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-Arnol’d 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 $l$ 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 $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ 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 $k=2\pi/3$. 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, $q$, 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, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (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 $q$ 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