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

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

Shadowing Effects on the Nuclear Suppression Factor, R_dAu, in d+Au Interactions

We explore how nuclear modifications to the nucleon parton distributions affect production of high transverse momentum hadrons in deuteron-nucleus collisions. We calculate the charged hadron spectra to leading order using standard fragmentation functions and shadowing parameterizations. We obtain the d+Au to pp ratio both in minimum bias collisions and as a function of centrality. The minimum bias results agree reasonably well with the BRAHMS data while the calculated centrality dependence underestimates the data and is a stronger function of p_T than the data indicate.Comment: 18 pages, 3 figures, final version, Phys. Rev. C in pres

Near-Infrared Spectroscopy of Molecular Hydrogen Emission in Four Reflection Nebulae: NGC 1333, NGC 2023, NGC 2068, and NGC 7023

We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2) emission from NGC 1333, NGC 2023, NGC 2068, and NGC 7023 and derive the physical properties of the molecular material in these reflection nebulae. Our observations of NGC 2023 and NGC 7023 and the physical parameters we derive for these nebulae are in good agreement with previous studies. Both NGC 1333 and NGC 2068 have no previously-published analysis of near-infrared spectra. Our study reveals that the rotational-vibrational states of molecular hydrogen in NGC 1333 are populated quite differently from NGC 2023 and NGC 7023. We determine that the relatively weak UV field illuminating NGC 1333 is the primary cause of the difference. Further, we find that the density of the emitting material in NGC 1333 is of much lower density, with n ~ 10^2 - 10^4 cm^-3. NGC 2068 has molecular hydrogen line ratios more similar to those of NGC 7023 and NGC 2023. Our model fits to this nebula show that the bright, H_2-emitting material may have a density as high as n ~ 10^5 cm^-3, similar to what we find for NGC 2023 and NGC 7023. Our spectra of NGC 2023 and NGC 7023 show significant changes in both the near-infrared continuum and H_2 intensity along the slit and offsets between the peaks of the H_2 and continuum emission. We find that these brightness changes may correspond to real changes in the density and temperatures of the emitting region, although uncertainties in the total column of emitting material along a given line of sight complicates the interpretation. The spatial difference in the peak of the H_2 and near-infrared continuum peaks in NGC 2023 and NGC 7023 shows that the near-infrared continuum is due to a material which can survive closer to the star than H_2 can.Comment: Submitted for publication in ApJ. 34 pages including 12 embedded postscript figures. Also available at http://www.astronomy.ohio-state.edu/~martini/pub

'Against the World': Michael Field, female marriage and the aura of amateurism'

This article considers the case of Katherine Bradley and Edith Cooper, an aunt and niece who lived and wrote together as ‘Michael Field’ in the fin-de-siècle Aesthetic movement. Bradley’s bold statement that she and Cooper were ‘closer married’ than the Brownings forms the basis for a discussion of their partnership in terms of a ‘female marriage’, a union that is reflected, as I will argue, in the pages of their writings. However, Michael Field’s exclusively collaborative output, though extensive, was no guarantee for success. On the contrary, their case illustrates the notion, valid for most products of co-authorship, that the jointly written work is always surrounded by an aura of amateurism. Since collaboration defied the ingrained notion of the author as the solitary producer of his or her work, critics and readers have time and again attempted to ‘parse’ the collaboration by dissecting the co-authored work into its constituent halves, a treatment that the Fields too failed to escape

Biogeographic analysis of the Tortugas Ecological Reserve: Examining the refuge effect following reserve establishment

