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

A generalization of the economic order quantity (EOQ) model is taken into account to study the memory effect in the inventory model. Fractional calculus is one of the efficient medium to establish the existence of memory effect in the economic system. This paper deals with a system of two fractional order differential equations to govern the fractional order EOQ model with partial backlogging. The fractional order differential equation is considered here in Caputo sense. The theory of memory kernel is applied to set up the memory dependent EOQ model. Using primal geometric programming method, analytical solution of the proposed problem is found. Using empirical values of the system parameters, we have established the concept of short and long memory effect. It is clear from the investigations that the strength of memory can be controlled by the order of fractional derivative or integration. Sensitivity analysis has been carried out for long memory and short memory affected problem both to identify the important model parameters for different situations. Finally, the manuscript is concluded with some recommendation about the memory dependent EOQ model. © 2020 Elsevier Ltd

World University root node

Computers and Industrial Engineering

Study of memory effect in an inventory model for deteriorating items with partial backlogging

Synchronized firing of neurons is considered as one of the crucial characteristics for signal transmission and neuronal coding. In this article, spatiotemporal synchronization of coupled chaotic Chialvo maps is studied over a network where the connection topology changes at every time instance with chaotically changing rewiring probability. However, the main objective of this study is to investigate the effect of time delay in the ensemble behavior of neurons. As it is well known that delay is unavoidable in neuronal system, we introduce a delay parameter in the coupling term. Examining the bifurcation diagrams, we observe interesting changes in the synchronization behavior with the increment of delay. These results are complemented by the linear stability analysis of the synchronized state of the system using master stability function technique. Moreover, effects of time delay on synchronization behavior of the coupled system are investigated by evaluating average synchronization error and synchronization time. We observe non-monotonic variation of synchronization time with respect to coupling strength for non-delayed system, whereas this characteristic does not persist with the increment of delay. It is observed that the synchronized region of the considered model appears as a combination of homogeneous steady state and homogeneous chaotic state for both delayed and non-delayed systems. Our key finding in this study is the enhancement of synchronized chaotic region and consequently reduction of synchronized steady state with the increasing values of time delay in the system. Global stability of the synchronized state is examined by basin stability measure. It is also observed that depending on different values of delay, the system exhibits various spatiotemporal patterns. © 2020, Springer Nature B.V.

Nonlinear Dynamics

Enhancement of synchronized chaotic state in a delay-coupled complex neuronal network

Nonlinear properties of ion-acoustic waves (IAWs) are studied in electron-ion (EI) degenerate plasma with the electron exchange-correlation effects by using the quantum hydrodynamic (QHD) model. To investigate arbitrary amplitude IAWs, we have reduced the model equations into a system of ordinary differential equations using a traveling wave transformation. Computational investigations have been performed to examine the combined effect of Bohm potential and exchange-correlation potential significantly modifies the dynamics of IAWs by employing the concept of dynamical systems. The equilibrium points of the model are determined and its stability natures are analyzed. The phase portrait and Poincaré return map of the dynamical system are displayed numerically. Quasiperiodic as well as chaotic dynamics of the system are confirmed through the Poincaré return map diagrams. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Nonlinear dynamics of ion-acoustic waves in quantum plasmas with exchange-correlation effects

In this article, we are proposing a model of anisotropic compact star possessing density profile of pseudo-isothermal dark matter satisfying a linear equation of state (EoS). The stellar system supported by this density profile is physically possible and in equilibrium fulfilling all the energy conditions including the TOV-equation. The solution also satisfies the causality condition, static stability criterion, Abreu’s stability and Bondi’s criteria. The fulfillment of Rhoades–Ruffini criterion makes our solution more physically viable as well. The M–R curve is plotted for b= 12.55 km and Bg= 60 MeV/fm3. © 2020, The Author(s).

