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.

&nbsp;

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.

&nbsp;

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 analysis of free vibrations of a thermoelastic hollow sphere with voids is investigated under dual-phase-lag generalized thermoelasticity and Erigen’s nonlocal elasticity. By implementing the stress-free thermal boundary conditions, the frequency relation is obtained for possible modes in a compact form. Numerical iteration technique with the help of MATLAB is used for generating numerical data to determine free vibrations. The analytical results are presented graphically with the help of numerical computations and simulations. At the end, the frequency shift, and the thermoelastic damping with and without voids are presented graphically for various cases of interest and analyzed the results. © 2020 Taylor & Francis Group, LLC.

World University root node

Mechanics Based Design of Structures and Machines

Effect of dual-phase-lag model on free vibrations of isotropic homogenous nonlocal thermoelastic hollow sphere with voids

We explore the analysis of exact three-dimensional free vibrations of visco-thermoelastic solid cylinder, which has been considered at a uniform temperature and undeformed initially in the framework of generalized thermoelasticity. The formulation has been implemented with two relaxation time parameters, i.e., mechanical and thermal relaxation parameters. The series solution has been implemented to solve the differential equations along with the evaluation of stresses, displacements, and temperature by applying stress-free, rigidly fixed, thermally insulated and isothermal boundary conditions. The relations of frequency equations for the existence of different modes of visco-thermoelastic solid cylinder have been developed in compact form using assumed boundary conditions. Thermoelastic damping and frequency shift are presented graphically from the data generated by computations and simulations of numerical results. Also, the natural frequencies are represented in the form of tables which show that with an increase in the ratio of length to the radius and axial wave-number, the variation of vibrations keeps increasing. © 2020 Taylor & Francis Group, LLC.

Journal of Thermal Stresses

Analysis of three–dimensional free vibrations of isotropic visco-thermoelastic solid cylinder with two relaxation time parameters

D-dimensional fractional Klein–Gordon equation with fractional vector and scalar potential has been studied. Both fractional potentials are taken as attractive Coulomb-type with different multiplicative parameters, namely v and s. Jumarie-type definitions for fractional calculus have been used. We have succeeded in achieving Whittaker-type classical differential equation in fractional mode for the required eigenfunction. Fractional Whittaker equation has been manipulated using the behaviour of the eigenfunction at asymptotic distance and origin. This manipulation delivers fractional-type confluent hypergeometric equation to solve. Power series method has been employed to do the task. All the obtained results agree with the existing results in literature when fractional parameter α is unity. Finally, we furnish numerical results with a few eigenfunction graphs for different spatial dimensions and fractional parameters. © 2020, Indian Academy of Sciences.

Pramana - Journal of Physics

Analytical study of D-dimensional fractional Klein–Gordon equation with a fractional vector plus a scalar potential

The present novel coronavirus (SARS-CoV-2) infection has created a global emergency situation by spreading all over the world in a large scale within very short time period. But there is no vaccine, anti-viral medicine for such infection. So at this moment, a major worldwide problem is that how we can control this pandemic. On the other hand, India is high population density country, where the coronavirus infection disease (COVID-19) has started from 1 March 2020. Due to high population density, human to human social contact rate is very high in India. So controlling pandemic COVID-19 in early stage is very urgent and challenging problem of India. Mathematical models are employed to study the disease dynamics, identify the influential parameters and access the proper prevention strategies for reduction outbreak size. In this work, we have formulated a deterministic compartmental model to study the spreading of COVID-19 and estimated the model parameters by fitting the model with reported data of ongoing pandemic in India. Sensitivity analysis has been done to identify the influential model parameters. The basic reproduction number has been estimated from actual data and the effective basic reproduction number has been studied on the basis of reported cases. Some effective preventive measures and their impact have also been studied. Prediction are given on the future trends of the virus transmission under some control measures. Finally, the positive measures to control the disease have been summarized in the conclusion section. © 2020, Springer Nature B.V.

Fulltext

Nonlinear Dynamics

COVID-19 pandemic in India: a mathematical model study

Genuine steering is still not well understood enough in contrast to genuine entanglement and nonlocality. Here, we provide a protocol which can reveal genuine steering under some restricted operations compared to the existing witnesses of genuine multipartite steering. Our method has an impression of some sort of ‘hidden’ protocol in the same spirit of hidden nonlocality, which is well understood in bipartite scenario. We also introduce a genuine steering measure which indicates the enhancement of genuine steering in the final state of our protocol compared to the initial states. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Quantum Information Processing

Revealing genuine steering under sequential measurement scenario

Nonlinear evolution equations, correct up to fourth order in wave steepness, are derived for a pair of obliquely interacting wave packets in the presence of a thin pycnocline. These evolution equations are then employed to perform stability analysis of a pair of obliquely interacting uniform wave trains. Figures plotted here reveal that the growth rate of instability decreases with the increase in pycnocline depth and also with the increase in density difference across the pycnocline. When the angle of interaction between the two wave packets is less than certain critical value the growth rate of instability decreases with the increase in angle and beyond this critical value the result is reversed. © 2020 Elsevier Masson SAS

European Journal of Mechanics, B/Fluids

Modulational instability of two obliquely interacting waves in presence of a thin pycnocline

A generalized viscoelastic quantum hydrodynamic model is proposed for the dynamics of strongly correlated degenerate isothermal fluid. The quantum forces associated with the quantum diffraction effect along with the strong correlation effects are embedded in this transport equation through the viscoelastic relaxation of correlations. The collective dynamics of linear and nonlinear modes in such correlated degenerate fluid are also investigated. In the high-frequency oscillation (kinetic regime), the dynamics of the weakly nonlinear mode is found to be governed by a novel equation with a memory dependent non-local nonlinear term that describes the strong correlation effect. This novel equation is solved analytically and numerically. In the low-frequency oscillation (hydrodynamic regime), the weakly nonlinear mode is found to be governed by a Korteweg–de Vries Burgers' equation that exhibits dispersive shock wave. In both the dynamics, quantum diffraction introduces the dispersive effect. © 2021 Informa UK Limited, trading as Taylor & Francis Group.

Waves in Random and Complex Media

Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid

This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed. Copyright © 2020 by ASME.

Journal of Heat Transfer

Reflection of thermoelastic waves from the insulated surface of a solid half-space with time-delay

The present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient have been analysed. Two types of caps (for example, concave upwards and concave downwards) have been considered for the numerical results. The effect of the concavity on added mass and damping coefficient has also been studied. The present study should be helpful to understand the nature of waves generated by a heaving submerged body in an ice-covered ocean. © 2020 Oxford University Press. All rights reserved.

Quarterly Journal of Mechanics and Applied Mathematics

Radiation of waves by a thin cap submerged in ice-covered ocean

The problem of oblique water wave diffraction by three asymmetrically arranged vertical porous barriers with different widths in infinitely deep water is investigated. Reflection and transmission coefficients are evaluated, applying single-term Galerkin approximation. The amount of energy loss is derived employing Green's integral theorem. Wave force is determined using the linear Bernoulli equation of dynamic pressure jump, on the porous barriers. Forces and energy of the wave are studied to understand the effect of the dissipation of wave energy due to the presence porous barriers. Numerical results for the reflection coefficient, wave force, and wave energy dissipation are analysed graphically. The comparison of the numerical results are carried out for the validity of the derived solution. It is observed that porosity affects significantly on reflection coefficient and amount of energy dissipation. It is also found that more energy is dissipated if the permeability of the barriers is increased. © 2020 Informa UK Limited, trading as Taylor & Francis Group.