Pralay Karmakar - Academia.edu (original) (raw)

Papers by Pralay Karmakar

Physics Research International, Nov 10, 2011

Journal of physics, Feb 1, 2010

A plasma-based Gravito-Electrostatic Sheath (GES) model for theoretical description of the basic ... more A plasma-based Gravito-Electrostatic Sheath (GES) model for theoretical description of the basic physics of the surface emission mechanism of the quasi-neutral Solar Interior Plasma (SIP) on a bounded scale, and subsequently, its transonic transition into Solar Wind Plasma (SWP) on an unbounded scale with a simplified field-free fluid model approach has already been proposed. An autonomous closed set of self-consistently coupled nonlinear eigenvalue equations for analyzing the dynamical stability of the steady GES model on both the scales is developed. The focussed aim of the present contribution is only to study the electric current profiles associated with the SIP as well as SWP, and hence to investigate conservative dynamical features thereof. Applying the developed set of coupled nonlinear dynamical evolution equations, the profiles of electric currents associated with both SIP as well as SWP have been obtained numerically under a wide range spectrum of initial values of relevant physical parameters (by nonlinear stability analysis). Interestingly, it is conjectured that the dynamical evolution of solar electric currents is found fairly to be conservative (divergence-free) in nature except some deviations near the defined solar surface boundary. Results, discussions and conclusions on the basis of the obtained numerical results are presented in brief.

Astrophysics and Space Science, May 13, 2015

ABSTRACT In this paper we propose a gravito-electro-magnetic sheath (GEMS) model to explore the e... more ABSTRACT In this paper we propose a gravito-electro-magnetic sheath (GEMS) model to explore the equilibrium properties of the solar plasma system. It describes the solar interior plasma (SIP) on the bounded scale and the solar wind plasma (SWP) on the unbounded scale from the viewpoint of plasma-based theory. This differs from the previously reported gravito-electrostatic sheath (GES) model employed to precisely define the solar surface boundary (SSB) on the fact that the present investigation incorporates variable temperature, magnetic field and collisional processes on the solar plasma flow dynamics. We show that the included parameters play important roles in the solar plasma dynamics. We demonstrate that the SSB location shifts outward as a result of the magnetic field by 14 % in comparison with that predicted by the GES model. As a consequence of the interaction of the plasma with magnetic field, the width of the sheath broadens by 25 % in comparison with the GES model predicted value. This physically means that the magnetic field decreases the distribution of the tiny (inertialess) electrons relative to the massive (inertial) ions, which in turn increases the confining wall potential value resulting in the increased width. Besides, the sonic point moves inward by 8 % as a result of collisions in the SIP that leads to rapid acceleration. Here, collisional dynamics plays an important role in the conversion process of the electron thermal energy into the bulk plasma flow energy. An interesting feature of continuous and smooth transition of the electric current density from the SIP to the SWP (with finite positive divergence on both the scales) through the SSB under inhomogeneous temperature distribution is also reported. Finally, the analyses may be applied to understand the realistic equilibrium dynamics of stellar plasmas never addressed before within the earlier GES framework like establishment of current-field correlation, properties of the slow solar wind and its effects on the interaction mechanism with the magnetic field, heliospheric current sheet, etc.

Contributions To Plasma Physics, Jun 4, 2013

A theoretical evolutionary model for new nonlinear self-gravitational fluctuations associated wit... more A theoretical evolutionary model for new nonlinear self-gravitational fluctuations associated with the solar plasma system is developed. The lowest-order inertial correction of the plasma thermal electrons is considered. We try to present our calculation scheme leading to the fluctuation patterns evolving as a new class of nonlinear coherent structures. It is demonstrated that they are mainly monotonous shock-like eigenmodes governed by a unique type of driven Korteweg-de Vries Burger (d-KdVB) equation obtained by multiscale analysis over the gravito-electrostatic equilibrium structure equations. The self-consistent new and unique nonlinear driving source here appears due to the inclusion of weak electron inertia. The d-KdVB system is studied analytically, graphically and numerically in detail to show the detailed features of the eigenmodes. Our conclusions are in good qualitative agreement with multispace satellite and imaging detections made by others. Main results significant to diverse solar, stellar and other astrophysical contexts along with future directions are summarily highlighted.

