Studies in the application of recurrence relations to special perturbation methods

Using the rectangular equations of motion for the restricted three-body problem a comparison is made of the integration of these equations by the Encke method and by a set of perturbational equations. Each set of differential equations is integrated using Taylor series expansions where the coefficients of the powers of time are determined by recurrence relations. It is shown that for very small perturbations the use of the perturbational equations is more efficient than the use of the Encke method. A discussion is also given of when Cowell's method is more efficient than either of these techniques.     

Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates

A primitive equation ocean circulation model in nonlinear terrain-following coordinates is applied to a decadal-length simulation of the circulation in the North Atlantic Ocean. In addition to the stretched sigma coordinate, novel features of the model include the utilization of a weakly dissipative, third-order scheme for tracer advection, and a conservative and constancy-preserving time-stepping algorithm. The objectives of the study are to assess the quality of the new terrain-following model in the limit of realistic basin-scale simulations, and to compare the results obtained with it against those of other North Atlantic models used in recent multi-model comparison studies.The new model is able to reproduce many features of both the wind-driven and thermohaline circulation, and to do so within error bounds comparable with prior model simulations (e.g., CME and DYNAMO). Quantitative comparison with comparable results obtained with the Miami Isopycnic Coordinate Model (MICOM) show our terrain-following solutions are of similar overall quality when viewed against known measures of merit including meridional overturning and heat flux, Florida Straits and Gulf Stream transport, seasonal cycling of temperature and salinity, and upper ocean currents and tracer fields in the eastern North Atlantic Basin. Sensitivity studies confirm that the nonlinear vertical coordinate contributes significantly to model fidelity, and that the global inventories and spatial structure of the tracer fields are affected in important ways by the choice of lateral advection scheme.     

A model for the magmatic–hydrothermal system at Mount Rainier,Washington, from seismic and geochemical observations

 Mount Rainier is one of the most seismically active volcanoes in the Cascade Range, with an average of one to two high-frequency volcano-tectonic (or VT) earthquakes occurring directly beneath the summit in a given month. Despite this level of seismicity, little is known about its cause. The VT earthquakes occur at a steady rate in several clusters below the inferred base of the Quaternary volcanic edifice. More than half of 18 focal mechanisms determined for these events are normal, and most stress axes deviate significantly from the regional stress field. We argue that these characteristics are most consistent with earthquakes in response to processes associated with circulation of fluids and magmatic gases within and below the base of the edifice.Circulation of these fluids and gases has weakened rock and reduced effective stress to the point that gravity-induced brittle fracture, due to the weight of the overlying edifice, can occur. Results from seismic tomography and rock, water, and gas geochemistry studies support this interpretation. We combine constraints from these studies into a model for the magmatic system that includes a large volume of hot rock (temperatures greater than the brittle–ductile transition) with small pockets of melt and/or hot fluids at depths of 8–18 km below the summit. We infer that fluids and heat from this volume reach the edifice via a narrow conduit, resulting in fumarolic activity at the summit, hydrothermal alteration of the edifice, and seismicity. Received: 10 February 1999 / Accepted: 26 June 1999     

Ecologically Sustainable Fishing in Theory and Practice: Individual transferable quotas in Australia's South East Fishery

In 1988, responding to international legislation that requires sustainable fishery management, the Australian Fishery Management Authority (AFMA) implemented an individual transferable quota (ITQ) management system to address the environmental crisis in the South East Fishery. Defining sustainability in its broadest context to include social as well as economic and ecological dimensions, this paper firstly describes the environmental crisis and the South East Fishery's ITQ management system. Secondly, Christy's (1973) paper is employed as a catalyst to compare the theoretical socio-economic outcomes with the actual operation of ITQs. The brief South East Fishery experience suggests that the logic behind ITQs is correct. Production has become reorganised. Operators are not only fewer, but also embrace professionalism, quality, efficiency, and the operation of the free market within the industry. However, because of the local idiosyncrasies of this multi-species fishery, the legislation over territorial waters, and the absence of alternative employment, fishers have adopted non-quota fishing techniques and entered seas under New South Wales jurisdiction. Without a social re-adjustment policy or buy-out scheme, the AFMA's objective of ecologically sustainable development cannot be attained.     

