Delaunay Ends of Constant Mean Curvature Surfaces

The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mean curvature surface which has a properly immersed end that is asymptotically Delaunay. Furthermore, that end is embedded if the Delaunay surface is unduloidal

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

We present a theorem on the unitarizability of loop group valued monodromy representations and apply this to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply-connected 3-dimensional space forms $\R^3$, \bbS^3 and \bbH^3. Additionally, we compute the extended frame for any associated family of Delaunay surfaces.Comment: 18 pages, revised versio

Constant mean curvature surfaces of any positive genus

We show the existence of several new families of non-compact constant mean curvature surfaces: (i) singly-punctured surfaces of arbitrary genus $g \geq 1$, (ii) doubly-punctured tori, and (iii) doubly periodic surfaces with Delaunay ends.Comment: 14 pages, 10 figure

Multistable alignment states in nematic liquid crystal filled wells

Two distinct, stable alignment states have been observed for a nematic liquid crystal confined in a layer with thickness of 12 μm and in square wells with sides of length between 20 and 80 μm. The director lies in the plane of the layer and line defects occur in two corners of the squares. The positions of the defects determine whether the director orientation is across the diagonal or is parallel to two opposite edges of the square. The device is multistable because both the diagonal and parallel states are stable when rotated by multiples of 90° in plane

C II abundances in early-type stars: solution to a notorious non-LTE problem

We address a long-standing discrepancy between non-LTE analyses of the prominent C II 4267 and 6578/82 A multiplets in early-type stars. A comprehensive non-LTE model atom of C II is constructed based on critically selected atomic data. This model atom is used for an abundance study of six apparently slow-rotating main-sequence and giant early B-type stars. High-resolution and high-S/N spectra allow us to derive highly consistent abundances not only from the classical features but also from up to 18 further C II lines in the visual - including two so far unreported emission features equally well reproduced in non-LTE. These results require the stellar atmospheric parameters to be determined with care. A homogeneous (slightly) sub-solar present-day carbon abundance from young stars in the solar vicinity (in associations and in the field) of log C/H +12= 8.29+/-0.03 is indicated.Comment: 8 pages, 5 figure

Correlation length in cuprates deduced from the impurity-induced magnetization

We report a new multi-nuclei based NMR method which allows us to image the staggered polarization induced by nonmagnetic Li impurities in underdoped O6.6 and slightly overdoped O7 YBa2Cu3O6+y above T_C. The spatial extension of the polarization xi_imp approximately follows a Curie law, increasing up to six lattice constants at T=80K at O6.6 in the pseudogap regime. Near optimal doping, the staggered magnetization has the same shape, with xi_imp reduced by a factor 2. xi_imp is argued to reveal the intrinsic magnetic correlation length of the pure system. It is found to display a smooth evolution through the pseudogap regime.Comment: 8 latex pages + 8 figures, to appear in Physical Review B, this resubmitted version is twice longer than the previous one : we detail here our method to determine the impurity-induced magnetizatio

Pseudo-axions in Little Higgs models

Little Higgs models have an enlarged global symmetry which makes the Higgs boson a pseudo-Goldstone boson. This symmetry typically contains spontaneously broken U(1) subgroups which provide light electroweak-singlet pseudoscalars. Unless such particles are absorbed as the longitudinal component of $Z'$ states, they appear as pseudoscalars in the physical spectrum at the electroweak scale. We outline their significant impact on Little Higgs phenomenology and analyze a few possible signatures at the LHC and other future colliders in detail. In particular, their presence significantly affects the physics of the new heavy quark states predicted in Little Higgs models, and inclusive production at LHC may yield impressive diphoton resonances.Comment: 28 pages, 9 figs., accepted to PRD; footnote added, typos correcte

Mechanical Competence and Bone Quality Develop During Skeletal Growth.

Bone fracture risk is influenced by bone quality, which encompasses bone's composition as well as its multiscale organization and architecture. Aging and disease deteriorate bone quality, leading to reduced mechanical properties and higher fracture incidence. Largely unexplored is how bone quality and mechanical competence progress during longitudinal bone growth. Human femoral cortical bone was acquired from fetal (n = 1), infantile (n = 3), and 2- to 14-year-old cases (n = 4) at the mid-diaphysis. Bone quality was assessed in terms of bone structure, osteocyte characteristics, mineralization, and collagen orientation. The mechanical properties were investigated by measuring tensile deformation at multiple length scales via synchrotron X-ray diffraction. We find dramatic differences in mechanical resistance with age. Specifically, cortical bone in 2- to 14-year-old cases exhibits a 160% greater stiffness and 83% higher strength than fetal/infantile cases. The higher mechanical resistance of the 2- to 14-year-old cases is associated with advantageous bone quality, specifically higher bone volume fraction, better micronscale organization (woven versus lamellar), and higher mean mineralization compared with fetal/infantile cases. Our study reveals that bone quality is superior after remodeling/modeling processes convert the primary woven bone structure to lamellar bone. In this cohort of female children, the microstructural differences at the femoral diaphysis were apparent between the 1- to 2-year-old cases. Indeed, the lamellar bone in 2- to 14-year-old cases had a superior structural organization (collagen and osteocyte characteristics) and composition for resisting deformation and fracture than fetal/infantile bone. Mechanistically, the changes in bone quality during longitudinal bone growth lead to higher fracture resistance because collagen fibrils are better aligned to resist tensile forces, while elevated mean mineralization reinforces the collagen scaffold. Thus, our results reveal inherent weaknesses of the fetal/infantile skeleton signifying its inferior bone quality. These results have implications for pediatric fracture risk, as bone produced at ossification centers during children's longitudinal bone growth could display similarly weak points. © 2019 American Society for Bone and Mineral Research