Sagar Chakraborty

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. While 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 therefore opens up the possibility to induce synchrony in (biological or technical) systems whose parameters are fixed and cannot be modified continuously.

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 IR and UV 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.

Why Does the Sun's Torsional Oscillation Begin before the Sunspot Cycle?

Although the Suns torsional oscillation is believed to be driven by the Lorentz force associated with the sunspot cycle, this oscillation begins 2-3 yr before the sunspot cycle. We provide a theoretical explanation of this with the help of a solar dynamo model having a meridional circulation penetrating slightly below the bottom of the convection zone, because only in such dynamo models does the strong toroidal field form a few years before the sunspot cycle and at a higher latitude.

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. The insights gained via these studies have led to a significant improvement of our understanding of the processes that determine the physical evolution and observational properties of the intracluster medium (ICM) permeating galaxy clusters. These studies have been carried out under the assumption that the ICM is a homogeneous medium. This, however, might not be a good approximation if heavy elements are able to sediment in the inner region of the galaxy cluster. Motivated by the need to obtain a more complete picture of the dynamical properties of the ICM, 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 also find that there are new modes which are driven by heat conduction and particle diffusion. 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., (∇μ)/μ > (∇T)/T. This study constitutes a first step toward understanding the interaction between magnetic turbulence and the diffusion of heavy elements, and its consequences for the long-term evolution and observational signatures of the ICM in galaxy clusters.

Center or limit cycle: renormalization group as a probe

Abstract 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.

Signatures of two-dimensionalisation of 3D turbulence in the presence of rotation

A reason has been given for the inverse energy cascade in the two-dimensionalised rapidly rotating 3D incompressible turbulence. For such system, the literature shows a possibility for the wave number exponent in the energy spectrums relation to lie between −2 and −3. We argue the existence of a stricter range of −2 to −7/3 for the exponent in the case of rapidly rotating turbulence which is in accordance with the recent experiments. Also, a derivation for the two-point third-order structure function has been provided helping one to argue that even with slow rotation one gets, though dominated, a spectrum with the exponent −2.87, thereby hinting at the initiation of the two-dimensionalisation effect with rotation.

Third-order structure function for rotating three-dimensional homogeneous turbulent flow

A form for the two-point third-order structure function has been calculated for three-dimensional (3D) homogeneous incompressible slowly rotating turbulent fluid. It has been argued that it may possibly hint at the initiation of the phenomenon of two-dimensionalization of the 3D incompressible turbulence owing to rotation.

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 an even wider range of nonconservative systems.

On the use of the Kolmogorov-Landau approach in deriving various correlation functions in two-dimensional incompressible turbulence

We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in two-dimensional (2D) isotropic homogeneous decaying turbulence. We adopt the more intuitive approach due to Kolmogorov (and subsequently Landau in his text on fluid dynamics) and show that how the 2D turbulence results, obtainable using other methods, may be established in a simpler way. Also, some experimentally verifiable correlation functions in the dissipation range have been derived for the same system. The paper also showcases the inability of the Kolmogorov-Landau approach to get the “one-eighth law” in the enstrophy cascade region. As discussed in the paper, this may raise the spectre of logarithmic corrections once again in 2D turbulence.

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 (RXTE). 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 make 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.