Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

The homotopy type of the loops on (n−1)(n-1)-connected (2n+1)(2n+1)-manifolds

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are determined by the rank of the free Abelian part of the homology. Moreover, we show that these $p$-local homotopy groups can be expressed as a direct sum of $p$-local homotopy groups of spheres. The integral homotopy type of the loop space is also computed and shown to depend only on the rank of the free Abelian part and the torsion subgroup.Comment: Trends in Algebraic Topology and Related Topics, Trends Math., Birkhauser/Springer, 2018. arXiv admin note: text overlap with arXiv:1510.0519

Coastally Trapped Wind Reversals: Progress toward Understanding

Coastally trapped wind reversals along the U.S. west coast, which are often accompanied by a northward surge of fog or stratus, are an important warm-season forecast problem due to their impact on coastal maritime activities and airport operations. Previous studies identified several possible dynamic mechanisms that could be responsible for producing these events, yet observational and modeling limitations at the time left these competing interpretations open for debate. In an effort to improve our physical understanding, and ultimately the prediction, of these events, the Office of Naval Research sponsored an Accelerated Research Initiative in Coastal Meteorology during the years 1993â 98 to study these and other related coastal meteorological phenomena. This effort included two field programs to study coastally trapped disturbances as well as numerous modeling studies to explore key dynamic mechanisms. This paper describes the various efforts that occurred under this program to provide an advancement in our understanding of these disturbances. While not all issues have been solved, the synoptic and mesoscale aspects of these events are considerably better understood.Most of the authors were supported through the Office of Naval Research Coastal Meteorology Accelerated Research Initiative, one of the authors (WTT) was supported by Program Element 0601153N, Naval Research Laboratory

Theory and computation of covariant Lyapunov vectors

Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate these directions. Though the concept of these vectors has been known for a long time, they became practically computable only recently due to algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in covariant Lyapunov vectors and their wide range of potential applications, in this article we summarize the available information related to Lyapunov vectors and provide a detailed explanation of both the theoretical basics and numerical algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The angles between these vectors and the original covariant vectors are norm-independent and can be considered as characteristic numbers. Moreover, we present and study in detail an improved approach for computing covariant Lyapunov vectors. Also we describe, how one can test for hyperbolicity of chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure

Atmospheric forcing of the Oregon coastal ocean during the 2001 upwelling season

Copyrighted by American Geophysical Union. Meteorological conditions during an intensive oceanographic observational program in May through August 2001 along the central Oregon coast are described and related to larger-scale and longer-term conditions. Southward wind stresses of 0.05-0.1 N m⁻² occurred roughly 75% of the time, with a sustained period of dominantly southward stress from mid-June through July. Wind variations were correlated with variations in the large-scale Aleutian Low and North Pacific High pressure centers; correlations with the continental Thermal Low were small. Intraseasonal oscillations in alongshore wind stress (periods near 20 days) correlated with the north-south position of the jet stream. These stress oscillations drove 20 day oscillations in upper ocean temperature, with a lag of roughly 5 days for maximum correlation and amplitudes near 4°C. The sum of sensible and latent air-sea heat fluxes was generally into the atmosphere through June, then weakly into the ocean thereafter, with fluctuations on synoptic timescales. Semidiurnal fluctuations in surface air temperature were observed at two northern moorings, apparently forced indirectly by nonlinear internal ocean tides. The diurnal cycle of wind stress was similar for both southward and northward wind conditions, with the diurnal alongshore fluctuation southward in the evening and northward in the morning. During southward winds the marine atmospheric boundary layer (MABL) was typically defined clearly by a strong temperature inversion, and a shallow stable internal boundary layer often formed within the MABL over cool upwelled waters, with surface air temperature roughly 1°C lower inshore than offshore. During northward winds, essentially no low-level temperature stratification was observed

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are "magnetic bions" which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are "neutral bions" which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics - which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Ecalle's resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of supersymmetric models added at the end of section 8.1, reference adde

The CLIMODE field campaign : observing the cycle of convection and restratification over the Gulf Stream

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009): 1337-1350, doi:10.1175/2009BAMS2706.1.A major oceanographic field experiment is described, which is designed to observe, quantify, and understand the creation and dispersal of weakly stratified fluid known as “mode water” in the region of the Gulf Stream. Formed in the wintertime by convection driven by the most intense air–sea fluxes observed anywhere over the globe, the role of mode waters in the general circulation of the subtropical gyre and its biogeo-chemical cycles is also addressed. The experiment is known as the CLIVAR Mode Water Dynamic Experiment (CLIMODE). Here we review the scientific objectives of the experiment and present some preliminary results.Physical Oceanography program of NS

