From symplectic integrator to Poincare map: Spline expansion of a map generator in Cartesian coordinates

Data from orbits of a symplectic integrator can be interpolated so as to construct an approximation to the generating function of a Poincare map. The time required to compute an orbit of the symplectic map induced by the generator can be much less than the time to follow the same orbit by symplectic integration. The construction has been carried out previously for full-turn maps of large particle accelerators, and a big saving in time (for instance a factor of 60) has been demonstrated. A shortcoming of our work to date arose from the use of canonical polar coordinates, which precluded map construction in small regions of phase space near coordinate singularities. This paper shows that Cartesian coordinates can also be used, thus avoiding singularities. The generator is represented in a basis of tensor product B-splines. Under weak conditions the spline expansion converges uniformly as the mesh is refined, approaching the exact generator of the Poincare map as defined by the symplectic integrator, in some parallelepiped of phase space centered at the origin. (orig.)SIGLEAvailable from TIB Hannover: RA 2999(97-163) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDepartment of Energy, Washington, DC (United States)DEGerman

First-order averaging principles for maps with applications to beam dynamics in particle accelerators

For slowly evolving, discrete-time-dependent systems of difference equations (iterated maps), we believe the simplest means of demonstrating the validity of the averaging method at first order is by way of a lemma that we call Besjes' inequality. In this paper, we develop the Besjes inequality for identity maps with perturbations that are (i) at low-order resonance (periodic with short period) and (ii) far from low-order resonance in the discrete time. We use these inequalities to prove corresponding first-order averaging principles, together with a principle of adiabatic invariance on extended timescales; and we generalize and apply these mathematical results to model problems in accelerator beam dynamics, and to the Henon map. (orig.)Available from TIB Hannover: RA 2999(03-169) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Hip resurfacing in a district general hospital: 6-year clinical results using the ReCap hip resurfacing system

<p>Abstract</p> <p>Background</p> <p>The purpose of our study was to prospectively report the clinical results of 280 consecutive hips (240 patients) who received a ReCap Hip Resurfacing System implant (Biomet Inc., Warsaw, USA) in a single district general hospital. Literature reports a large variation in clinical results between different resurfacing designs and published results using this particular design are scarce.</p> <p>Methods</p> <p>Mean follow up was 3.3 years (1.0 to 6.3) and four patients were lost to follow-up. All patients were diagnosed with end-stage hip osteoarthritis, their mean age was 54 years and 76.4% of all patients were male.</p> <p>Results</p> <p>There were 16 revisions and four patients reported a Harris Hip Score <70 points at their latest follow up. There were no pending revisions. Kaplan-Meier implant survival probability, with revision for any reason as endpoint, was 93.5% at six years follow-up (95%-CI: 88.8-95.3). There were no revisions for Adverse Reactions to Metal Debris (ARMD) and no indications of ARMD in symptomatic non-revised patients, although diagnostics were limited to ultrasound scans.</p> <p>Conclusions</p> <p>This independent series confirms that hip resurfacing is a demanding procedure, and that implant survival of the ReCap hip resurfacing system is on a critical level in our series. In non-revised patients, reported outcomes are generally excellent.</p> <p>Trial registration</p> <p>ClinicalTrials.gov Identifier: NCT00603395</p