arXiv subjects

S. Sridhar

Publications and source records attributed to S. Sridhar.

At least 19 recordsLinked to original sources

arXiv2026

Turbulent Convection: Modal Equations and Energy Pathways

We present a framework for studying high Rayleigh number turbulent convection to better understand stellar and planetary convection zones. Utilizing the statistical symmetries of the fully developed turbulent state of Boussinesq convection, we identify relevant mean and fluctuating quantities. After validating these symmetry assumptions through numerical simulations, we formulate the governing equations. Vertical profiles of key physical quantities in the saturated turbulent state are explored in the simulations. To develop a modal theory, we use Fourier expansions, review linear theory, and use the Craya-Herring velocity decomposition. The modal equations we derive describe high Rayleigh-number turbulent convection dynamics self-consistently in terms of nonlinear interactions between three mode types: growing gravity modes, decaying gravity modes, and horizontal modes. Energy extracted by the growing modes from the superadiabatic background subsequently follows multiple pathways toward dissipation, enabled by the mode couplings. Among these, the traditionally dominant pathway is the turbulent cascade of the growing modes themselves. Reduced modal equations capture this pathway, precisely describing (i) mutual interactions between growing modes, and (ii) the excitation of decaying and horizontal modes, which are subordinate to the growing modes. Determining the relative efficiency of the pathways requires investigating their modal spectra using numerical simulations and kinetic models.

astro-ph.SR↗

arXiv2025

MeerKAT observations of the spiral galaxy NGC 2997 in the S band. Detection of high dynamo modes

We seek to exploit the expanded observational range of the MeerKAT radio telescope with the new S-band receivers (2.0-2.8 GHz). To showcase its enhanced capabilities, we conducted new S-band observations of the galaxy NGC 2997 in full polarization. The S band is ideal for studying magnetic fields in spiral galaxies due to the weak Faraday depolarization. Performing a rotation measure (RM) synthesis allowed us to measure Faraday RMs in the galaxy, a signature of regular magnetic fields. A fast Fourier transform (FFT) algorithm was used to study the various azimuthal modes found in the RM data of the galaxy. The RM synthesis analysis indicates the direction of the magnetic field along the line of sight throughout the entire disk. Leveraging the sensitivity and high resolution provided by MeerKAT's S-band capability, this study achieves an unprecedented level of detail of the magnetic field structure. Our sector-based analysis of the RMs across azimuthal regions reveals the existence of modes of the large-scale magnetic field in NGC 2997. The variations in the RM values along the azimuthal angle reveal smoothly changing phase shifts between the rings, without the previously reported field reversal at about 3 kpc radius between the central region and disk. In this work, for the first time, a Fourier analysis has been applied to RM data averaged in sectors of rings in the disk plane of a spiral galaxy. Our Fourier analysis of the RM map shows three different large-scale field modes detected in the disk of NGC 2997. After applying a geometric modification, even multiples of the first mode were detected, as predicted from theoretical studies of dynamo action in a spiral galaxy with symmetric spiral structure. Our new method opens up new possibilities for investigating magnetic fields in spiral galaxies.

astro-ph.GA↗

arXiv2023

Fibroblast mediated dynamics in diffusively uncoupled myocytes -- a simulation study using 2-cell motifs

In healthy hearts myocytes are typically coupled to nearest neighbours through gap junctions. Under pathological conditions such as fibrosis, or in scar tissue, or across ablation lines myocytes can uncouple from their neighbours. Electrical conduction may still occur via fibroblasts that not only couple proximal myocytes but can also couple otherwise unconnected regions. We hypothesise that such coupling can alter conduction between myocytes via introduction of delays or by initiation of premature stimuli that can potentially result in reentry or conduction blocks. To test this hypothesis we have developed several $2$-cell motifs and investigated the effect of fibroblast mediated electrical coupling between uncoupled myocytes. We have identified various regimes of myocyte behaviour that depend on the strength of gap-junctional conductance, connection topology, and parameters of the myocyte and fibroblast models. These motifs are useful in developing a mechanistic understanding of long-distance coupling on myocyte dynamics and enable the characterisation of interaction between different features such as myocyte and fibroblast properties, coupling strengths and pacing period. They are computationally inexpensive and allow for incorporation of spatial effects such as conduction velocity. They provide a framework for constructing scar tissue boundaries and enable linking of cellular level interactions with scar induced arrhythmia.

