Stripe-hexagon competition in forced pattern forming systems with broken up-down symmetry

We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a $1:2$ and $1:1$ ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore depending on the modulation amplitude the transition between stripes and distorted hexagons is either sub- or supercritical.Comment: 10 pages, 12 figures, submitted to Physical Review

A systematic review of the etiopathogenesis of Kienböck's disease and a critical appraisal of its recognition as an occupational disease related to hand-arm vibration

<p>Abstract</p> <p>Background</p> <p>We systematically reviewed etiological factors of Kienböck’s disease (osteonecrosis of the lunate) discussed in the literature in order to examine the justification for including Kienböck’s disease (KD) in the European Listing of Occupational Diseases.</p> <p>Methods</p> <p>We searched the Ovid/Medline and the Cochrane Library for articles discussing the etiology of osteonecrosis of the lunate published since the first description of KD in 1910 and up until July 2012 in English, French or German. Literature was classified by the level of evidence presented, the etiopathological hypothesis discussed, and the author's conclusion about the role of the etiopathological hypothesis. The causal relationship between KD and hand-arm vibration was elucidated by the Bradford Hill criteria.</p> <p>Results</p> <p>A total of 220 references was found. Of the included 152 articles, 140 (92%) reached the evidence level IV (case series). The four most frequently discussed factors were negative ulnar variance (n=72; 47%), primary arterial ischemia of the lunate (n=63; 41%), trauma (n=63; 41%) and hand-arm vibration (n=53; 35%). The quality of the cohort studies on hand-arm vibration did not permit a meta-analysis to evaluate the strength of an association to KD. Evidence for the lack of consistency, plausibility and coherence of the 4 most frequently discussed etiopathologies was found. No evidence was found to support any of the nine Bradford Hill criteria for a causal relationship between KD and hand-arm vibration.</p> <p>Conclusions</p> <p>A systematic review of 220 articles on the etiopathology of KD and the application of the Bradford Hill criteria does not provide sufficient scientific evidence to confirm or refute a causal relationship between KD and hand-arm vibration. This currently suggests that, KD does not comply with the criteria of the International Labour Organization determining occupational diseases. However, research with a higher level of evidence is required to further determine if hand-arm vibration is a risk factor for KD.</p