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

Purpose: Free vibrations of non-homogenous (functionally graded material (FGM)) axisymmetric nonlocal thermoelastic hollow sphere has been taken into consideration for investigation. The material of nonlocal thermoelastic sphere is supposed to be graded using power law in radial direction. Methods: The solution of continued power series is employed to resolve the differential equations and to investigate the analytical solutions for field functions i.e. temperature, stress and displacement. Results and Conclusions: The analytical results have been authenticated using numerical computations with computer based software like MATLAB. The numerical results have been shown graphically for the comparison of frequency shift and thermoelastic damping for local and nonlocal elastic materials. Deduction of results has been validated with the already published literature. © 2020, Krishtel eMaging Solutions Private Limited.

World University root node

Journal of Vibration Engineering and Technologies

On the Analysis of Free Vibrations of Nonlocal Elastic Sphere of FGM Type in Generalized Thermoelasticity

In this research article, we consider a tri-trophic food chain model with one prey and two predators such as- prey, intermediate predator and top predator. In this model, the prey and intermediate predator follows non-monotonic functional response; top predator consumes prey and intermediate predator following Holling type I functional response. The positivity, boundedness of solutions of the proposed model and stability conditions of different equilibrium points are discussed here. Then using Center Manifold theorem, the nature of non-hyperbolic type equilibrium points are discussed. After that, different local bifurcations such as- Saddle-node, Transcritical and Hopf bifurcations are studied theoretically as well as numerically by considering half-saturation constant and death rate of intermediate predator as the bifurcation parameters. Finally, the dynamics of the proposed model has been illustrated with the help of some numerical simulations. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

International Journal of Applied and Computational Mathematics

Study of Stability and Bifurcation of Three Species Food Chain Model with Non-monotone Functional Response

In this paper, the semi-inverse method is applied to derive the Lagrangian of the 5αth Korteweg de Vries equation (KdV). Then the time and space differential operators of the Lagrangian are replaced by corresponding fractional derivatives. The variation of the functional of this Lagrangian is devoted to lead the fractional Euler Lagrangian via Agrawal's method, which gives the space-time fractional KdV equation. Jumarie derivative is used to obtain the space-time fractional KdV equations. The homotopy analysis method (HAM) is applied to solve the derived space-time fractional KdV equation. Then numerical solutions are compared with the known analytical solutions by tables and figures. © 2021 World Scientific Publishing Company.

International Journal of Computational Methods

Approximate Solution of Homogeneous and Nonhomogeneous 5 α th-Order Space-Time Fractional KdV Equations

Abstract: Weakly nonlinear ion acoustic wave group dynamics at critical non-thermal parameter is investigated in the frame work of Gardner equation in non-thermal plasmas. Also the wave modulation due to self-interactions near the critical parameter is investigated by a nonlinear Schrödinger equation. The non-thermal parameter modifies the wave dispersion and the parameter space of wave modulation. At the boundary of this parameter space, the wave group dynamics is shown to be governed by a modified nonlinear Schrödinger equation. These equations are solved numerically with the help of a pseudo-spectral scheme and the solutions predict a wide class of nonlinear structures related to wave and wave group dynamics of the weakly nonlinear wave. The numerical solutions and the growth rate of the modified nonlinear Schrödinger equation confirm that the ion acoustic wave is modulationally unstable near the marginal state. The results are discussed in the context of astrophysical observations in auroral region. Graphic abstract: [Figure not available: see fulltext.] © 2021, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.

European Physical Journal D

Ion acoustic wave group dynamics near critical non-thermal parameter in non-thermal plasmas

The propagation dynamics of nonlinear electron acoustic waves (EAW) are explored analytically and numerically in collisionless unmagnetized plasmas. The dynamics of the nonlinear wave is shown to be governed by a Boussinesq equation. In the supersonic range, the wave becomes unstable in the short wave limit. In the nonlinear stage, this unstable mode reaches a maximum values and after that it damps. Different limiting cases of the general solutions are discussed. Analytical and computational results predict that the nonlinear EAW possesses breather structures apart from the usual solitary wave solutions. The results are discussed in the context of astrophysical plasmas. © 2021 Elsevier B.V.