q-bio.TO↗

arXiv2019

Frequency gradients in heterogeneous oscillatory media can spatially localize self-organized wave sources that coordinate system-wide activity

Rhythmogenesis, which is critical for many biological functions, involves a transition to coherent activity through cell-cell communication. In the absence of centralized coordination by specialized cells (pacemakers), competing oscillating clusters impede this global synchrony. We show that spatial symmetry-breaking through a frequency gradient results in the emergence of localized wave sources driving system-wide activity. Such gradients, arising through heterogeneous inter-cellular coupling, may explain directed rhythmic activity during labor in the uterus despite the absence of pacemakers.

nlin.AO↗

arXiv2019

Renewal of Transient Spiral Modes in Disk Galaxies

Spiral structure in disk galaxies could arise from transient modes that create conditions conducive for their regeneration; this is the proposal of Sellwood and Carlberg, based on simulations of stellar disks. The linear response of an axisymmetric stellar disk, to an adiabatic non-axisymmetric transient mode, gives a final distribution function (DF) that is equal to the initial DF everywhere in phase space, except at the Lindblad and corotation resonances where the final DF is singular. We use the nonlinear theory of adiabatic capture into resonance to resolve the singularities and calculate the finite changes in the DF. These take the form of axisymmetric "scars" concentrated around resonances, whose DFs have simple general forms. Global changes in the physical properties are explored for a cool Mestel disk: we calculate the DFs of scars, and estimate the changes in the disk angular momentum, surface density and orbital frequencies leading to shifts of resonances. Resonant torques between disk stars and any new linear non-axisymmetric mode are suppressed within a scar, as is epicyclic heating. Since all the resonances of a linear mode with the same angular wavenumber and pattern speed as its precursor lie inside the scars of the precursor, it suffers less damping. Hence, scars filter the spectrum of noise-generated modes, promoting the renewal of a few select modes. Relic scars sustained by a galaxy disk, due to past tidal interaction with a passing companion, may still be active enablers of non-axisymmetric modes, such as the two-armed "grand design" spiral patterns.

astro-ph.GA↗

arXiv2018

Generation of large-scale magnetic fields due to fluctuating $α$ in shearing systems

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan-Moffatt model of zero-mean stochastic fluctuations of the $α$ parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the $α$-statistics. This enables construction of a model that is non-perturbative in the shearing rate $S$ and the $α$-correlation time $τ_α$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero $τ_α$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, Shear and a non-zero correlation time. Of particular interest is dynamo action when the $α$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large scale dynamo action with growth rate $γ\propto |S|$.

astro-ph.GA↗

arXiv2018

Stalling of Globular Cluster Orbits in Dwarf Galaxies

We apply the Tremaine-Weinberg theory of dynamical friction to compute the orbital decay of a globular cluster (GC), on an initially circular orbit inside a cored spherical galaxy with isotropic stellar velocities. The retarding torque on the GC, T(rp) < 0 , is a function of its orbital radius rp . The torque is exerted by stars whose orbits are resonant with the GC's orbit, and given as a sum over the infinitely many possible resonances by the Lynden-Bell Kalnajs (LBK) formula. We calculate the LBK torque T(rp) and determine rp(t), for a GC of mass Mp = 2 x 10^5 M_sun and an Isochrone galaxy of core mass Mc = 4 x 10^8 M_sun and core radius b = 1000pc. (i) When rp > 300 pc many strong resonances are active and, as expected, T = T_C , the classical Chandrasekhar torque. (ii) For rp < 300 pc, T comes mostly from stars nearly co-rotating with the GC, trailing or leading it slightly; Trailing resonances exert stronger torques. (iii) As rp decreases the number and strength of resonances drop, so |T| also decreases, with |T| < 10^{-2} |T_C| at rp = r* = (Mp/Mc)^{1/5} b = 220 pc , a characteristic `filtering' radius. (iv) Many resonances cease to exist inside r* ; this includes all Leading and low-order Trailing ones. (v) The higher-order Trailing resonances inside r* are very weak, with |T| < 10^{-4} |T_C| at rp = 150 pc. (vi) Inspiral times for rp(t) to decay from 300 pc to r* far exceed 10 Gyr.

