4,833 research outputs found

    Rate of parity violation from measure concentration

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    We present a geometric argument determining the kinematic (phase-space) factor contributing to the relative rate at which degrees of freedom of one chirality come to dominate over degrees of freedom of opposite chirality, in models with parity violation. We rely on the measure concentration of a subset of a Euclidean cube which is controlled by an isoperimetric inequality. We provide an interpretation of this result in terms of ideas of Statistical Mechanics.Comment: 10 pages, no figure

    The geodesic rule for higher codimensional global defects

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    We generalize the geodesic rule to the case of formation of higher codimensional global defects. Relying on energetic arguments, we argue that, for such defects, the geometric structures of interest are the totally geodesic submanifolds. On the other hand, stochastic arguments lead to a diffusion equation approach, from which the geodesic rule is deduced. It turns out that the most appropriate geometric structure that one should consider is the convex hull of the values of the order parameter on the causal volumes whose collision gives rise to the defect. We explain why these two approaches lead to similar results when calculating the density of global defects by using a theorem of Cheeger and Gromoll. We present a computation of the probability of formation of strings/vortices in the case of a system, such as nematic liquid crystals, whose vacuum is RP2\mathbb{R}P^2.Comment: 17 pages, no figures. To be published in Mod. Phys. Lett.

    Spina bifida-predisposing heterozygous mutations in Planar Cell Polarity genes and Zic2 reduce bone mass in young mice

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    Fractures are a common comorbidity in children with the neural tube defect (NTD) spina bifida. Mutations in the Wnt/planar cell polarity (PCP) pathway contribute to NTDs in humans and mice, but whether this pathway independently determines bone mass is poorly understood. Here, we first confirmed that core Wnt/PCP components are expressed in osteoblasts and osteoclasts in vitro. In vivo, we performed detailed µCT comparisons of bone structure in tibiae from young male mice heterozygous for NTD-associated mutations versus WT littermates. PCP signalling disruption caused by Vangl2 (Vangl2Lp/+) or Celsr1 (Celsr1Crsh/+) mutations significantly reduced trabecular bone mass and distal tibial cortical thickness. NTD-associated mutations in non-PCP transcription factors were also investigated. Pax3 mutation (Pax3Sp2H/+) had minimal effects on bone mass. Zic2 mutation (Zic2Ku/+) significantly altered the position of the tibia/fibula junction and diminished cortical bone in the proximal tibia. Beyond these genes, we bioinformatically documented the known extent of shared genetic networks between NTDs and bone properties. 46 genes involved in neural tube closure are annotated with bone-related ontologies. These findings document shared genetic networks between spina bifida risk and bone structure, including PCP components and Zic2. Genetic variants which predispose to spina bifida may therefore independently diminish bone mass
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