1,038 research outputs found
Emergence of chaotic behaviour in linearly stable systems
Strong nonlinear effects combined with diffusive coupling may give rise to
unpredictable evolution in spatially extended deterministic dynamical systems
even in the presence of a fully negative spectrum of Lyapunov exponents. This
regime, denoted as ``stable chaos'', has been so far mainly characterized by
numerical studies. In this manuscript we investigate the mechanisms that are at
the basis of this form of unpredictable evolution generated by a nonlinear
information flow through the boundaries. In order to clarify how linear
stability can coexist with nonlinear instability, we construct a suitable
stochastic model. In the absence of spatial coupling, the model does not reveal
the existence of any self-sustained chaotic phase. Nevertheless, already this
simple regime reveals peculiar differences between the behaviour of finite-size
and that of infinitesimal perturbations. A mean-field analysis of the truly
spatially extended case clarifies that the onset of chaotic behaviour can be
traced back to the diffusion process that tends to shift the growth rate of
finite perturbations from the quenched to the annealed average. The possible
characterization of the transition as the onset of directed percolation is also
briefly discussed as well as the connections with a synchronization transition.Comment: 30 pages, 8 figures, Submitted to Journal of Physics
Hi Spin Temperatures and Heating Requirements in Outer Regions of Disk Galaxies
ABSRACT:We show how to use 21-cm emission and absorption studies to estimate
the heat inputs to the neutral gas in low pressure environments, such as in
outer disks of spiral galaxies, in galactic halos or in intergalactic space.
For a range of model parameters we calculate the gas kinetic and spin
temperatures ( and ) and the relation between and the heat
input to the gas. We outline the conditions for a ``two phase medium'' to
exist. We find that although can be much smaller than , is
always K for column densities greater that
cm. This excludes the possibility that relevant HI masses at the
periphery of galaxies are invisible at 21-cm in emission. The outermost
interstellar gas in a disk galaxy is more directly affected by external
processes and in this paper we estimate the intensity of the extragalactic
background at energies close to 0.1 keV by comparing our theoretical results
with HI emission/absorption studies. We take into account the possibility that
some energy produced in the inner regions affects the energy balance in outer
regions. We find that in the absence of any other local heat source QSO
dominated background models are still compatible with the spin temperature
limits derived for the two best documented HI emission/absorption studies in
outer regions.Comment: 24 pages, 8 figures ARCETRI-PR-93-2
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