Geology of the Snap Lake kimberlite intrusion, Northwest Territories, Canada: field observations and their interpretation

The Cambrian (523 Ma) Snap Lake hypabyssal kimberlite intrusion, Northwest Territories, Canada, is a complex segmented diamond-bearing ore-body. Detailed geological investigations suggest that the kimberlite is a multi-phase intrusion with at least four magmatic lithofacies. In particular, olivine-rich (ORK) and olivine-poor (OPK) varieties of hypabyssal kimberlite have been identified. Key observations are that the olivine-rich lithofacieshas a strong tendency to be located where the intrusion is thickest and that there is a good correlation between intrusion thickness, olivine crystal size and crystal content. Heterogeneities in the lithofacies are attributed to variations in intrusion thickness and structural complexities. The geometry and distribution of lithofacies points to magmaticco-intrusion, and flow segregation driven by fundamental rheological differences between the two phases. We envisage that the low-viscosity OPK magma acted as a lubricant for the highly viscous ORK magma. The presenceof such low-viscosity, crystal-poor magmas may explain how crystal-laden kimberlite magmas (>60 vol.%) are able to reach the surface during kimberlite eruptions. We also document the absence of crystal settling and the development of an unusual subvertical fabric of elongate olivine crystals, which are explained by rapid degassing-induced quench crystallization of the magmas during and after intrusio

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

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

Neural processing of imminent collision in humans

Detecting a looming object and its imminent collision is imperative to survival. For most humans, it is a fundamental aspect of daily activities such as driving, road crossing and participating in sport, yet little is known about how the brain both detects and responds to such stimuli. Here we use functional magnetic resonance imaging to assess neural response to looming stimuli in comparison with receding stimuli and motion-controlled static stimuli. We demonstrate for the first time that, in the human, the superior colliculus and the pulvinar nucleus of the thalamus respond to looming in addition to cortical regions associated with motor preparation. We also implicate the anterior insula in making timing computations for collision events

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

On the symmetry breaking phenomenon

We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases

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

Polarization of Astronomical Maser Radiation. IV. Circular Polarization Profiles

Profile comparison of the Stokes parameters $V$ and $I$ is a powerful tool for maser data analysis, providing the first direct methods for unambiguous determination of (1) the maser saturation stage, (2) the amplification optical depth and intrinsic Doppler width of unsaturated masers, and (3) the comparative magnitudes of Zeeman splitting and Doppler linewidth. Circular polarization recently detected in OH 1720 MHz emission from the Galactic center appears to provide the first direct evidence for maser saturation.Comment: 14 pages, 1 Postscript figures (included), uses aaspp4.sty. To appear in Astrophysical Journa

The Indirect Limit on the Standard Model Higgs Boson Mass from the Precision FERMILAB, LEP and SLD Data

Standard Model fits are performed on the most recent leptonic and b quark Z decay data from LEP and SLD, and FERMILAB data on top quark production, to obtain $m_t$ and $m_H$. Poor fits are obtained, with confidence levels $\simeq$ 2%. Removing the b quark data improves markedly the quality of the fits and reduces the 95% CL upper limit on $m_H$ by $\simeq$ 50 GeV.Comment: 6 pages 3 tables i figur

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