4,572 research outputs found
Chaotic Escape from an Open Vase-shaped Cavity. I. Numerical and Experimental Results
We present part I in a two-part study of an open chaotic cavity shaped as a vase. The vase possesses an unstable periodic orbit in its neck. Trajectories passing through this orbit escape without return. For our analysis, we consider a family of trajectories launched from a point on the vase boundary. We imagine a vertical array of detectors past the unstable periodic orbit and, for each escaping trajectory, record the propagation time and the vertical detector position. We find that the escape time exhibits a complicated recursive structure. This recursive structure is explored in part I of our study. We present an approximation to the Helmholtz equation for waves escaping the vase. By choosing a set of detector points, we interpolate trajectories connecting the source to the different detector points. We use these interpolated classical trajectories to construct the solution to the wave equation at a detector point. Finally, we construct a plot of the detector position versus the escape time and compare this graph to the results of an experiment using classical ultrasound waves. We find that generally the classical trajectories organize the escaping ultrasound waves
Kinks Dynamics in One-Dimensional Coupled Map Lattices
We examine the problem of the dynamics of interfaces in a one-dimensional
space-time discrete dynamical system. Two different regimes are studied : the
non-propagating and the propagating one. In the first case, after proving the
existence of such solutions, we show how they can be described using Taylor
expansions. The second situation deals with the assumption of a travelling wave
to follow the kink propagation. Then a comparison with the corresponding
continuous model is proposed. We find that these methods are useful in simple
dynamical situations but their application to complex dynamical behaviour is
not yet understood.Comment: 17pages, LaTex,3 fig available on cpt.univ-mrs.fr directory
pub/preprints/94/dynamical-systems/94-P.307
Separability of Black Holes in String Theory
We analyze the origin of separability for rotating black holes in string
theory, considering both massless and massive geodesic equations as well as the
corresponding wave equations. We construct a conformal Killing-Stackel tensor
for a general class of black holes with four independent charges, then identify
two-charge configurations where enhancement to an exact Killing-Stackel tensor
is possible. We show that further enhancement to a conserved Killing-Yano
tensor is possible only for the special case of Kerr-Newman black holes. We
construct natural null congruences for all these black holes and use the
results to show that only the Kerr-Newman black holes are algebraically special
in the sense of Petrov. Modifying the asymptotic behavior by the subtraction
procedure that induces an exact SL(2)^2 also preserves only the conformal
Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black
hole possesses a conformal Killing-Stackel tensor but has no further
enhancements.Comment: 27 page
Explicitly solvable cases of one-dimensional quantum chaos
We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact
A new derivation of Luscher F-term and fluctuations around the giant magnon
15 pages, no figures; v2: added assumption on diagonal scattering and a section on generalizations; v3: minor changes, version accepted for publication in JHEPIn this paper we give a new derivation of the generalized Luscher F-term formula from a summation over quadratic fluctuations around a given soliton. The result is very general providing that S-matrix is diagonal and is valid for arbitrary dispersion relation. We then apply this formalism to compute the leading finite size corrections to the giant magnon dispersion relation coming from quantum fluctuations.Peer reviewe
Spectra of regular quantum graphs
We consider a class of simple quasi one-dimensional classically
non-integrable systems which capture the essence of the periodic orbit
structure of general hyperbolic nonintegrable dynamical systems. Their behavior
is simple enough to allow a detailed investigation of both classical and
quantum regimes. Despite their classical chaoticity, these systems exhibit a
``nonintegrable analog'' of the Einstein-Brillouin-Keller quantization formula
which provides their spectra explicitly, state by state, by means of convergent
periodic orbit expansions.Comment: 32 pages, 10 figure
The interaction of multiple bubbles in a Hele-Shaw channel
We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a single-bubble system we establish that, in general, the bubble propagation speed monotonically increases with bubble volume so that two bubbles of different sizes, in the absence of any hydrodynamic interactions, will either coalesce or separate in a finite time. However, our experiments indicate that the bubbles interact and that an unstable two-bubble state is responsible for the eventual dynamical outcome: coalescence or separation. These results motivate us to develop an edge-tracking routine and to calculate these weakly unstable two-bubble steady states from the governing equations. The steady states consist of pairs of âalignedâ bubbles that appear on the same side of the centreline with the larger bubble leading. We also discover, through time-dependent simulations and physical experiment, another class of two-bubble states that, surprisingly, are stable. In contrast to the âalignedâ steady states, these bubbles appear on either side of the centreline and are âoffsetâ from each other. We calculate the bifurcation structures of both classes of steady states as the flow rate and bubble volume ratio are varied. We find that they exhibit intriguing similarities to the single-bubble bifurcation structure, which has implications for the existence of n -bubble steady states
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