On the zero set of G-equivariant maps

Let $G$ be a finite group acting on vector spaces $V$ and $W$ and consider a smooth $G$-equivariant mapping $f:V\to W$. This paper addresses the question of the zero set near a zero $x$ of $f$ with isotropy subgroup $G$. It is known from results of Bierstone and Field on $G$-transversality theory that the zero set in a neighborhood of $x$ is a stratified set. The purpose of this paper is to partially determine the structure of the stratified set near $x$ using only information from the representations $V$ and $W$. We define an index $s(\Sigma)$ for isotropy subgroups $\Sigma$ of $G$ which is the difference of the dimension of the fixed point subspace of $\Sigma$ in $V$ and $W$. Our main result states that if $V$ contains a subspace $G$-isomorphic to $W$, then for every maximal isotropy subgroup $\Sigma$ satisfying $s(\Sigma)>s(G)$, the zero set of $f$ near $x$ contains a smooth manifold of zeros with isotropy subgroup $\Sigma$ of dimension $s(\Sigma)$. We also present a systematic method to study the zero sets for group representations $V$ and $W$ which do not satisfy the conditions of our main theorem. The paper contains many examples and raises several questions concerning the computation of zero sets of equivariant maps. These results have application to the bifurcation theory of $G$-reversible equivariant vector fields

The nature of turbulence in OMC1 at the star forming scale: observations and simulations

Aim: To study turbulence in the Orion Molecular Cloud (OMC1) by comparing observed and simulated characteristics of the gas motions. Method: Using a dataset of vibrationally excited H2 emission in OMC1 containing radial velocity and brightness which covers scales from 70AU to 30000AU, we present the transversal structure functions and the scaling of the structure functions with their order. These are compared with the predictions of two-dimensional projections of simulations of supersonic hydrodynamic turbulence. Results: The structure functions of OMC1 are not well represented by power laws, but show clear deviations below 2000AU. However, using the technique of extended self-similarity, power laws are recovered at scales down to 160AU. The scaling of the higher order structure functions with order deviates from the standard scaling for supersonic turbulence. This is explained as a selection effect of preferentially observing the shocked part of the gas and the scaling can be reproduced using line-of-sight integrated velocity data from subsets of supersonic turbulence simulations. These subsets select regions of strong flow convergence and high density associated with shock structure. Deviations of the structure functions in OMC1 from power laws cannot however be reproduced in simulations and remains an outstanding issue.Comment: 12 pages, 8 figures, accepted A&A. Revised in response to referee. For higher resolution, see http://www.astro.phys.au.dk/~maikeng/sim_paper

A Toy Model of Flying Snake's Glide

We have developed a toy model of flying snake's glide [J.J. Socha, Nature vol. 418 (2002) 603.] by modifying a model for a falling paper. We have found that asymmetric oscillation is a key about why snake can glide. Further investigation for snake's glide will provide us details about how it can glide without a wing.Comment: 6 pages, to be submitted to J. Phys. Soc. Jpn. Revised Version submitted to the abov

Higgs boson production with one bottom quark including higher-order soft-gluon corrections

A Higgs boson produced in association with one or more bottom quarks is of great theoretical and experimental interest to the high-energy community. A precise prediction of its total and differential cross-section can have a great impact on the discovery of a Higgs boson with large bottom-quark Yukawa coupling, like the scalar (h^0 and H^0) and pseudoscalar (A^0) Higgs bosons of the Minimal Supersymmetric Standard Model (MSSM) in the region of large \tan\beta. In this paper we apply the threshold resummation formalism to determine both differential and total cross-sections for b g \to b\Phi (where \Phi = h^0, H^0), including up to next-to-next-to-next-to-leading order (NNNLO) soft plus virtual QCD corrections at next-to-leading logarithmic (NLL) accuracy. We present results for both the Fermilab Tevatron and the CERN Large Hadron Collider (LHC).Comment: revtex4, 13 pages, 11 figures; new references and additional comment

Market forces influence helping behaviour in cooperatively breeding paper wasps

This is the final version of the article. Available from Nature Publishing Group via the DOI in this record.Biological market theory is potentially useful for understanding helping behaviour in animal societies. It predicts that competition for trading partners will affect the value of commodities exchanged. It has gained empirical support in cooperative breeders, where subordinates help dominant breeders in exchange for group membership, but so far without considering one crucial aspect: outside options. We find support for a biological market in paper wasps, Polistes dominula. We first show that females have a choice of cooperative partners. Second, by manipulating entire subpopulations in the field, we increase the supply of outside options for subordinates, freeing up suitable nesting spots and providing additional nesting partners. We predicted that by intensifying competition for help, our manipulation would force dominants to accept a lower price for group membership. As expected, subordinates reduce their foraging effort following our treatments. We conclude that to accurately predict the amount of help provided, social units cannot be viewed in isolation: the surrounding market must also be considered.This work was funded by Natural Environment Research Council grant NE/K00655X/1 to J.F