astro-ph.GA↗

arXiv2018

Deformation of the Galactic Centre stellar cusp due to the gravity of a growing gas disc

The nuclear star cluster surrounding the massive black hole at the Galactic Centre consists of young and old stars, with most of the stellar mass in an extended, cuspy distribution of old stars. The compact cluster of young stars was probably born in situ in a massive accretion disc around the black hole. We investigate the effect of the growing gravity of the disc on the orbits of the old stars, using an integrable model of the deformation of a spherical star cluster with anisotropic velocity dispersions. A formula for the perturbed phase space distribution function is derived using linear theory, and new density and surface density profiles are computed. The cusp undergoes a spheroidal deformation with the flattening increasing strongly at smaller distances from the black hole; the intrinsic axis ratio ~ 0.8 at ~ 0.15 pc. Stellar orbits are deformed such that they spend more time near the disc plane and sample the dense inner parts of the disc; this could result in enhanced stripping of the envelopes of red giant stars. Linear theory accounts only for orbits whose apsides circulate. The non-linear theory of adiabatic capture into resonance is needed to understand orbits whose apsides librate. The mechanism is a generic dynamical process, and it may be common in galactic nuclei.

astro-ph.GA↗

arXiv2018

Secular Instabilities of Keplerian Stellar Discs

We present idealized models of a razor-thin, axisymmetric, Keplerian stellar disc around a massive black hole, and study non-axisymmetric secular instabilities in the absence of either counter-rotation or loss cones. These discs are prograde mono-energetic waterbags, whose phase space distribution functions are constant for orbits within a range of eccentricities (e) and zero outside this range. The linear normal modes of waterbags are composed of sinusoidal disturbances of the edges of distribution function in phase space. Waterbags which include circular orbits (polarcaps) have one stable linear normal mode for each azimuthal wavenumber m. The m = 1 mode always has positive pattern speed and, for polarcaps consisting of orbits with e < 0.9428, only the m = 1 mode has positive pattern speed. Waterbags excluding circular orbits (bands) have two linear normal modes for each m, which can be stable or unstable. We derive analytical expressions for the instability condition, pattern speeds, growth rates and normal mode structure. Narrow bands are unstable to modes with a wide range in m. Numerical simulations confirm linear theory and follow the non-linear evolution of instabilities. Long-time integration suggests that instabilities of different m grow, interact non-linearly and relax collisionlessly to a coarse-grained equilibrium with a wide range of eccentricities.

astro-ph.GA↗

arXiv2017

Plane shearing waves of arbitrary form: exact solutions of the Navier-Stokes equations

We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin's investigations into linearized disturbances in an unbounded Couette flow. We obtain explicit formulae for all three components of a Kelvin mode in terms of elementary functions. We then prove that Kelvin modes with parallel (though time-dependent) wave vectors can be superposed to construct the most general plane transverse shearing wave. An explicit solution is given, with any specified initial orientation, profile and polarization structure, with either unbounded or shear-periodic boundary conditions.

astro-ph.GA↗

arXiv2016

When the clock strikes: Modeling the relation between circadian rhythms and cardiac arrhythmias

