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Sagar Chakraborty

Publications and source records attributed to Sagar Chakraborty.

At least 73 records · Page 4Linked to original sources
arXiv2017

Equivalent linearization finds nonzero frequency corrections beyond first order

We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the conservative anharmonic oscillators and the nonconservative van der Pol oscillator that are respectively paradigmatic systems for modeling center-type oscillatory states and limit cycle type oscillatory states. The choice of these systems is also prompted by the fact that first order frequency corrections may vanish for both these types of oscillators, thereby rendering the calculation of the higher order corrections rather important. The method presented herein is very general in nature and, hence, in principle applicable to any arbitrary periodic oscillator.

nlin.CD↗
arXiv2017

On the Helium fingers in the intracluster medium

In this paper we investigate the convection phenomenon in the intracluster medium (the weakly-collisional magnetized inhomogeneous plasma permeating galaxy clusters) where the concentration gradient of the Helium ions is not ignorable. To this end, we build upon the general machinery employed to study the salt finger instability found in the oceans. The salt finger instability is a form of double diffusive convection where the diffusions of two physical quantities---heat and salt concentrations---occur with different diffusion rates. The analogous instability in the intracluster medium may result owing to the magnetic field mediated anisotropic diffusions of the heat and the Helium ions (in the sea of the Hydrogen ions and the free electrons). These two diffusions have inherently different diffusion rates. Hence the convection caused by the onset of this instability is an example of double diffusive convection in the astrophysical settings. A consequence of this instability is the formation of the vertical filamentary structures having more concentration of the Helium ions with respect to the immediate neighbourhoods of the filaments. We term these structures as Helium fingers in analogy with the salt fingers found in the case of the salt finger instability. Here we show that the width of a Helium finger scales as one-fourth power of the radius of the inner region of the intracluster medium in the supercritical regime. We also determine the explicit mathematical expression of the criterion for the onset of the heat-flux-driven buoyancy instability modified by the presence of inhomogeneously distributed Helium ions.

astro-ph.GA↗
arXiv2016

Revisiting Evidence of Chaos in X-ray Light Curves: The Case of GRS 1915+105

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer. With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 makes it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed, keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.

astro-ph.HE↗
arXiv2016

Synchronizing noisy nonidentical oscillators by transient uncoupling

Synchronization is the process of achieving identical dynamics among coupled identical units. If the units are different from each other, their dynamics cannot become identical; yet, after transients, there may emerge a functional relationship between them -- a phenomenon termed "generalized synchronization." Here, we show that the concept of transient uncoupling, recently introduced for synchronizing identical units, also supports generalized synchronization among nonidentical chaotic units. Generalized synchronization can be achieved by transient uncoupling even when it is impossible by regular coupling. We furthermore demonstrate that transient uncoupling stabilizes synchronization in the presence of common noise. Transient uncoupling works best if the units stay uncoupled whenever the driven orbit visits regions that are locally diverging in its phase space. Thus, to select a favorable uncoupling region, we propose an intuitive method that measures the local divergence at the phase points of the driven unit's trajectory by linearizing the flow and subsequently suppresses the divergence by uncoupling.

nlin.CD↗
arXiv2016

Stability Analysis of Convection in the Intracluster Medium

We use the machinery usually employed for studying the onset of Rayleigh--Bénard convection in hydro- and magnetohydro-dynamic settings to address the onset of convection induced by the magnetothermal instability and the heat-flux-buoyancy-driven-instability in the weakly-collisional magnetized plasma permeating the intracluster medium. Since most of the related numerical simulations consider the plasma being bounded between two `plates' on which boundary conditions are specified, our strategy provides a framework that could enable a more direct connection between analytical and numerical studies. We derive the conditions for the onset of these instabilities considering the effects of induced magnetic tension resulting from a finite plasma beta. We provide expressions for the Rayleigh number in terms of the wave vector associated with a given mode, which allow us to characterize the modes that are first to become unstable. For both the heat-flux-buoyancy-driven-instability and the magnetothermal instability, oscillatory marginal stable states are possible.

physics.flu-dyn↗
arXiv2016

Stability of Rotating Self-Gravitating Filaments:Stability of Rotating Self-Gravitating Filaments: Effects of Magnetic Field

We have performed systemmatic local linear stability analysis on a radially stratified infinite self-gravitating cylinder of rotating plasma under the influence of magnetic field. In order to render the system analytically tractable, we have focussed solely on the axisymmetric modes of perturbations. Using cylindrical coordinate system, we have derived the critical linear mass density of a non-rotating filament required for gravitational collapse to ensue in the presence of azimuthal magnetic field. Moreover, for such filaments threaded by axial magnetic field, we show that the growth rates of the modes having non-zero radial wavenumber are reduced more strongly by the magnetic field than that of the modes having zero radial wavenumber. More importantly, our study contributes to the understanding of the stability property of rotating astrophysical filaments that are more often than not influenced by magnetic fields. In addition to complementing many relevant numerical studies reported the literature, our results on filaments under the influence of magnetic field generalize some of the very recent analytical works (e.g.,~\citet{jog2014}, etc.). For example, here we prove that even a weak magnetic field can play a dominant role in determining stability of the filament when the rotation timescale is larger than the free fall timescale. A filamentary structure with faster rotation is, however, comparatively more stable for the same magnetic field. The results reported herein, due to strong locality assumption, are strictly valid for the modes for which one can ignore the radial variations in the density and the magnetic field profiles.

astro-ph.GA↗
arXiv2016

Conservative perturbation theory for nonconservative systems

In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it can be applied only to a class of conservative systems, viz.,~Hamiltonian systems. In the process, we also find Hamiltonian structure for an important subset of Liénard system--- a paradigmatic system for modeling isolated and asymptotic oscillatory state. We discuss the possibility of extending our method to encompass even wider range of non-conservative systems.

