Cross-correlation-aided transport in stochastically driven accretion flows

Abstract

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers [Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a "cold" accretion flow at 3000 K is too "hot" in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Arrested states in persistent active matter: Gelation without attraction

“…We study a model of hard-core particles on the square lattice with exclusion up to third nearest-neighbors [31,34,[37][38][39]. Each particle can be represented as a hard, cross-shaped object occupying five lattice sites, see Fig.…”

“…(b) The cross at the central site (green) is prevented from rotating by the presence of neighboring crosses occupying the fourth and fifth nearest-neighbor sites. a lattice that exhibits a first-order transition from a fluid to solid phase, with coexistence of fluid at density ρ fluid ≈ 0.16 with a crystalline solid at ρ solid ≈ 0.19 [31,34,[37][38][39]. There are 10 distinct sublattice orderings possible for the crystalline packings.…”

“…2. In the passive limit, this is the simplest lattice-gas that exhibits a finite-density first-order transition from a fluid phase to a sublattice-ordered phase with tenfold symmetry [31]. The sublattice-ordered states can be further grouped into right-handed and left-handed chiral or- 1: (a)-(f) Snapshots of the system obtained at the end of simulations runs, t max = 2 × 10 6 .…”

Three stable phases and thermodynamic anomaly in a binary mixture of hard particles

“…The ordering transition in these hard-LGs is usually studied considering molecules which exclude up to their kth nearest-neighbors (NN) -the so-called kNN models. These are discrete versions of hard disks and hard spheres in two-and threedimensions, respectively, which have been numerically investigated for a broad range of k's on the square (see 2,3 and refs. therein) and simple cubic lattices 4 .…”

Thermodynamic behavior of binary mixtures of hard spheres: Semianalytical solutions on a Husimi lattice built with cubes

“…For larger k's, discussions on the behavior can be found in Refs. [22,25] for the square and [23] for the cubic lattice.…”