5,459 research outputs found
Systematic experimental exploration of bifurcations with non-invasive control
We present a general method for systematically investigating the dynamics and
bifurcations of a physical nonlinear experiment. In particular, we show how the
odd-number limitation inherent in popular non-invasive control schemes, such as
(Pyragas) time-delayed or washout-filtered feedback control, can be overcome
for tracking equilibria or forced periodic orbits in experiments. To
demonstrate the use of our non-invasive control, we trace out experimentally
the resonance surface of a periodically forced mechanical nonlinear oscillator
near the onset of instability, around two saddle-node bifurcations (folds) and
a cusp bifurcation.Comment: revised and extended version (8 pages, 7 figures
Semiclassical Theory of Chaotic Quantum Transport
We present a refined semiclassical approach to the Landauer conductance and
Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for
systems with uniformly hyperbolic dynamics that including off-diagonal
contributions to double sums over classical paths gives a weak-localization
correction in quantitative agreement with results from random matrix theory. We
further discuss the magnetic field dependence. This semiclassical treatment
accounts for current conservation.Comment: 4 pages, 1 figur
Semiclassical universality of parametric spectral correlations
We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor which depends on a scaled parameter difference . For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.Comment: 18 pages, no figure
Escape Orbits for Non-Compact Flat Billiards
It is proven that, under some conditions on , the non-compact flat
billiard
has no orbits going {\em directly} to . The relevance of such
sufficient conditions is discussed.Comment: 9 pages, LaTeX, 3 postscript figures available at
http://www.princeton.edu/~marco/papers/ . Minor changes since previously
posted version. Submitted to 'Chaos
A generic map has no absolutely continuous invariant probability measure
Let be a smooth compact manifold (maybe with boundary, maybe
disconnected) of any dimension . We consider the set of maps
which have no absolutely continuous (with respect to Lebesgue)
invariant probability measure. We show that this is a residual (dense
C^1$ topology.
In the course of the proof, we need a generalization of the usual Rokhlin
tower lemma to non-invariant measures. That result may be of independent
interest.Comment: 12 page
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism
Models incorporating delay have been frequently used to understand climate
variability phenomena, but often the delay is introduced through an ad-hoc
physical reasoning, such as the propagation time of waves. In this paper, the
Mori-Zwanzig formalism is introduced as a way to systematically derive delay
models from systems of partial differential equations and hence provides a
better justification for using these delay-type models. The Mori-Zwanzig
technique gives a formal rewriting of the system using a projection onto a set
of resolved variables, where the rewritten system contains a memory term. The
computation of this memory term requires solving the orthogonal dynamics
equation, which represents the unresolved dynamics. For nonlinear systems, it
is often not possible to obtain an analytical solution to the orthogonal
dynamics and an approximate solution needs to be found. Here, we demonstrate
the Mori-Zwanzig technique for a two-strip model of the El Nino Southern
Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The
resulting nonlinear delay model contains an additional term compared to
previously proposed ad-hoc conceptual models. This new term leads to a larger
ENSO period, which is closer to that seen in observations.Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figure
Pulsar Magnetospheric Emission Mapping: Images and Implications of Polar-Cap Weather
The beautiful sequences of ``drifting'' subpulses observed in some radio
pulsars have been regarded as among the most salient and potentially
instructive characteristics of their emission, not least because they have
appeared to represent a system of subbeams in motion within the emission zone
of the star. Numerous studies of these ``drift'' sequences have been published,
and a model of their generation and motion articulated long ago by Ruderman &
Sutherland (1975); but efforts thus far have failed to establish an
illuminating connection between the drift phemomenon and the actual sites of
radio emission. Through a detailed analysis of a nearly coherent sequence of
``drifting'' pulses from pulsar B0943+10, we have in fact identified a system
of subbeams circulating around the magnetic axis of the star. A mapping
technique, involving a ``cartographic'' transform and its inverse, permits us
to study the character of the polar-cap emission ``map'' and then to confirm
that it, in turn, represents the observed pulse sequence. On this basis, we
have been able to trace the physical origin of the ``drifting-subpulse''
emission to a stably rotating and remarkably organized configuration of
emission columns, in turn traceable possibly to the magnetic polar-cap ``gap''
region envisioned by some theories.Comment: latex with five eps figure
Critical review of Ames Life Science participation in Spacelab Mission Development Test 3: The SMD 3 management study
A management study was conducted to specify activities and problems encountered during the development of procedures for documentation and crew training on experiments, as well as during the design, integration, and delivery of a life sciences experiment payload to Johnson Space Center for a 7 day simulation of a Spacelab mission. Conclusions and recommendations to project management for current and future Ames' life sciences projects are included. Broader issues relevant to the conduct of future scientific missions under the constraints imposed by the environment of space are also addressed
Periodic orbit bifurcations and scattering time delay fluctuations
We study fluctuations of the Wigner time delay for open (scattering) systems
which exhibit mixed dynamics in the classical limit. It is shown that in the
semiclassical limit the time delay fluctuations have a distribution that
differs markedly from those which describe fully chaotic (or strongly
disordered) systems: their moments have a power law dependence on a
semiclassical parameter, with exponents that are rational fractions. These
exponents are obtained from bifurcating periodic orbits trapped in the system.
They are universal in situations where sufficiently long orbits contribute. We
illustrate the influence of bifurcations on the time delay numerically using an
open quantum map.Comment: 9 pages, 3 figures, contribution to QMC200
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