It has recently been observed that the occurrence of sudden cardiac death has a close statistical relationship with the time of day, viz., ventricular fibrillation is most likely to occur between 12 am-6 am, with 6 pm-12 am being the next most likely period. Consequently there has been significant interest in understanding how cardiac activity is influenced by the circadian clock, i.e., temporal oscillations in physiological activity with a period close to 24 hours and synchronized with the day-night cycle. Although studies have identified the genetic basis of circadian rhythms at the intracellular level, the mechanisms by which they influence cardiac pathologies are not yet fully understood. Evidence has suggested that diurnal variations in the conductance properties of ion channel proteins that govern the excitation dynamics of cardiac cells may provide the crucial link. In this paper, we investigate the relationship between the circadian rhythm as manifested in modulations of ion channel properties and the susceptibility to cardiac arrhythmias by using a mathematical model that describes electrical activity in ventricular tissue. We show that changes in the channel conductance that lead to extreme values for the duration of action potentials in cardiac cells can result either in abnormally high-frequency reentrant activity or spontaneous conduction block of excitation waves. Both phenomena increase the likelihood of wavebreaks that are known to initiate potentially life-threatening arrhythmias. Thus, disruptive cardiac excitation dynamics are most likely to occur in time-intervals of the day-night cycle during which the channel properties are closest to these extreme values, providing an intriguing relation between circadian rhythms and cardiac pathologies.

q-bio.TO↗

arXiv2016

Stellar Dynamics around a Massive Black Hole I: Secular Collisionless Theory

We present a theory in three parts, of the secular dynamics of a (Keplerian) stellar system of mass $M$ orbiting a black hole of mass $M_\bullet \gg M$. Here we describe the collisionless dynamics; Papers II and III are on the (collisional) theory of Resonant Relaxation. The mass ratio, $\varepsilon = M/M_\bullet \ll 1$, is a natural small parameter implying a separation of time scales between the short Kepler orbital periods and the longer orbital precessional periods. The collisionless Boltzmann equation (CBE) for the stellar distribution function (DF) is averaged over the fast Kepler orbital phase using the method of multiple scales. The orbit-averaged system is described by a secular DF, $F$, in a reduced phase space. $F$ obeys a secular CBE that includes stellar self-gravity, general relativistic corrections up to 1.5 post-Newtonian order, and external sources varying over secular times. Secular dynamics, even with general time dependence, conserves the semi-major axis of every star. This additional integral of motion promotes extra regularity of the stellar orbits, and enables the construction of equilibria, $F_0$, through a secular Jeans theorem. A linearized secular CBE determines the response and stability of $F_0$. Spherical, non-rotating equilibria may support long-lived, warp-like distortions. We also prove that an axisymmetric, zero-thickness, flat disc is secularly stable to all in-plane perturbations, when its DF, $F_0$, is a monotonic function of the angular momentum at fixed energy.

astro-ph.GA↗

arXiv2016

Stellar Dynamics around a Massive Black Hole II: Resonant Relaxation

We present a first-principles theory of Resonant Relaxation (RR) of a low mass stellar system orbiting a more massive black hole (MBH). We first extend the kinetic theory of Gilbert (1968) to include the Keplerian field of a black hole of mass $M_\bullet$. Specializing to a Keplerian stellar system of mass $M \ll M_\bullet$, we use the orbit-averaging method of Sridhar & Touma (2015; Paper I) to derive a kinetic equation for RR. This describes the collisional evolution of a system of $N \gg 1$ Gaussian Rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 PN and 1.5 PN relativistic effects of the MBH and an arbitrary external potential. In general geometries RR is driven by both apsidal and nodal resonances, so the distinction between scalar-RR and vector-RR disappears. The system passes through a sequence of quasi-steady secular collisionless equilibria, driven by irreversible 2-Ring correlations that accrue through gravitational interactions, both direct and collective. This correlation function is related to a `wake function', which is the linear response of the system to the perturbation of a chosen Ring. The wake function is easier to appreciate, and satisfies a simpler equation, than the correlation function. We discuss general implications for the interplay of secular dynamics and non-equilibrium statistical mechanics in the evolution of Keplerian stellar systems toward secular thermodynamic equilibria, and set the stage for applications to the RR of axisymmetric discs in Paper III.

