3,279 research outputs found
Scattering Phases and Density of States for Exterior Domain
For a bounded open domain with connected complement and
piecewise smooth boundary, we consider the Dirichlet Laplacian -\DO on
and the S-matrix on the complement . Using the restriction
of to the boundary of , we establish that
is trace class when is negative and
give bounds on the energy dependence of this difference. This allows for
precise bounds on the total scattering phase, the definition of a
-function, and a Krein spectral formula, which improve similar results
found in the literature.Comment: 15 pages, Postscript, A
Controllability for chains of dynamical scatterers
In this paper, we consider a class of mechanical models which consists of a
linear chain of identical chaotic cells, each of which has two small lateral
holes and contains a rotating disk at its center. Particles are injected at
characteristic temperatures and rates from stochastic heat baths located at
both ends of the chain. Once in the system, the particles move freely within
the cells and will experience elastic collisions with the outer boundary of the
cells as well as with the disks. They do not interact with each other but can
transfer energy from one to another through collisions with the disks. The
state of the system is defined by the positions and velocities of the particles
and by the angular positions and angular velocities of the disks. We show that
each model in this class is controllable with respect to the baths, i.e. we
prove that the action of the baths can drive the system from any state to any
other state in a finite time. As a consequence, one obtains the existence of at
most one regular invariant measure characterizing its states (out of
equilibrium)
Lyapunov Mode Dynamics in Hard-Disk Systems
The tangent dynamics of the Lyapunov modes and their dynamics as generated
numerically - {\it the numerical dynamics} - is considered. We present a new
phenomenological description of the numerical dynamical structure that
accurately reproduces the experimental data for the quasi-one-dimensional
hard-disk system, and shows that the Lyapunov mode numerical dynamics is linear
and separate from the rest of the tangent space. Moreover, we propose a new,
detailed structure for the Lyapunov mode tangent dynamics, which implies that
the Lyapunov modes have well-defined (in)stability in either direction of time.
We test this tangent dynamics and its derivative properties numerically with
partial success. The phenomenological description involves a time-modal linear
combination of all other Lyapunov modes on the same polarization branch and our
proposed Lyapunov mode tangent dynamics is based upon the form of the tangent
dynamics for the zero modes
Testing for Chaos in Deterministic Systems with Noise
Recently, we introduced a new test for distinguishing regular from chaotic
dynamics in deterministic dynamical systems and argued that the test had
certain advantages over the traditional test for chaos using the maximal
Lyapunov exponent.
In this paper, we investigate the capability of the test to cope with
moderate amounts of noisy data. Comparisons are made between an improved
version of our test and both the ``tangent space'' and ``direct method'' for
computing the maximal Lyapunov exponent. The evidence of numerical experiments,
ranging from the logistic map to an eight-dimensional Lorenz system of
differential equations (the Lorenz 96 system), suggests that our method is
superior to tangent space methods and that it compares very favourably with
direct methods
Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems
We consider nonequilibrium transport in a simple chain of identical
mechanical cells in which particles move around. In each cell, there is a
rotating disc, with which these particles interact, and this is the only
interaction in the model. It was shown in \cite{eckmann-young} that when the
cells are weakly coupled, to a good approximation, the jump rates of particles
and the energy-exchange rates from cell to cell follow linear profiles. Here,
we refine that study by analyzing higher-order effects which are induced by the
presence of external gradients for situations in which memory effects, typical
of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a
set of balance equations for the particle number and energy in terms of the
reflection probabilities of the cell and solve it phenomenologically. Using
this approximate theory we explain how these asymmetries affect various aspects
of heat and particle transport in systems of the general type described above
and obtain in the infinite volume limit the deviation from the theory in
\cite{eckmann-young} to first-order. We verify our assumptions with extensive
numerical simulations.Comment: Several change
Method of constructing exactly solvable chaos
We present a new systematic method of constructing rational mappings as
ergordic transformations with nonuniform invariant measures on the unit
interval [0,1]. As a result, we obtain a two-parameter family of rational
mappings that have a special property in that their invariant measures can be
explicitly written in terms of algebraic functions of parameters and a
dynamical variable. Furthermore, it is shown here that this family is the most
generalized class of rational mappings possessing the property of exactly
solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x).
Based on the present method, we can produce a series of rational mappings
resembling the asymmetric shape of the experimentally obtained first return
maps of the Beloussof-Zhabotinski chemical reaction, and we can match some
rational functions with other experimentally obtained first return maps in a
systematic manner.Comment: 12 pages, 2 figures, REVTEX. Title was changed. Generalized Chebyshev
maps including the precise form of two-parameter generalized cubic maps were
added. Accepted for publication in Phys. Rev. E(1997
POOL File Catalog, Collection and Metadata Components
The POOL project is the common persistency framework for the LHC experiments
to store petabytes of experiment data and metadata in a distributed and grid
enabled way. POOL is a hybrid event store consisting of a data streaming layer
and a relational layer. This paper describes the design of file catalog,
collection and metadata components which are not part of the data streaming
layer of POOL and outlines how POOL aims to provide transparent and efficient
data access for a wide range of environments and use cases - ranging from a
large production site down to a single disconnected laptops. The file catalog
is the central POOL component translating logical data references to physical
data files in a grid environment. POOL collections with their associated
metadata provide an abstract way of accessing experiment data via their logical
grouping into sets of related data objects.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics
(CHEP03), La Jolla, Ca, USA, March 2003, 4 pages, 1 eps figure, PSN MOKT00
Covariant Lyapunov vectors for rigid disk systems
We carry out extensive computer simulations to study the Lyapunov instability
of a two-dimensional hard disk system in a rectangular box with periodic
boundary conditions. The system is large enough to allow the formation of
Lyapunov modes parallel to the x axis of the box. The Oseledec splitting into
covariant subspaces of the tangent space is considered by computing the full
set of covariant perturbation vectors co-moving with the flow in tangent-space.
These vectors are shown to be transversal, but generally not orthogonal to each
other. Only the angle between covariant vectors associated with immediate
adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the
probability of this angle to vanish approaches zero. The stable and unstable
manifolds are transverse to each other and the system is hyperbolic.Comment: 23 pages, 17 figures; Chemical Physics, in press, June 2010. Chem.
Phys. (2010): cited as: H. Bosetti, H.A. Posch, Chem. Phys. (2010),
doi:10.1016/j.chemphys.2010.06.01
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