Journal of Mathematical Physics, Mar 1, 2006

A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium... more A new idea of electron inertia-induced ion sound wave excitation for transonic plasma equilibrium has already been reported. In such unstable plasma equilibrium, a linear source driven Korteweg-de Vries (d-KdV) equation describes the nonlinear ion sound wave propagation behavior. By numerical techniques, two distinct classes of solution (soliton and oscillatory shocklike structures) are obtained. Present contribution deals with the systematic methodological efforts to find out its (d-KdV) analytical solutions. As a first step, we apply the Painleve method to test whether the derived d-KdV equation is analytically integrable or not. We find that the derived d-KdV equation is indeed analytically integrable since it satisfies Painleve property. Hirota’s bilinearization method and the modified sine-Gordon method (also termed as sine-cosine method) are used to derive the analytical results. Perturbative technique is also applied to find out quasistationary solutions. A few graphical plots are provided to offer a glimpse of the structural profiles obtained by different methods applied. It is conjectured that these solutions may open a new scope of acoustic spectroscopy in plasma hydrodynamics.

Physica Scripta, Nov 18, 2014

ABSTRACT An analytical model to explore the weakly nonlinear gravito-electrostatic waves in a fie... more ABSTRACT An analytical model to explore the weakly nonlinear gravito-electrostatic waves in a field-free polytropic dust molecular cloud on the astrophysical scales of space and time is proposed. The polytrope consists of the lighter electrons, ions and massive dust grains with full ionization. This is a nonthermalized situation due to the cold grains, and the mutually thermalized hot electrons and hot ions. A quasi-hydrostatic equilibrium in one-dimensional (1D, Cartesian) configuration is adopted with presumed global quasi-neutrality. The grain dynamics considered is such that exact gravito-electrostatic equilibrium is facilitated with their first-order perturbed self-gravitational potential. The analytical infrastructure is developed by a standard multi-scale analysis of stretched variables centered on the assumed initially ‘homogeneous’ equilibrium in accordance with the Jeans swindle. We derive a new gravito-electrostatically coupled pair of modified Korteweg–de Vries (m-KdV) equations having unique self-consistent nonlinear sources arising due to gravito-electrostatic intermixed coupling. A detailed numerical shape analysis of the fluctuations is carried out in order to see their parametric excitations as solitary spectral patterns. Interestingly, it is seen that the electrostatic fluctuations undergo bi-periodicity, while the self-gravitational counterparts retain uni-periodicity in phase space. Nontrivial aspects of the results relevant in space and astrophysical environments are summarily indicated.

Journal of Plasma Physics, Mar 14, 2016

The plasmas in space, cosmic and astrophysical environments are long known to consist of numerous... more The plasmas in space, cosmic and astrophysical environments are long known to consist of numerous massive ionic components contributing to various wave instability fluctuation phenomena. Indeed, the ion-inertial effects need to be incorporated into realistic analyses, rather than treating the gravitating ionic species traditionally as a Boltzmann distributed fluid. Herein, we present an atypical theoretical model setup to study gravito-electrostatic mode-fluctuations in self-gravitating inhomogeneous interstellar dust molecular clouds (DMCs) on the astrophysical fluid scales of space and time. The main goal is focused on investigating the influence of self-consistent dynamic ion-inertial effects on the stability. Methodological application of standard multiple scaling techniques reduces the basic plasma structure equations into a unique pair of decoupled Korteweg-de Vries (KdV) equations for the weak fluctuations. In contrast, the fully nonlinear counterparts are shown to evolve as a new gravito-electrostatically coupled pair of the Sagdeev energy-integral equations. In both the perturbation regimes, excitation of two distinct eigenmode classes-electrostatic compressive solitons and self-gravitational rarefactive solitons with unusual and unique parametric features-is demonstrated and portrayed. The graphical shape analysis reflects new plasma conditions for such eigenspectral patterns to coevolve in realistic interstellar parameter windows hitherto remaining unexplored. It is seen that the inertial ions play a destabilizing influential role leading to enhanced fluctuations toward establishing a reorganized gravito-electrostatic equilibrium structure. Finally, we discuss the consistency of our results in the framework of existing inertialess ion theories, experimental findings and multiple space satellite-based observations, together with new implications.

