University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Applied Mathematics

The effects of the time delay on the stability of different synchronized states of a globally coupled network are investigated. Conditions for the stability of the synchronized fixed points, synchronized periodic orbits, or synchronized chaos in a network of globally coupled chaotic smooth maps over a ring lattice with a homogeneous delay are derived analytically. Our analysis reveals that the stability properties of the synchronized dynamics are significantly different for odd and even time delays. The conditions for the stability of a synchronized fixed point and synchronized period-2 orbits for both odd and even delays are determined analytically. The range of parameter values for the stability of synchronized chaos has been calculated for a unit delay. All theoretical results are illustrated with the help of numerical examples. © 2020 Author(s).

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Chaos

Effects of time delay on the synchronized states of globally coupled network

A novel approach is presented in this paper to predict the viscosity of nanofluids by developing a deep neural network (DNN) based smart generalized model. This study is conducted with a large experimental dataset containing Al2O3, CuO, SiO2, TiO2, Ag, and Fe2O3 nanoparticles and the DNN model is trained by Nadam optimization technique. This proposed DNN model has the learning capability of non-linearities from a training dataset automatically. The novelty of this study with the advantages of deep learning has been described in this paper. To the best of the author’s knowledge, deep learning-based model was never used to predict viscosity before. The detailed analysis of the performance of this DNN model shows that it performs better than any other existing model and overcomes all of their limitations. Also, it gives an excellent prediction on the unseen data and it takes very less amount of time to train this DNN model comparing to other traditional data-driven models. A sensitivity analysis of this smart model has also be presented. This novel DNN-based smart model can predict the viscosity of nanofluids with the highest level of accuracy with a coefficient determination 0.9999. © 2020 Satyasaran Changdar, Susmita Saha and Soumen De.

Smart Science

A smart model for prediction of viscosity of nanofluids using deep learning

The explicit solutions exist for normal incidence of the surface wave train or a single thin plane vertical barrier partially immersed or completely submerged in deep water. However, for oblique incidence of the wave train and/or for finite depth water, no such explicit solution is possible to obtain. Some approximate mathematical techniques are generally employed to solve them approximately in the sense that quantities of physical interest associated with each problem, namely the reflection and transmission coefficients, can be obtained approximately either analytically or numerically. The method of Galerkin approximations has been widely used to investigate such water wave scattering problems involving thin vertical barriers. Use of Galerkin method with basis functions involving somewhat complicated functions in solving these problems has been carried out in the literature. Choice of basis functions as simple polynomials multiplied by appropriate weights dictated by the edge conditions at the submerged end points of the barrier providing fairly good numerical estimates for the reflection and transmission coefficients have been demonstrated in this article. © 2020, Springer Nature Switzerland AG.

Studies in Systems, Decision and Control

Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

In this study, Bernstein polynomial approximation method is used to obtain the expressions of velocity, temperature, wall shear stress and stream function, to portray the transport characteristics of Newtonian gold-blood nanofluid flowing through stenosed artery in the presence of magnetic field. The impact of various flow parameters on velocity profile, wall shear stress and stream function is also investigated. The effect of nanoparticle volume fraction in the presence and absence of external magnetic field is studied. The results reveal that the temperature of the nanofluid and wall shearing stress are increased, whereas the velocity is decreased due to increase in the particle concentration in the presence of magnetic field. © 2020 Taylor & Francis Group, LLC.

International Journal for Computational Methods in Engineering Science and Mechanics

Study of nanoparticle as a drug carrier through stenosed arteries using Bernstein polynomials

Fractal dimension which is developed using linear regression method (area)-log(perimeter) gives the overall shape of the landscape patches relating to their internal structure while the individual patch provides the geometrical complexity that can be obtained using the modified definition of fractal dimension. Here we have considered north-western part of Orissa, India as the sampled landscape. The fractal dimension as obtained from linear regression method indicates wasteland and agriculture patches with low fractal value but the forest patches have high fractal dimension, i.e., forest patches are more fragmented compared to the other. The modified definition of fractal dimension gives high values of fractal dimension for all the landscape patches and consequently geometrical complexity is reflected. © 2020, Springer Nature Singapore Pte Ltd.

