Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

The ``Newtonian'' theory of spatially unbounded, self--gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space $\R^3$ from closed models based (without loss of generality) on a flat torus \T^3. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous ``background'' model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.Comment: submitted to G.R.G., TeX 30 pages; AEI preprint 01

Population Dynamics and Angler Exploitation of the Unique Muskellunge Population in Shoepack Lake, Voyageurs National Park, Minnesota

A unique population of muskellunge Esox masquinongy inhabits Shoepack Lake in Voyageurs National Park, Minnesota. Little is known about its status, dynamics, and angler exploitation, and there is concern for the long-term viability of this population. We used intensive sampling and mark–recapture methods to quantify abundance, survival, growth, condition, age at maturity and fecundity and angler surveys to quantify angler pressure, catch rates, and exploitation. During our study, heavy rain washed out a dam constructed by beavers Castor canadensis which regulates the water level at the lake outlet, resulting in a nearly 50% reduction in surface area. We estimated a population size of 1,120 adult fish at the beginning of the study. No immediate reduction in population size was detected in response to the loss of lake area, although there was a gradual, but significant, decline in population size over the 2-year study. Adults grew less than 50 mm per year, and relative weight (W r) averaged roughly 80. Anglers were successful in catching, on average, two fish during a full day of angling, but harvest was negligible. Shoepack Lake muskellunge exhibit much slower growth rates and lower condition, but much higher densities and angler catch per unit effort (CPUE), than other muskellunge populations. The unique nature, limited distribution, and location of this population in a national park require special consideration for management. The results of this study provide the basis for assessing the long-term viability of the Shoepack Lake muskellunge population through simulations of long-term population dynamics and genetically effective population size

Distinctive reactivities of surface-bound H and bulk H for the catalytic hydrogenation of acetylene

We report that both surface-bound H atoms and bulk H atoms, upon moving out from the bulk of a Ni single crystal to its surface of a (111) orientation, are reactive with adsorbed C2H2, but the two kinds of H atoms have unique product distributions. Both bulk H and surface-bound H react with C2H2 to produce adsorbed ethylidyne, CCH3, while only bulk H hydrogenates C2H2 to gas-phase ethylene and ethane, the products of interest in acetylene hydrogenation catalysis for the purification of ethylene streams. Their distinct reactivities arise from both their different directions of approach to the Π orbitals of the unsaturated hydrocarbon and their substantially different energetics. These observations demonstrate that H embedded in the metal catalyst is a reactant in alkyne hydrogenation and is not solely a source of surface-bound H which then reacts with acetylene, as proposed from correlations between the hydrogenation activity of Raney Ni and Pd catalysts and the amount of H absorbed in these catalysts. The reactivities of these two kinds of H atoms are clearly distinguished in this experiment because of the capability to synthesize either bulk H or surface-bound H cleanly in an ultrahigh vacuum environment

Catalytic hydrogenation of acetylene on Ni(111) by surface-bound H and bulk H

The reactions of hydrogen atoms adsorbed on a Ni(111) surface (surface-bound H) and hydrogen atoms just below the surface (bulk H) with coadsorbed acetylene are probed under ultrahigh vacuum conditions. Bulk H is observed to react with acetylene upon emerging onto the surface at 180 K. Gas-phase hydrogenation products, ethylene and ethane, are produced as well as an adsorbed species, ethylidyne. Ethylidyne is identified by high-resolution electron energy loss spectroscopy. Surface-bound H reacts with adsorbed acetylene above 250 K to produce a single product, adsorbed ethylidyne. No gas-phase hydrogenation products, such as ethylene or ethane, are observed. The reaction of surface-bound H is extremely slow, with a rate constant determined from measurements of the initial reaction rate to be in the range of 10-5−10-3 (ML s)-1 for a temperature range of 250−280 K. The activation energy for the rate-determining step, which is shown to be the addition of the first surface-bound H to acetylene to form an adsorbed vinyl species, increases from 9 to 17 kcal/mol as the total coverage decreases from 0.92 to 0.74 ML. The reaction rate cannot be described by a simple first-order dependence on the coverage of either reactant, indicating the presence of strong interactions between reactants. Measurements of the equilibrium constant reveal strong interactions between the reactant surface H and the product ethylidyne, possibly resulting in island formation. Mechanisms for the formation of ethylidyne by the reactions of both surface-bound and bulk H are proposed, as well as mechanisms for the formation of ethylene and ethane by bulk H. The different product distributions resulting from the reaction of acetylene with the two forms of hydrogen are discussed in terms of the large energy difference between bulk and surface-bound H

Synthesis and spectroscopic identification of ethylidyne adsorbed on Ni(111)&perp

The interaction of ethylene adsorbed on Ni(111) with gas-phase H atoms has been investigated. The major adsorbed reaction product is identified by high-resolution electron energy loss spectroscopy to be ethylidyne (C−CH3). This study is the first direct spectroscopic observation of a C−CH3 species adsorbed on Ni in an ultrahigh-vacuum environment. Spectra of four isotopomers, C−CH3, 13C−13CH3, C−CD3, and 13C−13CD3, are reported, and a complete and consistent vibrational assignment of their fundamental modes is presented. Based on this assignment, a force field is derived from the measured vibrational frequencies using a normal-modes analysis and is found to be in good agreement with that deduced from IR spectra of an ethylidyne species in an organometallic complex. Inspection of the eigenvectors of the normal-mode displacements reveals that substantial mixing of harmonic bond motions is the origin of the unusual upshift in frequency of the C−C stretching mode upon deuteration. A quantitative determination of the relative dynamic bond dipole moments demonstrates that the changes in intensity and dipole activity of the C−C stretching and symmetric CH3 deformation modes upon deuteration, phenomena common to all C−CD3 spectra, also arise from extensive mixing of bond motions. A detailed analysis of the spectra strongly suggests a C3v or C3 local environment for ethylidyne and a 3-fold hollow adsorption site