New Astronomy, Oct 1, 2015

A theoretical model is developed to study the equilibrium electromagnetic properties of a spheric... more A theoretical model is developed to study the equilibrium electromagnetic properties of a spherically symmetric dust molecular cloud (DMC) structure on the Jeans scale. It applies a technique based on the modified LaneEmden equation (mLEE). It considers an inhomogeneous distribution of dust grains in fieldfree hydrodynamic equilibrium configuration within the framework of exact gravitoelectrostatic pressure balancing condition. Although weak relative to the massive grains, but finite, the efficacious inertial roles of the thermal species (electrons and ions) are included. A full portrayal of the lowestorder cloud surface boundary (CSB) and associated parameter signatures on the Jeans scale is made numerically for the first time. The multiorder extremization of the mLEE solutions specifies the CSB at a radial point 12 10 58 8 ´. m relative to the centre. It gets biased negatively due to the interplay of plasmaboundary wall interaction (global) and plasma sheathsheath coupling (local) processes. The CSB acts as an interfacial transition layer coupling the bounded and unbounded scaledynamics. The geometrical patterns of the biscale plasma coupling are elaborately analyzed. Application of the proposed technique to neutron stars, other observed DMCs and double layers is stressed together with possible future expansion.

Waves in Random and Complex Media, Jun 1, 2023

Optical and Quantum Electronics, Jul 18, 2016

We report here the transmission characteristics of a step index multimode–single mode–multimode f... more We report here the transmission characteristics of a step index multimode–single mode–multimode fiber (MSM) optic integrated system. Owing to a good coupling between the fibers, the designed system reveals band-elimination filter characteristics. The variability of the stop-bandwidth for this system is incurred by altering the length and core diameter of the mid-single mode fiber. The observed stop band in the range of 80 nm, having good consistency with numerical results, is found to be dependent on the length of the mid-single mode fiber (SMF). Further, the core diameter of the SMF is also varied to tune the band eliminated output from the proposed MSM structure, which results in a narrow bandwidth of 50 nm, giving a margin of 30 nm with respect to the former. The attained results possess higher potential in the field of optical communications, such as a trimmer, etc.

Journal of physics, May 31, 2017

Pramana, Feb 6, 2021

The evolutionary dynamics of bimodal pulsational mode, arising because of the long-range conjugat... more The evolutionary dynamics of bimodal pulsational mode, arising because of the long-range conjugational gravito-electrostatic interplay in viscoelastic polytropic complex multicomponent astroclouds with partial ionisation, is classically examined using a non-relativistic generalised hydrodynamic model approach. The equilibrium distribution of the diversified constitutive species forms a globally quasi-neutral hydrostatic homogeneous configuration. The primitive set of the astrocloud structuring equations specifically includes polytropic (hydrodynamic action) and nonlinear logatropic barotropic (turbulence action) effects simultaneously. A normal mode analysis over the perturbed cloud results in a unique form of sextic polynomial dispersion relation with variable poly-parametric coefficients. A numerical analysis technique is provided to show the exact nature of the modified viscoelastic (turbo-viscoelastic) pulsational mode in the two extreme hydrodynamic and kinetic regimes. It is seen that, in the former regime, the dust–charge ratio (negatively-to-positively charged grains) plays a destabilising role to the instability. In contrast, the dust–mass ratio (negatively-to-positively charged grains) develops a stabilising influence in the wave-dynamical processes. In the latter regime, the viscoelastic relaxation velocity associated with the positively charged grains acts as an amplitude stabiliser. Conversely, the viscoelastic relaxation velocity of the negatively charged grain fluid introduces destabilising influences. The unique features of the propagatory and non-propagatory mode characteristics are elaborately illustrated. The reliability of the investigated results is judiciously validated by comparing the results with the specific reports available in the literature. Lastly, the first-hand astronomical implications and applications of our study are summarily outlined.

