3,838 research outputs found
Localised edge states nucleate turbulence in extended plane Couette cells
We study the turbulence transition of plane Couette flow in large domains
where localised perturbations are observed to generate growing turbulent spots.
Extending previous studies on the boundary between laminar and turbulent
dynamics we determine invariant structures intermediate between laminar and
turbulent flow. In wide but short domains we find states that are localised in
spanwise direction, and in wide and long domains the states are also localised
in downstream direction. These localised states act as critical nuclei for the
transition to turbulence in spatially extended domains.Comment: 15 pages, 5 figure
Turbulence transition and the edge of chaos in pipe flow
The linear stability of pipe flow implies that only perturbations of
sufficient strength will trigger the transition to turbulence. In order to
determine this threshold in perturbation amplitude we study the \emph{edge of
chaos} which separates perturbations that decay towards the laminar profile and
perturbations that trigger turbulence. Using the lifetime as an indicator and
methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006))
we show that superimposed on an overall -scaling predicted and studied
previously there are small, non-monotonic variations reflecting folds in the
edge of chaos. By tracing the motion in the edge we find that it is formed by
the stable manifold of a unique flow field that is dominated by a pair of
downstream vortices, asymmetrically placed towards the wall. The flow field
that generates the edge of chaos shows intrinsic chaotic dynamics.Comment: 4 pages, 5 figure
A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems
We derive a trace formula for , where
is the diagonal matrix element of the operator in the energy basis
of a chaotic system. The result takes the form of a smooth term plus
periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller
factor times , where is the average of the classical
observable along the periodic orbit . This structure for the orbit
corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on
the basis of numerical evidence.Comment: 8 pages; analysis made more rigorous in the revised versio
Black Panther: Thrills, Postcolonial Discourse, and Blacktopia
Black Panther challenges traditional depictions of African nations in film by showcasing the fictional African country of Wakanda as a global technological leader, its citizens as being comfortable in global settings, and by having Wakanda deliver social aid to the US, reversing the typical global flow of assistance. Wakanda is depicted as a Blacktopia, where societies thrive beyond the reach of white supremacy as they have not been subject to colonization
Echoes in classical dynamical systems
Echoes arise when external manipulations to a system induce a reversal of its
time evolution that leads to a more or less perfect recovery of the initial
state. We discuss the accuracy with which a cloud of trajectories returns to
the initial state in classical dynamical systems that are exposed to additive
noise and small differences in the equations of motion for forward and backward
evolution. The cases of integrable and chaotic motion and small or large noise
are studied in some detail and many different dynamical laws are identified.
Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.
Approach to ergodicity in quantum wave functions
According to theorems of Shnirelman and followers, in the semiclassical limit
the quantum wavefunctions of classically ergodic systems tend to the
microcanonical density on the energy shell. We here develop a semiclassical
theory that relates the rate of approach to the decay of certain classical
fluctuations. For uniformly hyperbolic systems we find that the variance of the
quantum matrix elements is proportional to the variance of the integral of the
associated classical operator over trajectory segments of length , and
inversely proportional to , where is the Heisenberg
time, being the mean density of states. Since for these systems the
classical variance increases linearly with , the variance of the matrix
elements decays like . For non-hyperbolic systems, like Hamiltonians
with a mixed phase space and the stadium billiard, our results predict a slower
decay due to sticking in marginally unstable regions. Numerical computations
supporting these conclusions are presented for the bakers map and the hydrogen
atom in a magnetic field.Comment: 11 pages postscript and 4 figures in two files, tar-compressed and
uuencoded using uufiles, to appear in Phys Rev E. For related papers, see
http://www.icbm.uni-oldenburg.de/icbm/kosy/ag.htm
Symmetry Decomposition of Chaotic Dynamics
Discrete symmetries of dynamical flows give rise to relations between
periodic orbits, reduce the dynamics to a fundamental domain, and lead to
factorizations of zeta functions. These factorizations in turn reduce the labor
and improve the convergence of cycle expansions for classical and quantum
spectra associated with the flow. In this paper the general formalism is
developed, with the -disk pinball model used as a concrete example and a
series of physically interesting cases worked out in detail.Comment: CYCLER Paper 93mar01
Semiclassical cross section correlations
We calculate within a semiclassical approximation the autocorrelation
function of cross sections. The starting point is the semiclassical expression
for the diagonal matrix elements of an operator. For general operators with a
smooth classical limit the autocorrelation function of such matrix elements has
two contributions with relative weights determined by classical dynamics. We
show how the random matrix result can be obtained if the operator approaches a
projector onto a single initial state. The expressions are verified in
calculations for the kicked rotor.Comment: 6 pages, 2 figure
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