6,802 research outputs found
Finding the complement of the invariant manifolds transverse to a given foliation for a 3D flow
A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan-Arnolâd Hamiltonian flows and for boundaryless submanifolds
Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps
We develop a Melnikov method for volume-preserving maps with codimension one
invariant manifolds. The Melnikov function is shown to be related to the flux
of the perturbation through the unperturbed invariant surface. As an example,
we compute the Melnikov function for a perturbation of a three-dimensional map
that has a heteroclinic connection between a pair of invariant circles. The
intersection curves of the manifolds are shown to undergo bifurcations in
homologyComment: LaTex with 10 eps figure
Conformal dimension and random groups
We give a lower and an upper bound for the conformal dimension of the
boundaries of certain small cancellation groups. We apply these bounds to the
few relator and density models for random groups. This gives generic bounds of
the following form, where is the relator length, going to infinity.
(a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model,
and
(b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at
densities .
In particular, for the density model at densities , as the relator
length goes to infinity, the random groups will pass through infinitely
many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to
density < 1/16. Many minor improvements. To appear in GAF
Stability of non-time-reversible phonobreathers
Non-time reversible phonobreathers are non-linear waves that can transport
energy in coupled oscillator chains by means of a phase-torsion mechanism. In
this paper, the stability properties of these structures have been considered.
It has been performed an analytical study for low-coupling solutions based upon
the so called {\em multibreather stability theorem} previously developed by
some of the authors [Physica D {\bf 180} 235]. A numerical analysis confirms
the analytical predictions and gives a detailed picture of the existence and
stability properties for arbitrary frequency and coupling.Comment: J. Phys. A.:Math. and Theor. In Press (2010
Monitoring Radiation Use in Cardiac Fluoroscopy Imaging Procedures
Objective: Timely identification of systematic changes in radiation delivery of an imaging system can lead to a reduction in risk for the patients involved. However, existing quality assurance programs involving the routine testing of equipment performance using phantoms are limited in their ability to effectively carry out this task. To address this issue we propose the implementation of an ongoing monitoring process that utilizes procedural data to identify unexpected large or small radiation exposures for individual patients, as well as to detect persistent changes in the radiation output of imaging platforms.
Methods: Data used in this study were obtained from records routinely collected during procedures performed in the cardiac catheterization imaging facility at St Andrew\u27s War Memorial Hospital, Brisbane, Australia over the period January 2008 to March 2010. A two stage monitoring process employing individual and exponentially weighted moving average (EWMA) control charts was developed and used to identify unexpectedly high or low radiation exposure levels for individual patients, as well as detect persistent changes in the radiation output delivered by the imaging systems. To increase sensitivity of the charts we account for variation in dose area product (DAP) values due to other measured factors (patient weight, fluoroscopy time, digital acquisition frame count) using multiple linear regression. Control charts are then constructed using the residual values from this linear regression. The proposed monitoring process was evaluated using simulation to model performance of the process under known conditions.
Results: Retrospective application of this technique to actual clinical data identified a number of cases in which the DAP result could be considered unexpected. Most of these, upon review, were attributed to data entry errors. The charts monitoring overall system radiation output trends demonstrated changes in equipment performance associated with relocation of the equipment to a new department. When tested under simulated conditions, the EWMA chart was capable of detecting a sustained 15% increase in average radiation output within 60 cases (\u3c 1 month of operation) while a 33% increase would be signalled within 20 cases.
Conclusion: This technique offers a valuable enhancement to existing quality assurance programs in radiology that rely upon the testing of equipment radiation output at discrete time frames to ensure performance security
Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones
(LJ) anharmonic lattices. Numerical simulations reveal the presence of high
energy strongly localized ``discrete'' kink-solitons (DK), which move with
supersonic velocities that are proportional to kink amplitudes. For small
amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous''
kink-soliton solutions of the modified Korteweg-de Vries equation. For high
amplitudes, we obtain a consistent description of these DK's in terms of
approximate solutions of the lattice equations that are obtained by restricting
to a bounded support in space exact solutions with sinusoidal pattern
characterized by the ``magic'' wavenumber . Relative displacement
patterns, velocity versus amplitude, dispersion relation and exponential tails
found in numerical simulations are shown to agree very well with analytical
predictions, for both FPU and LJ lattices.Comment: Europhysics Letters (in print
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Statistical mechanical aspects of joint source-channel coding
An MN-Gallager Code over Galois fields, , based on the Dynamical Block
Posterior probabilities (DBP) for messages with a given set of autocorrelations
is presented with the following main results: (a) for a binary symmetric
channel the threshold, , is extrapolated for infinite messages using the
scaling relation for the median convergence time, ;
(b) a degradation in the threshold is observed as the correlations are
enhanced; (c) for a given set of autocorrelations the performance is enhanced
as is increased; (d) the efficiency of the DBP joint source-channel coding
is slightly better than the standard gzip compression method; (e) for a given
entropy, the performance of the DBP algorithm is a function of the decay of the
correlation function over large distances.Comment: 6 page
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