Contributions To Plasma Physics, Nov 3, 2016

The global nonlinear gravito-electrostatic eigen-fluctuation behaviors in large-scale non-uniform... more The global nonlinear gravito-electrostatic eigen-fluctuation behaviors in large-scale non-uniform complex astroclouds in quasi-neutral hydrodynamic equilibrium are methodologically analyzed. Its composition includes warm lighter electrons, ions; and massive bi-polar multi-dust grains (inertial) with partial ionization sourced, via plasma-contact electrification, in the cloud plasma background. The multi-fluidic viscous drag effects are conjointly encompassed. The naturalistic equilibrium inhomogeneities, gradient forces and nonlinear convective dynamics are considered without any recourse to the Jeans swindle against the traditional perspective. An inhomogeneous multiscale analytical method is meticulously applied to derive a new conjugated non-integrable coupled (via zeroth-order factors) pair of variable-coefficient inhomogeneous Korteweg de-Vries Burger (i-KdVB) equations containing unique form of non-uniform linear self-consistent gradient-driven sinks. A numerical illustrative scheme is procedurally constructed to examine the canonical fluctuations. It is seen that the eigenspectrum coevolves as electrostatic rarefactive damped oscillatory shock-like structures and self-gravitational compressive damped oscillatory shock-like patterns. The irregular damping nature is attributable to the i-KdVB sinks. The aperiodicity in the hybrid rapid small downstream wavetrains is speculated to be deep-rooted in the quasi-linear gravito-electrostatic interplay. The phase-evolutionary dynamics grow as atypical non-chaotic fixed-point attractors. We, finally, indicate tentative astronomical applications relevant in large-scale cosmic structure formation aboard facts and faults.

Astrophysics and Space Science, Apr 15, 2016

In this paper a generalized hydrodynamic (GH) model to investigate acoustic-mode excitation and s... more In this paper a generalized hydrodynamic (GH) model to investigate acoustic-mode excitation and stability in simplified strongly coupled bi-component plasma is proposed. The goal is centered in seeing the viscoelasticityinfluences on the instability properties. The dispersive and nondispersive features are methodologically explored followed by numerical illustrations. It is seen that, unlike usual plasma acoustic mode, here the mode stability is drastically modified due to the considered viscoelastic effects contributed from both the electronic and ionic fluids. For example, it is found that there exists an excitation threshold value on angular wavenumber, K ≈ 3 in the K-space on the Debye scale, beyond which only dispersive characteristic features prevail. Further, it is demonstrated that the viscoelastic relaxation time plays a stabilizing influential role on the wave dynamics. In contrast, it is just opposite for the effective viscoelastic relaxation effect. Consistency with the usual viscoelasticity-free situations, with and without plasma approximation taken into account, is also established and explained. It is identified and conjectured that the plasma fluid viscoelasticity acts as unavoidable dispersive agency in attributing several new characteristics to acoustic wave excitation and propagation. The analysis is also exploited to derive a quantitative glimpse on the various basic properties and dimensionless numbers of the viscoelastic plasma. Finally, extended implications of our results tentative to different cosmic, space and astrophysical situations, amid the entailed facts and faults, are highlighted together with indicated future directions.

