6,895 research outputs found
The runaway instability in general relativistic accretion disks
When an accretion disk falls prey to the runaway instability, a large portion
of its mass is devoured by the black hole within a few dynamical times. Despite
decades of effort, it is still unclear under what conditions such an
instability can occur. The technically most advanced relativistic simulations
to date were unable to find a clear sign for the onset of the instability. In
this work, we present three-dimensional relativistic hydrodynamics simulations
of accretion disks around black holes in dynamical space-time. We focus on the
configurations that are expected to be particularly prone to the development of
this instability. We demonstrate, for the first time, that the fully
self-consistent general relativistic evolution does indeed produce a runaway
instability.Comment: 5 pages, 3 figures, minor corrections to match published version in
MNRAS, +link to animatio
Ordering of small particles in one-dimensional coherent structures by time-periodic flows
Small particles transported by a fluid medium do not necessarily have to
follow the flow. We show that for a wide class of time-periodic incompressible
flows inertial particles have a tendency to spontaneously align in
one-dimensional dynamic coherent structures. This effect may take place for
particles so small that often they would be expected to behave as passive
tracers and be used in PIV measurement technique. We link the particle tendency
to form one-dimensional structures to the nonlinear phenomenon of phase
locking. We propose that this general mechanism is, in particular, responsible
for the enigmatic formation of the `particle accumulation structures'
discovered experimentally in thermocapillary flows more than a decade ago and
unexplained until now
Bifurcation and Chaos in Coupled Ratchets exhibiting Synchronized Dynamics
The bifurcation and chaotic behaviour of unidirectionally coupled
deterministic ratchets is studied as a function of the driving force amplitude
() and frequency (). A classification of the various types of
bifurcations likely to be encountered in this system was done by examining the
stability of the steady state in linear response as well as constructing a
two-parameter phase diagram in the () plane. Numerical explorations
revealed varieties of bifurcation sequences including quasiperiodic route to
chaos. Besides, the familiar period-doubling and crises route to chaos
exhibited by the one-dimensional ratchet were also found. In addition, the
coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of
bifurcations. Chaotic behaviour is characterized by using the sensitivity to
initial condition as well as the Lyapunov exponent spectrum; while a perusal of
the phase space projected in the Poincar cross-section confirms some
of the striking features.Comment: 7 pages; 8 figure
Walls Inhibit Chaotic Mixing
We report on experiments of chaotic mixing in a closed vessel, in which a
highly viscous fluid is stirred by a moving rod. We analyze quantitatively how
the concentration field of a low-diffusivity dye relaxes towards homogeneity,
and we observe a slow algebraic decay of the inhomogeneity, at odds with the
exponential decay predicted by most previous studies. Visual observations
reveal the dominant role of the vessel wall, which strongly influences the
concentration field in the entire domain and causes the anomalous scaling. A
simplified 1D model supports our experimental results. Quantitative analysis of
the concentration pattern leads to scalings for the distributions and the
variance of the concentration field consistent with experimental and numerical
results.Comment: 4 pages, 3 figure
Network synchronization of groups
In this paper we study synchronized motions in complex networks in which
there are distinct groups of nodes where the dynamical systems on each node
within a group are the same but are different for nodes in different groups.
Both continuous time and discrete time systems are considered. We initially
focus on the case where two groups are present and the network has bipartite
topology (i.e., links exist between nodes in different groups but not between
nodes in the same group). We also show that group synchronous motions are
compatible with more general network topologies, where there are also
connections within the groups
The onset of synchronization in large networks of coupled oscillators
We study the transition from incoherence to coherence in large networks of
coupled phase oscillators. We present various approximations that describe the
behavior of an appropriately defined order parameter past the transition, and
generalize recent results for the critical coupling strength. We find that,
under appropriate conditions, the coupling strength at which the transition
occurs is determined by the largest eigenvalue of the adjacency matrix. We show
how, with an additional assumption, a mean field approximation recently
proposed is recovered from our results. We test our theory with numerical
simulations, and find that it describes the transition when our assumptions are
satisfied. We find that our theory describes the transition well in situations
in which the mean field approximation fails. We study the finite size effects
caused by nodes with small degree and find that they cause the critical
coupling strength to increase.Comment: To appear in PRE; Added an Appendix, a reference, modified two
figures and improved the discussion of the range of validity of perturbative
approache
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
Stellar dynamics in the Galactic Centre: proper motions and anisotropy
We report a new analysis of the stellar dynamics in the Galactic Centre, based on improved sky and line-of-sight velocities for more than 100 stars in the central few arcseconds from the black hole candidate SgrA*. The main results are as follows. (1)Overall, the stellar motions do not deviate strongly from isotropy. For those 32 stars with a determination of all three velocity components, the absolute, line-of-sight and sky velocities are in good agreement, consistent with a spherical star cluster. Likewise the sky-projected radial and tangential velocities of all 104 proper motion stars in our sample are also consistent with overall isotropy. (2)However, the sky-projected velocity components of the young, early-type stars in our sample indicate significant deviations from isotropy, with a strong radial dependence. Most of the bright He i emission-line stars at separations from 1 to 10 arcsec from SgrA* are on tangential orbits. This tangential anisotropy of the He i stars and most of the brighter members of the IRS 16 complex is largely caused by a clockwise (on the sky) and counter-rotating (line of sight, compared to the Galaxy), coherent rotation pattern. The overall rotation of the young star cluster may be a remnant of the original angular momentum pattern in the interstellar cloud from which these stars were formed. (3)The fainter, fast-moving stars within ≈1 arcsec of SgrA* may be largely moving on radial or very elliptical orbits. We have so far not detected deviations from linear motion (i.e., acceleration) for any of them. Most of the SgrA* cluster members are also on clockwise orbits. Spectroscopy indicates that they are early-type stars. We propose that the SgrA* cluster stars are those members of the early-type cluster that happen to have small angular momentum, and thus can plunge to the immediate vicinity of SgrA*. (4)We derive an anisotropy-independent estimate of the Sun—Galactic Centre distance between 7.8 and 8.2 kpc, with a formal statistical uncertainty of ±0.9 kpc. (5)We explicitly include velocity anisotropy in estimating the central mass distribution. We show how Leonard—Merritt and Bahcall—Tremaine mass estimates give systematic offsets in the inferred mass of the central object when applied to finite concentric rings for power-law clusters. Corrected Leonard—Merritt projected mass estimators and Jeans equation modelling confirm previous conclusions (from isotropic models) that a compact central mass concentration (central density ≥1012.6 M⊙ pc−3) is present and dominates the potential between 0.01 and 1 pc. Depending on the modelling method used, the derived central mass ranges between 2.6×106 and 3.3×106 M⊙ for R⊙=8.0 kp
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