appl. Anal., 15 (4), pp. 1285-1308; Lieb, E., Loss, M., Analysis (2001) Graduate Studies in Mathematics, , AMS Providence, Rhode Island; Lü, D., Xu, G., On nonlinear fractional Schrödinger equations with Hartree-type nonlinearity (2018) Appl. Anal., 97 (2), pp. 255-273; Molica Bisci, G., Radulescu, V.D., Servadei, R., Variational Methods for Nonlocal Fractional Problems (2016) Encyclopedia of Mathematics and Its Applications, , Cambridge University Press Cambridge; Moroz, V., Schaftingen, J.V., A guide to the Choquard equation (2017) J. Fixed Point Theory Appl., 19 (1), pp. 773-813; Mukherjee, T., Sreenadh, K., Critical growth fractional elliptic problem with singular nonlinearities (2016) Electron. J. Differential Equations, 54, pp. 1-23; Ros-Oton, X., Nonlocal equations in bounded domains: a survey (2016) Publ. Mat., 60, pp. 3-26; Ros-Oton, X., Serra, J., The extremal solution for the fractional Laplacian (2014) Calc. Var., 50, pp. 723-750; Servadei, R., Valdinoci, E., The Brezis–Nirenberg result for the fractional Laplacian (2015) Trans. Amer. Math. Soc., 367 (1), pp. 67-102; Shen, Z., Gao, F., Yang, M., Multiple solutions for nonhomogeneous Choquard equation involving Hardy–Littlewood–Sobolev critical exponent (2017) Z. Angew. Math. Phys.; Silvestre, L., Regularity of the obstacle problem for a fractional power of the Laplace operator (2007) Comm. Pure Appl. Math., 60, pp. 67-112; Tarantello, G., On nonhomogeneous elliptic equations involving critical Sobolev exponent (1992) Ann. Inst. H. Poincaré Anal. Non Linéaire, 9, pp. 281-304; Wang, K., Wei, J., On the uniqueness of solutions of a nonlocal elliptic system (2016) Math. Ann., 365 (1-2), pp. 105-153; Xiang, M., Zhang, B., Rădulescu, V.D., Existence of solutions for perturbed fractional p-Laplacian equations (2016) J. Differential Equations, 260 (2), pp. 1392-1413; Zhang, X., Zhang, B., Xiang, M., Ground states for fractional Schrödinger equations involving a critical nonlinearity (2016) Adv. Nonlinear Anal., 5 (3), pp. 293-314}, correspondence_address1={Giacomoni, J.; Université de Pau et des Pays de l'Adour, avenue de l'université, France; email: jacques.giacomoni@univ-pau.fr}, publisher={Academic Press Inc.}, issn={0022247X}, language={English}, abbrev_source_title={J. Math. Anal. Appl.}, document_type={Article}, source={Scopus},

Fulltext

Journal of Mathematical Analysis and Applications

Doubly nonlocal system with Hardy–Littlewood–Sobolev critical nonlinearity

A new design approach that enhances the bandwidth of conventional Salisbury Screen (SS) microwave absorber is investigated. The absorber comprises of, wire metamaterial printed on FR4 substrate, placed on the top of the SS. The SS consists of 50 Ω/sq resistive sheet placed on the metal backed dielectric spacer. The theoretical analysis indicates the bandwidth of SS for −10 dB reflection is 41.1% using FR4 as a spacer for the optimum sheet resistivity of 308 Ω/sq. The proposed absorber shows the bandwidth of 53.5% (8.9–15.4 GHz) for −10 dB reflection. The thickness of the absorber is 0.15 λL (lowest cut-off frequency for −10 dB reflection). The FR4 substrate with SS works as Jaumann configuration and introduces an additional resonance mode. The selective overlapping of resonant mode excited by wire metamaterial and the additional resonance mode enhances the bandwidth of the absorber. The wire metamaterial is physically realized using low-cost screen printing technique. The good agreement between the simulated and measured data has been observed. © 2018 Wiley Periodicals, Inc.

Microwave and Optical Technology Letters

Bandwidth enhancement of Salisbury screen microwave absorber using wire metamaterial

A simple and implementable design approach is investigated to improve the bandwidth of the Triple Layer Microwave Absorber (TLMA) using metallic square patches. The TLMA consists of a metal sheet, FR4 substrate, a resistive sheet of 100 Ω/sq, and FR4 substrate. The total thickness of TLMA is 6.13 mm. The fractional bandwidth for − 10 dB reflection for TLMA is 81.8% (7–16.7 GHz) which is attributed to the formation of Jaumann configuration. In contrast, the fractional bandwidth of 100% (5.6–16.8 GHz) for − 10 dB reflection is observed in the metallic square patch-based TLMA with nearly the same thickness of the TLMA. The improved bandwidth is attributed to the overlapping of the resonant mode excited by Jaumann configuration and additional mode introduced due to the metallic square patches. The good degree of correlation is observed between simulation and measurement data. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Applied Physics A: Materials Science and Processing

Bandwidth enhancement of triple layer microwave absorber using metallic square patch

Journal of Mathematical Analysis

A Variant of SQCQP Descent Scheme for Multi-objective Optimization Problem

We study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self-maps on a compact space X. We derive necessary and suﬃcient conditions for the system to exhibit complex dynamical behavior. In the process we discuss properties like transitivity, weakly mixing, topologically mixing, minimality, sensitivity, topological entropy, and Li-Yorke chaoticity for the non-autonomous system. We also give examples to prove that the dynamical behavior of the nonautonomous system in general cannot be characterized in terms of the dynamical behavior of its generating functions. © 2017 Topology Proceedings.

Topology Proceedings

Dynamics of non-autonomous discrete dynamical systems

We carried out a detailed balance calculation of quantum dot sensitized solar cell based on widely used TiO2 as electron transport material and polysulfide electrolyte as hole transport material, considering the finite electrochemical potential level for these layers. The findings suggest that detailed balance efficiency decreases much faster for higher band gap quantum dots absorber as compared to that of ideal electron and hole transport layers. The detailed balance efficiency values are close to 20% without carrier multiplication for Eg near exciplex quantum dots, closer to experimental observation with finite Ediff limitation and without considering carrier multiplication, much smaller than the ideal case, which is close to 30% for ideal open circuit voltage. Thus, the present study shows the impact of limited/finite electron and hole transport material energy levels in designing QDSSCs, towards more realistic photovoltaic efficiency values. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Limiting efficiency factors and their consequences on quantum dot sensitized solar cells: a detailed balance study

We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously. © Applied Probability Trust 2018.

Journal of Applied Probability

On optimal operational sequence of components in a warm standby system

In this paper, a novel image encryption technique is proposed based on reference sets with some prime numbers and polar decomposition. In this technique, a primary secret key and reference sets are used in the generation of feature vector using a recursive random number generation (RRNG) process. This feature vector is then used for encryption process. Finally, a reliable decryption process has been presented to reconstruct the original image. The Simulated results demonstrate the efficiency and robustness of the proposed technique. © 2018 IEEE.