The capacity of short-chain fructo-oligosaccharides to stimulate faecal bifidobacteria: a dose-response relationship study in healthy humans

BACKGROUND: Short-chain fructo-oligosaccharides (scFOS) are well-known for their bifidogenicity. In a large study comprising 200 healthy volunteers, we determined the bifidogenic properties of 7 non-digestible carbohydrates administered at a dose of 10 g/d in the diet; we analysed dose-response relationships of the bifidogenic substrates at doses ranging from 2.5 to 10 g/d in comparison with a placebo. The aim of this presentation is to give more details about the dose-response effects of short-chain fructo-oligosaccharides (scFOS). METHODS: Forty healthy volunteers (18 males, 22 females) eating their usual diets were randomly divided into 5 groups of 8 subjects and received scFOS at a dose of 2.5, 5.0, 7.5 and 10 g/d or a placebo for 7 d. Stools were collected before (day (d) 8) and at the end (day (d) 15) of sugar consumption, and tolerance was evaluated using a daily chart. RESULTS (M ± SEM): Bifidobacteria counts increase was higher in scFOS than in placebo group for all doses tested [2.5 g/d (from 9.15 ± 0.59 to 9.39 ± 0.70; P = 0.02); 5 g/d (from 10.21 ± 0.21 to 10.67 ± 0.22; P = 0.03); 7.5 g/d (from 9.28 ± 0.49 to 9.85 ± 0.35;P = 0.01); 10 g/d (from 9.00 ± 0.81 to 10.18 ± 0.60; P = 0.003)]. A significant correlation between the ingested dose of scFOS and faecal bifidobacteria counts was observed at d15 (r(2 )= 0.307, P < 0.001). Total anaerobes increased at the dose of 10 g/d. No significant differences were found for Bacteroides, Lactobacillus, enterobacteria or pH in any group. The frequency of digestive symptoms was not different between scFOS at any of the doses tested and placebo. Bloating was significantly more intense during scFOS ingestion at doses of 2.5 and 5 g/d, but not at doses of 7.5 and 10 g/d. Excess flatus, borborygmi and abdominal pain did not differ from the placebo at any of the doses tested. CONCLUSION: This study showed that scFOS is bifidogenic and well tolerated at doses ranging from 2.5 to 10 g/d, and that there is a dose-response relationship in healthy volunteers

Links between cardiovascular disease and osteoporosis in postmenopausal women: serum lipids or atherosclerosis per se?

INTRODUCTION AND HYPOTHESIS: Epidemiological observations suggest links between osteoporosis and risk of acute cardiovascular events and vice versa. Whether the two clinical conditions are linked by common pathogenic factors or atherosclerosis per se remains incompletely understood. We investigated whether serum lipids and polymorphism in the ApoE gene modifying serum lipids could be a biological linkage. METHODS: This was an observational study including 1176 elderly women 60–85 years old. Women were genotyped for epsilon (ɛ) allelic variants of the ApoE gene, and data concerning serum lipids (total cholesterol, triglycerides, HDL-C, LDL-C, apoA1, ApoB, Lp(a)), hip and spine BMD, aorta calcification (AC), radiographic vertebral fracture and self-reported wrist and hip fractures, cardiovascular events together with a wide array of demographic and lifestyle characteristics were collected. RESULTS: Presence of the ApoE ɛ4 allele had a significant impact on serum lipid profile, yet no association with spine/hip BMD or AC could be established. In multiple regression models, apoA1 was a significant independent contributor to the variation in AC. However, none of the lipid components were independent contributors to the variation in spine or hip BMD. When comparing the women with or without vertebral fractures, serum triglycerides showed significant differences. This finding was however not applicable to hip or wrist fractures. After adjustment for age, severe AC score (≥6) and/or manifest cardiovascular disease increased the risk of hip but not vertebral or wrist fractures. CONCLUSION: The contribution of serum lipids to the modulators of BMD does not seem to be direct but rather indirect via promotion of atherosclerosis, which in turn can affect bone metabolism locally, especially when skeletal sites supplied by end-arteries are concerned. Further studies are needed to explore the genetic or environmental risk factors underlying the association of low triglyceride levels to vertebral fractures