19,992 research outputs found

### 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

### Interaction of a Modulated Electron Beam with a Plasma

The results of a theoretical and experimental investigation of the high-frequency interaction of an electron beam with a plasma are reported. An electron beam, modulated at a microwave frequency, passes through a uniform region of a mercury arc discharge after which it is demodulated. Exponentially growing wave amplification along the electron beam was experimentally observed for the first time at a microwave frequency equal to the plasma frequency. Approximate theories of the effects of 1) plasma-electron collision frequencies, 2) plasma-electron thermal velocities and 3) finite beam diameter, are given. In a second experiment the interaction between a modulated electron beam and a slow electrostatic wave on a plasma column has been studied. A strong interaction occurs when the velocity of the electron beam is approximately equal to the velocity of the wave and the interaction is essentially the same as that which occurs in traveling-wave amplifiers, except that here the plasma colum replaces the usual helical slow-wave circuit. The theory predicting rates of growth is presented and compared with the experimental results

### 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

### Transition Radiation in QCD matter

In ultrarelativistic heavy ion collisions a finite size QCD medium is
created. In this paper we compute radiative energy loss to zeroth order in
opacity by taking into account finite size effects. Transition radiation occurs
on the boundary between the finite size medium and the vacuum, and we show that
it lowers the difference between medium and vacuum zeroth order radiative
energy loss relative to the infinite size medium case. Further, in all previous
computations of light parton radiation to zeroth order in opacity, there was a
divergence caused by the fact that the energy loss is infinite in the vacuum
and finite in the QCD medium. We show that this infinite discontinuity is
naturally regulated by including the transition radiation.Comment: 21 page, 22 figure

### 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

### 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

### 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

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