math.CA↗
arXiv2015

Transient Uncoupling Induces Synchronization

Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently uncoupling them. Specifically, systems coupled only in a fraction of their state space may synchronize even if fully coupled they do not. Although, for many standard systems, coupling strengths need to be bounded to ensure synchrony, transient uncoupling removes this bound and thus enables synchronization in an infinite range of effective coupling strengths. The presented coupling scheme thus opens up the possibility to induce synchrony in (biological or technical) systems whose parameters are fixed and cannot be modified continuously.

nlin.CD↗
arXiv2013

The Stability of Weakly Collisional Plasmas with Thermal and Composition Gradients

Over the last decade, substantial efforts have been devoted to understanding the stability properties, transport phenomena, and long-term evolution of weakly-collisional, magnetized plasmas which are stratified in temperature. These studies have improved our understanding of the physics governing the intra-cluster medium (ICM), but assumed that ICM is a homogeneous. This, however, might not be a good approximation if heavy elements sediment in the inner region of the galaxy cluster. In this paper, we analyze the stability of a weakly-collisional, magnetized plane-parallel atmosphere which is stratified in both temperature and composition. This allows us to discuss for the first time the dynamics of weakly-collisional environments where heat conduction, momentum transport, and ion-diffusion are anisotropic with respect to the direction of the magnetic field. We show that, depending on the relative signs and magnitudes of the gradients in the temperature and the mean molecular weight, the plasma can be subject to a wide variety of unstable modes which include modifications to the magnetothermal instability (MTI), the heat-flux-driven buoyancy instability (HBI), and overstable gravity modes previously studied in homogeneous media. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented. Our findings suggest that the core insulation that results from the magnetic field configurations that arise as a natural consequence of the HBI, which would be MTI stable in a homogeneous medium, could be alleviated if the mean molecular weight gradient is steep enough, i.e., $(\nabla μ)/μ> (\nabla T)/T$. This study constitutes a first step toward understanding the interaction between magnetic turbulence and the diffusion of heavy elements in the ICM. (abridged)

astro-ph.HE↗
arXiv2012

Oscillators with Parametrically Excited Nonlinearity: Resonance, Anti-resonance and Switch

We discover presence of a hitherto unexplored type of resonance in a parametrically excited Van der Pol oscillator. The oscillator also possesses a state of anti-resonance. In the weak non-linear limit, we explain how to practically get a complete picture of different states of limiting oscillations present in the oscillator when the non-linear term therein is excited by an arbitrary $2π$ periodic function of time. We also illustrate how two such oscillators can be coupled to behave like a two-state switch allowing an sharp change of value of amplitude for stable oscillations from one constant to another.

nlin.CD↗
arXiv2012

Nelkin scaling for the Burgers equation and the role of high-precision calculations

Nelkin scaling, the scaling of moments of velocity gradients in terms of the Reynolds number, is an alternative way of obtaining inertial-range information. It is shown numerically and theoretically for the Burgers equation that this procedure works already for Reynolds numbers of the order of 100 (or even lower when combined with a suitable extended self-similarity technique). At moderate Reynolds numbers, for the accurate determination of scaling exponents, it is crucial to use higher than double precision. Similar issues are likely to arise for three-dimensional Navier--Stokes simulations.

nlin.CD↗
arXiv2011

The Stability of Dilute Plasmas with Thermal and Composition Gradients. I. The Slow Conduction Limit: Overstable Gravity Modes

We analyze the stability of a dilute plasma with thermal and composition gradients in the limit where conduction is slow compared to the dynamical timescale. We find necessary and sufficient conditions for stability when the background magnetic field is either parallel or perpendicular to the thermal and composition gradients that are parallel to the gravitational field. We provide approximate solutions for all the relevant modes involved, which are driven by gravity, conduction, and diffusion. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented.

astro-ph.CO↗
arXiv2010

Center or Limit Cycle: Renormalization Group as a Probe

Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing across disciplines. The technique will be shown to have a non-trivial ability of classifying the solutions into limit cycles and periodic orbits surrounding a center. Moreover, the methodology has a definite advantage over linear stability analysis in analyzing centers.

nlin.CD↗
arXiv2010

Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.

cond-mat.stat-mech↗
arXiv2010

Three-dimensional turbulent relative dispersion by the Gledzer-Ohkitani-Yamada shell model

We study pair dispersion in a three-dimensional incompressible high Reynolds number turbulent flow generated by Fourier transforming the dynamics of the Gledzer-Ohkitani-Yamada (GOY) shell model into real space. We show that GOY shell model can successfully reproduce both the Batchelor and the Richardson-Obukhov regimes of turbulent relative dispersion. We also study how the crossover time scales with the initial separations of a particle pair and compare it to the prediction by Batchelor.

physics.flu-dyn↗
arXiv2010

On two-dimensionalization of three-dimensional turbulence in shell models

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case.

nlin.CD↗
arXiv2009

Extended Self Similarity works for the Burgers equation and why

Extended Self-Similarity (ESS), a procedure that remarkably extends the range of scaling for structure functions in Navier--Stokes turbulence and thus allows improved determination of intermittency exponents, has never been fully explained. We show that ESS applies to Burgers turbulence at high Reynolds numbers and we give the theoretical explanation of the numerically observed improved scaling at both the infrared and ultraviolet end, in total a gain of about three quarters of a decade: there is a reduction of subdominant contributions to scaling when going from the standard structure function representation to the ESS representation. We conjecture that a similar situation holds for three-dimensional incompressible turbulence and suggest ways of capturing subdominant contributions to scaling.

nlin.CD↗