Biological markets in cooperative breeders: quantifying outside options

This is the author's accepted manuscriptThe final version is available from The Royal Society via the DOI in this recordA major aim in evolutionary biology is to understand altruistic help and reproductive partitioning in cooperative societies, where subordinate helpers forego reproduction to rear dominant breeders' offspring. Traditional models of cooperation in these societies typically make a key assumption: that the only alternative to staying and helping is solitary breeding, an often unfeasible task. Using large-scale field experiments on paper wasps (Polistes dominula), we show that individuals have high-quality alternative nesting options available that offer fitness payoffs just as high as their actual chosen options, far exceeding payoffs from solitary breeding. Furthermore, joiners could not easily be replaced if they were removed experimentally, suggesting that it may be costly for dominants to reject them. Our results have implications for expected payoff distributions for cooperating individuals, and suggest that biological market theory, which incorporates partner choice and competition for partners, is necessary to understand helping behaviour in societies like that of P. dominula. Traditional models are likely to overestimate the incentive to stay and help, and therefore the amount of help provided, and may underestimate the size of reproductive concession required to retain subordinates. These findings are relevant for a wide range of cooperative breeders where there is dispersal between social groups.This work was funded by Natural Environment Research Council grant no. NE/K00655X/1 to J.F

Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation

It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. This formalism, making essential use of the 4-vector electromagnetic potential concept, provides a short derivation of the Lorentz force law of classical electrodynamics, the conventional definition of the magnetic field, in terms of spatial derivatives of the 4--vector potential and the Faraday-Lenz Law. An important distinction between the physical meanings of the space-time and energy-momentum 4--vectors is pointed out.Comment: 15 pages, no tables 1 figure. Revised and extended version of physics/0307133 Some typos removed and minor text improvements in this versio

A meta-analysis of transdiagnostic cognitive behavioural therapy in the treatment of child and young person anxiety disorders

Background: Previous meta-analyses of cognitive-behavioural therapy (CBT) for children and young people with anxiety disorders have not considered the efficacy of transdiagnostic CBT for the remission of childhood anxiety. Aim: To provide a meta-analysis on the efficacy of transdiagnostic CBT for children and young people with anxiety disorders. Methods: The analysis included randomized controlled trials using transdiagnostic CBT for children and young people formally diagnosed with an anxiety disorder. An electronic search was conducted using the following databases: ASSIA, Cochrane Controlled Trials Register, Current Controlled Trials, Medline, PsycArticles, PsychInfo, and Web of Knowledge. The search terms included “anxiety disorder(s)”, “anxi∗”, “cognitive behavio∗, “CBT”, “child∗”, “children”, “paediatric”, “adolescent(s)”, “adolescence”, “youth” and “young pe∗”. The studies identified from this search were screened against the inclusion and exclusion criteria, and 20 studies were identified as appropriate for inclusion in the current meta-analysis. Pre- and posttreatment (or control period) data were used for analysis. Results: Findings indicated significantly greater odds of anxiety remission from pre- to posttreatment for those engaged in the transdiagnostic CBT intervention compared with those in the control group, with children in the treatment condition 9.15 times more likely to recover from their anxiety diagnosis than children in the control group. Risk of bias was not correlated with study effect sizes. Conclusions: Transdiagnostic CBT seems effective in reducing symptoms of anxiety in children and young people. Further research is required to investigate the efficacy of CBT for children under the age of 6

Cracks Cleave Crystals

The problem of finding what direction cracks should move is not completely solved. A commonly accepted way to predict crack directions is by computing the density of elastic potential energy stored well away from the crack tip, and finding a direction of crack motion to maximize the consumption of this energy. I provide here a specific case where this rule fails. The example is of a crack in a crystal. It fractures along a crystal plane, rather than in the direction normally predicted to release the most energy. Thus, a correct equation of motion for brittle cracks must take into account both energy flows that are described in conventional continuum theories and details of the environment near the tip that are not.Comment: 6 page

Observations of spatial and velocity structure in the Orion Molecular Cloud

Observations are reported of H2 IR emission in the S(1) v=1-0 line at 2.121 microns in the Orion Molecular Cloud, OMC1, using the GriF instrument on the Canada-France-Hawaii Telescope. GriF is a combination of adaptive optics and Fabry-Perot interferometry, yielding a spatial resolution of 0.15" to 0.18" and a velocity discrimination as high as 1 km/s. Thanks to the high spatial and velocity resolution of the GriF data, 193 bright H2 emission regions can be identified in OMC1. The general characteristics of these features are described in terms of radial velocities, brightness and spatial displacement of maxima of velocity and brightness, the latter to yield the orientation of flows in the plane of the sky. Strong spatial correlation between velocity and bright H2 emission is found and serves to identify many features as shocks. Important results are: (i) velocities of the excited gas illustrate the presence of a zone to the south of BN-IRc2 and Peak 1, and the west of Peak 2, where there is a powerful blue-shifted outflow with an average velocity of -18 km/s. This is shown to be the NIR counterpart of an outflow identified in the radio from source I, a very young O-star. (ii) There is a band of weak velocity features (<5 km/s) in Peak 1 which may share a common origin through an explosive event, in the BN-IRc2 region, with the fast-moving fingers (or bullets) to the NW of OMC1. (iii) A proportion of the flows are likely to represent sites of low mass star formation and several regions show multiple outflows, probably indicative of multiple star formation within OMC1. The high spatial and velocity resolution of the GriF data show these and other features in more detail than has previously been possible.Comment: 27 pages, 19 figures, submitted to A&A Version 2: Several additions, including a section on protostellar candidates in OMC1, have been made based on the referee's suggestions v3: corrected typograph