7,834 research outputs found
Preservation of External Rays in non-Autonomous Iteration
We consider the dynamics arising from the iteration of an arbitrary sequence
of polynomials with uniformly bounded degrees and coefficients and show that,
as parameters vary within a single hyperbolic component in parameter space,
certain properties of the corresponding Julia sets are preserved. In
particular, we show that if the sequence is hyperbolic and all the Julia sets
are connected, then the whole basin at infinity moves holomorphically. This
extends also to the landing points of external rays and the resultant
holomorphic motion of the Julia sets coincides with that obtained earlier using
grand orbits. In addition, if a finite set of external rays separate the Julia
set for a particular parameter value, then the rays with the same external
angles separate the Julia set for every parameter in the same hyperbolic
component
Equilibrium states, pressure and escape for multimodal maps with holes
For a class of non-uniformly hyperbolic interval maps, we study rates of
escape with respect to conformal measures associated with a family of geometric
potentials. We establish the existence of physically relevant conditionally
invariant measures and equilibrium states and prove a relation between the rate
of escape and pressure with respect to these potentials. As a consequence, we
obtain a Bowen formula: we express the Hausdorff dimension of the set of points
which never exit through the hole in terms of the relevant pressure function.
Finally, we obtain an expression for the derivative of the escape rate in the
zero-hole limit.Comment: Minor edits. To appear in Israel J. Mat
Simulations of closed timelike curves
Proposed models of closed timelike curves (CTCs) have been shown to enable
powerful information-processing protocols. We examine the simulation of models
of CTCs both by other models of CTCs and by physical systems without access to
CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs)
are physically equivalent to postselection CTCs (P-CTCs), in the sense that one
model can simulate the other with reasonable overhead. As a consequence, their
information-processing capabilities are equivalent. We also describe a method
for quantum computers to simulate Deutschian CTCs (but with a reasonable
overhead only in some cases). In cases for which the overhead is reasonable, it
might be possible to perform the simulation in a table-top experiment. This
approach has the benefit of resolving some ambiguities associated with the
equivalent circuit model of Ralph et al. Furthermore, we provide an explicit
form for the state of the CTC system such that it is a maximum-entropy state,
as prescribed by Deutsch.Comment: 15 pages, 1 figure, accepted for publication in Foundations of
Physic
Numerical Simulations of Radiatively-Driven Dusty Winds
[abridged] Radiation pressure on dust grains may be an important mechanism in
driving winds in a wide variety of astrophysical systems. However, the
efficiency of the coupling between the radiation field and the dusty gas is
poorly understood in environments characterized by high optical depths. We
present a series of idealized numerical experiments, performed with the
radiation-hydrodynamic code ORION, in which we study the dynamics of such winds
and quantify their properties. We find that, after wind acceleration begins,
radiation Rayleigh-Taylor instability forces the gas into a configuration that
reduces the rate of momentum transfer from the radiation field to the gas by a
factor ~ 10 - 100 compared to an estimate based on the optical depth at the
base of the atmosphere; instead, the rate of momentum transfer from a driving
radiation field of luminosity L to the gas is roughly L/c multiplied by one
plus half the optical depth evaluated using the photospheric temperature, which
is far smaller than the optical depth one would obtain using the interior
temperature. When we apply our results to conditions appropriate to ULIRGs and
star clusters, we find that the asymptotic wind momentum flux from such objects
should not significantly exceed that carried by the direct radiation field,
L/c. This result constrains the expected mass loss rates from systems that
exceed the Eddington limit to be of order the so-called "single-scattering"
limit, and not significantly higher. We present an approximate fitting formula
for the rate of momentum transfer from radiation to dusty gas through which it
passes, which is suitable for implementation in sub-grid models of galaxy
formation. Finally, we provide a first map of the column density distribution
of gas in a radiatively-driven wind as a function of velocity, and velocity
dispersion.Comment: 19 pages, 17 figures, MNRAS in press; some additional discussion
compared to previous version, no changes in conclusion
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