EPL, May 20, 2019

We report the evolutionary dynamics of nonlinear nucleus-acoustic wave patterns excitable in a st... more We report the evolutionary dynamics of nonlinear nucleus-acoustic wave patterns excitable in a strongly coupled self-gravitating complex quantum degenerate plasma (QDP) systems. It is inertially composed of strongly correlated non-degenerate heavy nuclei and weakly coupled degenerate light nuclei treated classically. It is thermally constituted of non-relativistic and ultra-relativistic degenerate lighter electrons behaving quantum mechanically. Application of nonlinear perturbation analysis results in a conjugated pair of extended Korteweg-de Vries (e-KdV) equations of unique mathematical shape. The constructed numerical tapestry shows the collective excitations of a new conjugational pair of nonlinear eigenmode structures of gravito-electrosatic origin. The electrostatic potential fluctuations evolve as a distinct family of stable periodic symmetric waves resembling regular soliton-antisoliton pulse-trains; in contrast, the gravitational counterparts evolve as a unique extended class of asymmetric oscillatory solitons and non-monotonous compressive dispersive asymmetric pulse-trains. The microphysical influential dependencies of the eigenstructural patterns on various sensible plasma multi-parametric factors are illustratively analyzed in both the non-relativistic (NR) and ultra-relativistic (UR) limits of the non-local quantum electronic dynamics. The applicability of the explored results in wave kinetic phenomenological processes naturalistically relevant in diversified compact astro-objects and their ambient hydrodynamic atmospheres is summarily outlined

EPL, Nov 1, 2015

A generalized two-fluid model to study the equilibrium structure of plasma sheath in a normal two... more A generalized two-fluid model to study the equilibrium structure of plasma sheath in a normal two-component plasma with all the possible viscoelastic effects taken into account is methodologically constructed for the first time. It includes weak but finite (lowest-order) inertial correction of the plasma thermal electrons. The Bohm condition for the sheath formation in viscoelastically modified form is strategically derived and methodically tested for accuracy in exactly reproducing the earlier well-known results in idealized normal plasma conditions. A systematic strategy of numerical illustrations is presented to investigate the main characteristic features of the sheath structure. It is demonstrated that the sheath evolution is considerably affected by both plasma viscoelasticity and the active electron inertial dynamics. The results can be extensively useful to explore realistic plasma boundary-wall interaction processes via cross-border effects in the presence of correlative coordination encountered in diversified laboratory, starspace and other astrophysical environments.

European Physical Journal D, Sep 1, 2013

ABSTRACT We try to present a theoretical evolutionary model leading to the excitations of nonline... more ABSTRACT We try to present a theoretical evolutionary model leading to the excitations of nonlinear pulsational eigenmodes in a planar (1D) collisional dust molecular cloud (DMC) on the Jeans scale. The basis of the adopted model is the Jeans assumption of self-gravitating homogeneous uniform medium for simplification. It is a self-gravitating multi-fluid consisting of the Boltzmann distributed warm electrons and ions, and the inertial cold dust grains with partial ionization. Dust-charge fluctuations, convections and all the possible collisions are included. The grain-charge behaves as a dynamical variable owing mainly to the attachment of the electrons and ions to the grain-surfaces randomly. The adopted technique is centered around a mathematical model based on new solitary spectral patterns within the hydrodynamic framework. The collective dynamics of the patterns is governed by driven Korteweg-de Vries ( d-KdV) and Korteweg-de Vries (KdV) equations obtained by a standard multiscale analysis. Then, simplified analytical and numerical solutions are presented. The grain-charge fluctuation and collision processes play a key role in the DMC stability. The sensitive dependence of the eigenmode amplitudes on diverse relevant plasma parameters is discussed. The significance of the main results in astrophysical, laboratory and space environments are concisely summarized.

Journal of optics, Feb 16, 2012

We demonstrate here the quantum mechanical behavior of non-linear Faraday rotation exhibiting ste... more We demonstrate here the quantum mechanical behavior of non-linear Faraday rotation exhibiting steps with the support of experimental results. The step-like behavior, satisfying a well organized condition 1/θ0 (Kln)/h, is a consequence of resonant tunneling of magnetic moment. The degeneracy of quantum states arising from the projection of magnetic moments of the smaller sized quantum particles in adopting a series of discrete values, leads to 'Quantized Faraday effect'. Taking it into consideration, the Faraday Effect is studied through a non-local approach. The magnetodynamical equation is developed in magnetic space and solved analytically as well as numerically. The analytically obtained non-linear behavior of Faraday rotation is found to be in good agreement with the non-linear fit of the experimental result.