Almost 120 days at sea aboard three NOAA research vessels and one fishing vessel over the past three years have supported biogeographic characterization of Tortugas Ecological Reserve (TER). This work initiated measurement of post-implementation effects of TER as a refuge for exploited species. In Tortugas South, seafloor transect surveys were conducted using divers, towed operated vehicles (TOV), remotely operated vehicles (ROV), various sonar platforms, and the Deepworker manned submersible. ARGOS drifter releases, satellite imagery, ichthyoplankton surveys, sea surface temperature, and diver census were combined to elucidate potential dispersal of fish spawning in this environment. Surveys are being compiled into a GIS to allow resource managers to gauge benthic resource status and distribution. Drifter studies have determined that within the ~ 30 days of larval life stage for fishes spawning at Tortugas South, larvae could reach as far downstream as Tampa Bay on the west Florida coast and Cape Canaveral on the east coast. Together with actual fish surveys and water mass delineation, this work demonstrates that the refuge status of this area endows it with tremendous downstream spillover and larval export potential for Florida reef habitats and promotes the maintenance of their fish communities. In Tortugas North, 30 randomly selected, permanent stations were established. Five stations were assigned to each of the following six areas: within Dry Tortugas National Park, falling north of the prevailing currents (Park North); within Dry Tortugas National Park, falling south of the prevailing currents (Park South); within the Ecological Reserve falling north of the prevailing currents (Reserve North); within the Ecological Reserve falling south of the prevailing currents (Reserve South); within areas immediately adjacent to these two strata, falling north of the prevailing currents (Out North); and within areas immediately adjacent to these two strata, falling south of the prevailing currents (Out South). Intensive characterization of these sites was conducted using multiple sonar techniques, TOV, ROV, diver-based digital video collection, diver-based fish census, towed fish capture, sediment particle-size, benthic chlorophyll analyses, and stable isotope analyses of primary producers, fish, and, shellfish. In order to complement and extend information from studies focused on the coral reef, we have targeted the ecotone between the reef and adjacent, non-reef habitats as these areas are well-known in ecology for indicating changes in trophic relationships at the ecosystem scale. Such trophic changes are hypothesized to occur as top-down control of the system grows with protection of piscivorous fishes. Preliminary isotope data, in conjunction with our prior results from the west Florida shelf, suggest that the shallow water benthic habitats surrounding the coral reefs of TER will prove to be the source of a significant amount of the primary production ultimately fueling fish production throughout TER and downstream throughout the range of larval fish dispersal. Therefore, the status and influence of the previously neglected, non-reef habitat within the refuge (comprising ~70% of TER) appears to be intimately tied to the health of the coral reef community proper. These data, collected in a biogeographic context, employing an integrated Before-After Control Impact design at multiple spatial scales, leave us poised to document and quantify the postimplementation effects of TER. Combined with the work at Tortugas South, this project represents a multi-disciplinary effort of sometimes disparate disciplines (fishery oceanography, benthic ecology, food web analysis, remote sensing/geography/landscape ecology, and resource management) and approaches (physical, biological, ecological). We expect the continuation of this effort to yield critical information for the management of TER and the evaluation of protected areas as a refuge for exploited species. (PDF contains 32 pages.

Biomass for thermochemical conversion: targets and challenges

Includes bibliographical references (pages 13-20).Bioenergy will be one component of a suite of alternatives to fossil fuels. Effective conversion of biomass to energy will require the careful pairing of advanced conversion technologies with biomass feedstocks optimized for the purpose. Lignocellulosic biomass can be converted to useful energy products via two distinct pathways: enzymatic or thermochemical conversion. The thermochemical pathways are reviewed and potential biotechnology or breeding targets to improve feedstocks for pyrolysis, gasification, and combustion are identified. Biomass traits influencing the effectiveness of the thermochemical process (cell wall composition, mineral and moisture content) differ from those important for enzymatic conversion and so properties are discussed in the language of biologists (biochemical analysis) as well as that of engineers (proximate and ultimate analysis). We discuss the genetic control, potential environmental influence, and consequences of modification of these traits. Improving feedstocks for thermochemical conversion can be accomplished by the optimization of lignin levels, and the reduction of ash and moisture content. We suggest that ultimate analysis and associated properties such as H:C, O:C, and heating value might be more amenable than traditional biochemical analysis to the high-throughput necessary for the phenotyping of large plant populations. Expanding our knowledge of these biomass traits will play a critical role in the utilization of biomass for energy production globally, and add to our understanding of how plants tailor their composition with their environment.Published with support from the Colorado State University Libraries Open Access Research and Scholarship Fund