astro-ph.GA↗

arXiv2016

Stellar Dynamics around a Massive Black Hole III: Resonant Relaxation of Axisymmetric Discs

We study the Resonant Relaxation (RR) of an axisymmetric low mass (or Keplerian) stellar disc orbiting a more massive black hole (MBH). Our recent work on the general kinetic theory of RR is simplified in the standard manner by ignoring the effects of `gravitational polarization', and applied to a zero-thickness, flat, axisymmetric disc. The wake of a stellar orbit is expressed in terms of the angular momenta exchanged with other orbits, and used to derive a kinetic equation for RR under the combined actions of self-gravity, 1 PN and 1.5 PN relativistic effects of the MBH and an arbitrary external axisymmetric potential. This is a Fokker-Planck equation for the stellar distribution function (DF), wherein the diffusion coefficients are given self-consistently in terms of contributions from apsidal resonances between pairs of stellar orbits. The physical kinetics is studied for the two main cases of interest. (1) `Lossless' discs in which the MBH is not a sink of stars, and disc mass, angular momentum and energy are conserved: we prove that general H-functions can increase or decrease during RR, but the Boltzmann entropy is (essentially) unique in being a non-decreasing function of time. Therefore secular thermal equilibria are maximum entropy states, with DFs of the Boltzmann form; the two-Ring correlation function at equilibrium is computed. (2) Discs that lose stars to the MBH through an `empty loss-cone': we derive expressions for the MBH feeding rates of mass, angular momentum and energy in terms of the diffusive flux at the loss-cone boundary.

astro-ph.GA↗

arXiv2016

Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.

q-bio.TO↗

arXiv2015

Designer dynamics through chaotic traps: Controlling complex behavior in driven nonlinear systems

Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is achieved by a state-dependent dynamical selection of the input signal applied to the driven nonlinear system. An emergent property of the trapping process is that the signal changes in a chaotic sequence: a manifestation of chaos-induced order. The simplicity of the control scheme makes it easily implementable in experimental systems.

nlin.CD↗

arXiv2015

Migration into a Companion's Trap: Disruption of Multiplanet Systems in Binaries

Most exoplanetary systems in binary stars are of S--type, and consist of one or more planets orbiting a primary star with a wide binary stellar companion. Gravitational forcing of a single planet by a sufficiently inclined binary orbit can induce large amplitude oscillations of the planet's eccentricity and inclination through the Kozai-Lidov (KL) instability. KL cycling was invoked to explain: the large eccentricities of planetary orbits; the family of close--in hot Jupiters; and the retrograde planetary orbits in eccentric binary systems. However, several kinds of perturbations can quench the KL instability, by inducing fast periapse precessions which stabilize circular orbits of all inclinations: these could be a Jupiter--mass planet, a massive remnant disc or general relativistic precession. Indeed, mutual gravitational perturbations in multiplanet S--type systems can be strong enough to lend a certain dynamical rigidity to their orbital planes. Here we present a new and faster process that is driven by this very agent inhibiting KL cycling. Planetary perturbations enable secular oscillations of planetary eccentricities and inclinations, also called Laplace--Lagrange (LL) eigenmodes. Interactions with a remnant disc of planetesimals can make planets migrate, causing a drift of LL mode periods which can bring one or more LL modes into resonance with binary orbital motion. The results can be dramatic, ranging from excitation of large eccentricities and mutual inclinations to total disruption. Not requiring special physical or initial conditions, binary resonant driving is generic and could have profoundly altered the architecture of many S--type multiplanet systems. It can also weaken the multiplanet occurrence rate in wide binaries, and affect planet formation in close binaries.

astro-ph.EP↗

arXiv2015

Beyond Thomas--Fermi analysis of the density profiles of a miscible two-component Bose--Einstein condensate

We investigate a harmonically trapped two-component Bose--Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra- and inter-species interactions. We derive analytically a universal equation for the density around the different boundaries in one, two and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas--Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas--Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.

cond-mat.quant-gas↗