1,578 research outputs found
A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem
A computational procedure that allows the detection of a new type of
high-dimensional chaotic saddle in Hamiltonian systems with three degrees of
freedom is presented. The chaotic saddle is associated with a so-called
normally hyperbolic invariant manifold (NHIM). The procedure allows to compute
appropriate homoclinic orbits to the NHIM from which we can infer the existence
a chaotic saddle. NHIMs control the phase space transport across an equilibrium
point of saddle-centre-...-centre stability type, which is a fundamental
mechanism for chemical reactions, capture and escape, scattering, and, more
generally, ``transformation'' in many different areas of physics. Consequently,
the presented methods and results are of broad interest. The procedure is
illustrated for the spatial Hill's problem which is a well known model in
celestial mechanics and which gained much interest e.g. in the study of the
formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys
Bubbles and Filaments: Stirring a Cahn-Hilliard Fluid
The advective Cahn-Hilliard equation describes the competing processes of
stirring and separation in a two-phase fluid. Intuition suggests that bubbles
will form on a certain scale, and previous studies of Cahn-Hilliard dynamics
seem to suggest the presence of one dominant length scale. However, the
Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we
show that, by stirring the mixture at a sufficiently large amplitude, we excite
the diffusion and overwhelm the segregation to create a homogeneous liquid. At
intermediate amplitudes we see regions of bubbles coexisting with regions of
hyperdiffusive filaments. Thus, the problem possesses two dominant length
scales, associated with the bubbles and filaments. For simplicity, we use use a
chaotic flow that mimics turbulent stirring at large Prandtl number. We compare
our results with the case of variable mobility, in which growth of bubble size
is dominated by interfacial rather than bulk effects, and find qualitatively
similar results.Comment: 20 pages, 27 figures. RevTeX
Isomerization dynamics of a buckled nanobeam
We analyze the dynamics of a model of a nanobeam under compression. The model
is a two mode truncation of the Euler-Bernoulli beam equation subject to
compressive stress. We consider parameter regimes where the first mode is
unstable and the second mode can be either stable or unstable, and the
remaining modes (neglected) are always stable. Material parameters used
correspond to silicon. The two mode model Hamiltonian is the sum of a
(diagonal) kinetic energy term and a potential energy term. The form of the
potential energy function suggests an analogy with isomerisation reactions in
chemistry. We therefore study the dynamics of the buckled beam using the
conceptual framework established for the theory of isomerisation reactions.
When the second mode is stable the potential energy surface has an index one
saddle and when the second mode is unstable the potential energy surface has an
index two saddle and two index one saddles. Symmetry of the system allows us to
construct a phase space dividing surface between the two "isomers" (buckled
states). The energy range is sufficiently wide that we can treat the effects of
the index one and index two saddles in a unified fashion. We have computed
reactive fluxes, mean gap times and reactant phase space volumes for three
stress values at several different energies. In all cases the phase space
volume swept out by isomerizing trajectories is considerably less than the
reactant density of states, proving that the dynamics is highly nonergodic. The
associated gap time distributions consist of one or more `pulses' of
trajectories. Computation of the reactive flux correlation function shows no
sign of a plateau region; rather, the flux exhibits oscillatory decay,
indicating that, for the 2-mode model in the physical regime considered, a rate
constant for isomerization does not exist.Comment: 42 pages, 6 figure
Self-organized Beating and Swimming of Internally Driven Filaments
We study a simple two-dimensional model for motion of an elastic filament
subject to internally generated stresses and show that wave-like propagating
shapes which can propel the filament can be induced by a self-organized
mechanism via a dynamic instability. The resulting patterns of motion do not
depend on the microscopic mechanism of the instability but only of the filament
rigidity and hydrodynamic friction. Our results suggest that simplified
systems, consisting only of molecular motors and filaments could be able to
show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe
Self-Help: Extrajudicial Rights, Privileges and Remedies in Contemporary American Society
This Special Project examines the myriad forms of self-help currently available to persons in American society. It groups and discusses notable self-help rights, privileges, and remedies under topical classifications that parallel traditional jurisprudential categories. Parts H through VI of the Special Project sketch the legally fashioned contours and explore the legal, social, and political consequences of self-help methods in tort law, criminal law and law enforcement, commercial transactions, landlord-tenant relations,and family law matters. Part VII explores the attorney\u27s role in the development and implementation of curative self-help procedures such as mediation. Special Project concludes by examining the function, mechanisms, and merits of two increasingly popular alternative dispute resolution processes--rent-a-judge programs and the ombudsman--that offer hope for continued peaceable dispute resolution
General Framework for phase synchronization through localized sets
We present an approach which enables to identify phase synchronization in
coupled chaotic oscillators without having to explicitly measure the phase. We
show that if one defines a typical event in one oscillator and then observes
another one whenever this event occurs, these observations give rise to a
localized set. Our result provides a general and easy way to identify PS, which
can also be used to oscillators that possess multiple time scales. We
illustrate our approach in networks of chemically coupled neurons. We show that
clusters of phase synchronous neurons may emerge before the onset of phase
synchronization in the whole network, producing a suitable environment for
information exchanging. Furthermore, we show the relation between the localized
sets and the amount of information that coupled chaotic oscillator can
exchange
Smooth-filamental transition of active tracer fields stirred by chaotic advection
The spatial distribution of interacting chemical fields is investigated in
the non-diffusive limit. The evolution of fluid parcels is described by
independent dynamical systems driven by chaotic advection. The distribution can
be filamental or smooth depending on the relative strength of the dispersion
due to chaotic advection and the stability of the chemical dynamics. We give
the condition for the smooth-filamental transition and relate the H\"older
exponent of the filamental structure to the Lyapunov exponents. Theoretical
findings are illustrated by numerical experiments.Comment: 4 pages, 3 figure
Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence
The aim of this paper is to prove a Kolmogorov-type result for a
nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time
dependence. The existence of a torus with a prefixed Diophantine frequency is
shown in the forced system, provided that the perturbation is real-analytic and
(exponentially) decaying with time. The advantage consists of the possibility
to choose an arbitrarily small decaying coefficient, consistently with the
perturbation size.Comment: Several corrections in the proof with respect to the previous
version. Main statement unchange
Triplicity and Physical Characteristics of Asteroid (216) Kleopatra
To take full advantage of the September 2008 opposition passage of the M-type
asteroid (216) Kleopatra, we have used near-infrared adaptive optics (AO)
imaging with the W.M. Keck II telescope to capture unprecedented high
resolution images of this unusual asteroid. Our AO observations with the W.M.
Keck II telescope, combined with Spitzer/IRS spectroscopic observations and
past stellar occultations, confirm the value of its IRAS radiometric radius of
67.5 km as well as its dog-bone shape suggested by earlier radar observations.
Our Keck AO observations revealed the presence of two small satellites in orbit
about Kleopatra (see Marchis et al., 2008). Accurate measurements of the
satellite orbits over a full month enabled us to determine the total mass of
the system to be 4.64+/-0.02 10^18 Kg. This translates into a bulk density of
3.6 +/-0.4 g/cm3, which implies a macroscopic porosity for Kleopatra of ~
30-50%, typical of a rubble-pile asteroid. From these physical characteristics
we measured its specific angular momentum, very close to that of a spinning
equilibrium dumbbell.Comment: 35 pages, 3 Tables, 9 Figures. In press to Icaru
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