Physics Letters, Section A: General, Atomic and Solid State Physics

Nonlinear coherent structures of electron acoustic waves in unmagnetized plasmas

This paper presents the solution for the problem of oblique wave diffraction by the thick barriers in the presence of surface tension. Two different barrier configurations are considered namely, (i) bottom standing thick rectangular barrier, (ii) thick rectangular block. Reflection and transmission coefficients are evaluated by applying an appropriate multi-term Galerkin approximation technique. The basis functions are chosen in terms of the Gegenbauer polynomial of order 1/6 with suitable weights. For each configuration, reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying surface tension. The numerical solutions are compared with known results without the effect of surface tension. Thus, good agreement of the results implies the correctness of the present method. The effect of surface tension at the free surface is investigated by analyzing the reflection and transmission coefficients. It can be observed that surface tension plays a qualitatively relevant role in the present study. © 2021, Indian Association for the Cultivation of Science.

Indian Journal of Physics

Analysis of oblique wave diffraction by rectangular thick barrier in the presence of surface tension

A semi-analytical method is applied to investigate the propagation of flexural wave over multiple bottom-standing porous barriers with variable porosity beneath an ice cover under the assumption of linearised theory of water waves. Eigenfunction expansion method is used to express the velocity potential explicitly in terms of non-orthogonal eigenfunctions. Utilizing mode coupling relations satisfied by aforesaid eigenfunctions, the boundary value problem is reduced to a set of coupled Fredholm-type integral equations. These integral equations are solved by multi-term Galerkin’s method involving the Chebychev polynomials (multiplied by proper weights) as basis functions. The reflection and transmission coefficients, hydrodynamic forces and dissipated wave energy at the barriers are presented both analytically and graphically. A notable effect of the porosity of barriers and flexural rigidity of the ice cover on wave propagation is recorded. Bragg resonance of the flexural gravity waves due to the presence of four vertical porous barriers is observed and shown graphically. Efficiency of the present study is confirmed through a good agreement of the present results and the existing results available in the literature. © 2021, Springer Nature B.V.

Meccanica

Water wave propagation over multiple porous barriers with variable porosity in the presence of an ice cover

An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface. Reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable weights. The energy identity relation is derived by employing Green's integral theorem in the fluid region of the problem. Reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying several parameters. The correctness of the present method is confirmed by comparing the results available in the literature. The effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of parameters. It can be observed that surface tension plays a qualitatively relevant role in the present study. © 2020

Fulltext

Journal of Ocean Engineering and Science

Propagation of oblique water waves by an asymmetric trench in the presence of surface tension

The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases. © 2021 The Author(s). Published by Vilnius Gediminas Technical University.

Mathematical Modelling and Analysis

Use of galerkin technique to the rolling of a plate in deep water

The present work explores the origin of the formation of star clusters in our Galaxy and in the Small Magellanic Cloud (SMC) through simulated H-R diagrams and compare those with observed star clusters. The simulation study produces synthetic H-R diagrams through the Markov Chain Monte Carlo (MCMC) technique using the star formation history (SFH), luminosity function (LF), abundance of heavy metal (Z), and a big library of isochrones as basic inputs and compares them with observed H-R diagrams of various star clusters. The distance-based comparison between those two diagrams is carried out through two-dimensional matching of points in the color-magnitude diagram (CMD) after the optimal choice of bin size and appropriate distance function. It is found that in a poor medium of heavy elements (Z = 0.0004), the Gaia LF along with a mixture of multiple Gaussian distributions of the SFH may be the origin of formation of globular clusters (GCs). On the contrary, an enriched medium (Z = 0.019) is generally favored with the Gaia LF along with a double power law or Beta-type (i.e., unimodal) SFH, for the formation of globular clusters. For SMC clusters, the choice of an exponential LF and exponential SFH is the proper combination for a poor medium, whereas the Gaia LF with a Beta-type SFH is preferred for the formation of star clusters in an enriched medium. © 2021. The American Astronomical Society. All rights reserved.