Fulltext

European Physical Journal C

Relativistic compact stars with dark matter density profile

The analysis for wave attenuation by multiple thin porous walls submerged in water of uniform finite depth is carried out under the acceptance of linear theory of water waves. Two different types of barrier configurations are considered, namely partially immersed walls and bottom-standing walls. A set of coupled Fredholm-type integral equations are obtained for the boundary value problem by employing Havelock's inversion formulae and continuity of water wave potential across the gap below or above the walls. The methodology adopted to solve these integral equations is multi-term Galerkin's approximation with Chebychev's polynomials as a set of basis functions multiplied by suitable weights. Also, the square-root singularity of fluid velocity at the edge of the porous walls is precisely handled. The numerical results are depicted for reflection and transmission coefficients, dissipation of wave energy and dynamic wave force against wavenumber for different parametric values involving in the barrier configurations. This theory demonstrates that the dynamic wave forces exerted on the porous walls are reduced significantly as the magnitude of the porous effect parameter is increased. The present study is ratified with the existing results in the literature of water waves for a single as well as double rigid barriers and single porous barrier. © 2020 Elsevier Ltd

Ocean Engineering

Wave attenuation by multiple thin vertical porous walls in water of uniform finite depth

In this paper, the propagation of time-harmonic plane waves is investigated in an infinite elastic solid material by employing the modified Green–Lindsay (MGL) model of generalized thermoelasticity. It is found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type (SV-type) wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the thermoelastic coupling effect. In contrast to the Green–Lindsay (GL) as well as the Lord–Shulman (LS) models, the SV-type wave is not only dispersive in nature but also experiences attenuation. Reflection phenomenon of an incident coupled longitudinal wave from stress-free and thermally insulated boundary surface of a thermoelastic solid half-space is addressed. Using these boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, reflection coefficients and their respective energy ratios. The characteristics of employing the MGL model are discussed by comparing the numerical results obtained for the present model with those obtained in the case of the GL model. © 2020, © 2020 Taylor & Francis Group, LLC.

Journal of Thermal Stresses

Waves in magneto-thermoelastic solids under modified Green–Lindsay model

The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. © 2019 John Wiley &amp; Sons, Ltd.

Mathematical Methods in the Applied Sciences

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

In search of the scenario of the star formation process, fragmentation of molecular clouds has been modelled under two different conditions. In the first case, thermal instability along with an equation of state with negative polytropic indices (n) has been considered which give rise to minimal fragment masses in the range 0.001M⊙ to 8.5 M⊙ for −10 &lt; n &lt; 0, n≠−1. In the second case, an opacity limited fragmentation along with positive polytropic indices is considered which lead to a wide range of minimal fragment masses resulting in field stars, massive stars, and star bursts. This might be due to the effect of opacity which is responsible for slow dissipation of heat in a compressed medium. © 2018 Elsevier B.V.

GENERAL

New Astronomy

Fragmentation of molecular cloud in a polytropic medium

The present article deals with the investigation of the propagation of thermoelastic plane harmonic waves in a nonlocal thermoelastic medium. The Green and Naghdi theory II (without energy dissipation) of generalized thermoelasticity with elastic nonlocal effect is adopted to address this problem. The problem of reflection of thermoelastic waves due to an incident coupled longitudinal elastic wave from the rigid and thermally insulated boundary of a homogeneous, isotropic nonlocal thermoelastic half-space is also studied. The amplitude ratios of the reflected waves and their respective energy ratios are determined analytically. For a particular model, the effect of elastic nonlocality parameter on the variations of phase speeds, attenuation coefficients, amplitude ratios and corresponding energy ratios of the reflected waves is presented graphically and analysis of these results is given. © 2019, © 2019 Taylor & Francis Group, LLC.

Waves in nonlocal thermoelastic solids of type II

The problem of oblique water wave scattering by two vertical porous barriers with submerged gaps of different widths in infinitely deep water is investigated within the framework of two dimensional linearized potential theory. Using one-term Galerkin approximations, the reflection and transmission coefficients are evaluated involving definite integral. By employing Green’s integral theorem, amount of energy dissipation is derived for the permeable barriers. The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump, on the porous barriers. These hydrodynamic quantities are represented graphically against wave number in a number of figures. The derived result will coincide analytically and graphically with the results already present in the literature for some special cases. The problem of diffraction of oblique water wave by two nonidentical submerged porous barriers is studied and the results are presented as a special case. © 2019, Springer Nature B.V.