Lecture Notes in Mechanical Engineering

Characterization of Geometrical Complexity of the Landscape Patches Using Fractional Dimension

In this paper, we have developed and analyzed a deterministic Zika model considering both vector and sexual transmission route with the effect of human awareness and vector control in the absence of disease induce death. To formulate the model, we assume that the Zika virus is being first transmitted to human by mosquito bite, and then it is being transmitted to his or her sexual partner. The system contains at most three equilibrium points among them one is the disease free and other two are endemic equilibrium points, exists under certain conditions. The theoretical analysis shows that the diseases-free equilibrium is locally and globally asymptotically stable if the basic reproduction number is less than one. Theatrically we have established that endemic equilibrium point which is locally asymptotically stable if the basic reproduction number is greater than one. The system exhibits backward bifurcation when the transmission probability per biting of susceptible mosquito with infected humans crosses the critical value. We estimate the model parameters and validate the model by fitting the model with the reported Zika infected human data from 1 to 36 week of 2016 Zika outbreak in Colombia. Furthermore, using the normalised forward sensitivity index method we have established that the model parameter mosquito biting rate, recruitment rate of mosquito, transmission probability per biting of Susceptible (infected) humans with infected (susceptible) mosquito, rate of awareness in host population, recovery rates of infected human are most sensitive parameters of the considered Zika model. Lastly, some conclusions are given to control the spreading of the Zika disease. © 2019 The Authors

Infectious Disease Modelling

Mathematical model of zika virus dynamics with vector control and sensitivity analysis

In this article, the constitutive relations and the governing equations are derived for nonlocal thermoelastic solid in the presence of diffusion. The free vibration of a thermoelastic diffusive cylinder is investigated within the framework of the above newly derived model. Time-harmonic vibration is used to transform the governing equations into a system of ordinary differential equations. The frequency equation is taken under investigation for the survival of a range of possible modes in compact form for traction-free thermal boundary conditions: thermally insulated and isothermal boundary conditions. To explore the vibration analysis from frequency equations, we apply a numerical iteration technique for generating numerical data by taking assistance of the Matlab software. The numerically computed and simulated results for the frequency shift, natural frequency, and the thermoelastic damping are presented graphically. The effect of nonlocality on the above quantities is observed and shown graphically. © 2020, © 2020 Taylor & Francis Group, LLC.

Journal of Thermal Stresses

Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion

We investigate the thermoelastic interactions in an isotropic and homogeneous perfectly conducting two-dimensional semi-infinite elastic medium. The bounding surface of the medium is assumed as stress free and subjected to a time-dependent thermal shock. A new two-temperature generalized thermoelasticity theory with memory-dependent derivative is employed for this study. The combined Laplace–Fourier transforms are applied to solve the non-dimensional governing equations to find the solutions for the field variables in the transform domain. An application is considered to enable us to get complete solutions. Numerical results of the field variables are presented graphically to discuss the effect of various parameters of interest. © 2019, Indian Association for the Cultivation of Science.

Indian Journal of Physics

Two-dimensional problem of two-temperature generalized thermoelasticity using memory-dependent heat transfer: an integral transform approach

This is an attempt to design a dynamic model of nonlocal heat conduction in a nonlocal elastic bounded rod. This model is drafted using the Lord-Shulman theory of generalized thermoelasticity due to the involvement of one relaxation time to the heat conduction equation and the equation of motion. This model is then employed to discuss the thermal behavior of the rod when subjected to a moving heat source. Both ends of the rod are assumed to be rigidly fixed and thermally insulated. Analytical solutions for the distribution of temperature, displacement and thermal stresses are obtained using integral transform in the Laplace transform technique is used to obtain the analytical solutions for the field variables such as temperature, displacement and stress. The inverse Laplace transform based on the Zakian method is used to invert the results in the space-time domain. Specific attention is paid to study the effect of thermal nonlocal parameter and the velocity of the moving heat source on the distribution of the field variables. © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Thermoelastic responses of a nonlocal elastic rod due to nonlocal heat conduction

This paper aims to present the analysis of transient wave characteristics in a functionally graded viscothermoelastic infinite medium with spherical cavity in the context of generalized thermoelasticity. Continued series solution is used to solve simultanious differential equations for evaluating the field variables. Convergence of the series solution is implemented and investigated that the series of functions are absolutely and uniformly convergent. The formal solution for the field variables are obtained analytically and represented graphically. The effect of grading index and different theories of generalized thermoelasticity are also shown graphically to examine the behavior of the variations of the field variables. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.