Metastable energy strata in numerical discretizations of weakly nonlinear wave equations

The quadratic nonlinear wave equation on a one-dimensional torus with small initial values located in a single Fourier mode is considered. In this situation, the formation of metastable energy strata has recently been described and their long-time stability has been shown. The topic of the present paper is the correct reproduction of these metastable energy strata by a numerical method. For symplectic trigonometric integrators applied to the equation, it is shown that these energy strata are reproduced even on long time intervals in a qualitatively correct way.Comment: 28 pages, 9 figure

Numerical integrators for motion under a strong constraining force

This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and macro-steps for the integration of fast and slow parts, respectively, does not work satisfactorily on such problems. Here it is shown that variants of the impulse method with suitable projection preserve the actions as adiabatic invariants and yield accurate approximations, with macro-stepsizes that are not restricted by the stiffness parameter

Feature-based spline optimization in CAD: A step towards geometry-based structure creation

In this paper, an advanced method for CAD-based spline structure optimization is investigated. The method is based on the combination of the commonly known parameter-based spline shape optimization and a recently presented feature-based structure variation concept for commercial CAD tools. The aim is to extend common parameter-based spline shape variation by the additional possibility to automatically add and remove control points or entire splines directly in CAD space. Such advanced spline modification provides a new level of flexibility in general geometry-based structural optimization. Using these splines to build CAD models, entirely new structures may be automatically generated during an optimization run through this newly gained flexibility in spline manipulation. The idea is to roughly define a continuous design space by basic splines and to gradually increase their shape complexity by control point number variation during optimization. Thus, operating on a knowledge-lean initialization—a design space bounded by basic splines and filled with material—this combination further extends the search and solution spaces of CAD-based structural optimization. The paper provides an outlook towards automated geometry-based structure creation combining nowadays commercial CAD software and a dedicated variation and optimization framework for geometry-based structural optimizatio

Complications of circumcision in male neonates, infants and children: a systematic review.

BACKGROUND: Approximately one in three men are circumcised globally, but there are relatively few data on the safety of the procedure. The aim of this paper is to summarize the literature on frequency of adverse events following pediatric circumcision, with a focus on developing countries. METHODS: PubMed and other databasess were searched with keywords and MeSH terms including infant/newborn/pediatric/child, circumcision, complications and adverse events. Searches included all available years and were conducted on November 6th 2007 and updated on February 14th 2009. Additional searches of the Arabic literature included searches of relevant databases and University libraries for research theses on male circumcision.Studies were included if they contained data to estimate frequency of adverse events following neonatal, infant and child circumcision. There was no language restriction. A total of 1349 published papers were identified, of which 52 studies from 21 countries met the inclusion criteria. The Arabic literature searches identified 46 potentially relevant papers, of which six were included. RESULTS: Sixteen prospective studies evaluated complications following neonatal and infant circumcision. Most studies reported no severe adverse events (SAE), but two studies reported SAE frequency of 2%. The median frequency of any complication was 1.5% (range 0-16%). Child circumcision by medical providers tended to be associated with more complications (median frequency 6%; range 2-14%) than for neonates and infants. Traditional circumcision as a rite of passage is associated with substantially greater risks, more severe complications than medical circumcision or traditional circumcision among neonates. CONCLUSIONS: Studies report few severe complications following circumcision. However, mild or moderate complications are seen, especially when circumcision is undertaken at older ages, by inexperienced providers or in non-sterile conditions. Pediatric circumcision will continue to be practiced for cultural, medical and as a long-term HIV/STI prevention strategy. Risk-reduction strategies including improved training of providers, and provision of appropriate sterile equipment, are urgently needed