A milliarcsecond-resolution image of the OH masers in G34.3+0.2

We present measurements of the distribution of the OH masers at 1665 and 1667 MHz towards the cometary ultracompact H  ii region in the complex G34.3+0.2. The results are based on observations made in both senses of circular polarization with a very long baseline interferometry (VLBI) array having an angular resolution of 5×20 mas². 38 maser features are identified in the region. 33 of these lie on an arc at the edge of the cometary H  ii region. Five are located in a cluster offset toward the north-east by 3 arcsec, and are probably associated with an independent ultracompact H  ii region. There is a velocity gradient of 30 km s⁻¹ pc⁻¹ across the arc. We identify five Zeeman pairs and determine that the magnetic field varies between 1 and 7 mG, but is always directed away from the Earth.
The OH masers may arise in clumps in a shell of gas in a bow shock caused by the motion of the exciting star through the molecular cloud. The stand-off distance and the thickness of the shocked shell are roughly consistent with those predicted by such a bow-shock model. Also, the position of the exciting star(s), as estimated from the focus of the parabolic bow shock, closely matches that of the peak emission from the cometary H  ii region. However, the north–south velocity gradient in the ionized material remains difficult to explain in the context of the bow-shock model.     

Granular Controls on Periodicity of Stick-Slip Events: Kinematics and Force-Chains in an Experimental Fault

It is a long-standing question whether granular fault material such as gouge plays a major role in controlling fault dynamics such as seismicity and slip-periodicity. In both natural and experimental faults, granular materials resist shear and accommodate strain via interparticle friction, fracture toughness, fluid pressure, dilation, and interparticle rearrangements. Here, we isolate the effects of particle rearrangements on granular deformation through laboratory experiments. Within a sheared photoelastic granular aggregate at constant volume, we simultaneously visualize both particle-scale kinematics and interparticle forces, the latter taking the form of force-chains. We observe stick-slip deformation and associated force drops during an overall strengthening of the shear zone. This strengthening regime provides insight into granular rheology and conditions of stick-slip periodicity, and may be qualitatively analogous to slip that accompanies longer term interseismic strengthening of natural faults. Of particular note is the observation that increasing the packing density increases the stiffness of the granular aggregate and decreases the damping (increases time-scales) during slip events. At relatively loose packing density, the slip displacements during the events follow an approximately power-law distribution, as opposed to an exponential distribution at higher packing density. The system exhibits switching between quasi-periodic and aperiodic slip behavior at all packing densities. Higher packing densities favor quasi-periodic behavior, with a longer time interval between aperiodic events than between quasi-periodic events. This difference in the time-scale of aperiodic stick-slip deformation is reflected in both the kinematics of interparticle slip and the force-chain dynamics: all major force-chain reorganizations are associated with aperiodic events. Our experiments conceptually link observations of natural fault dynamics with current models for granular stick-slip dynamics. We find that the stick-slip dynamics are consistent with a driven harmonic oscillator model with damping provided by an effective viscosity, and that shear-transformation-zone, jamming, and crackling noise theories provide insight into the effective stiffness and patterns of shear localization during deformation.     

Defining an absolute reference frame for ‘clumped’ isotope studies of CO2

We present a revised approach for standardizing and reporting analyses of multiply substituted isotopologues of CO₂ (i.e., ‘clumped’ isotopic species, especially the mass-47 isotopologues). Our approach standardizes such data to an absolute reference frame based on theoretical predictions of the abundances of multiply-substituted isotopologues in gaseous CO₂ at thermodynamic equilibrium. This reference frame is preferred over an inter-laboratory calibration of carbonates because it enables all laboratories measuring mass 47 CO₂ to use a common scale that is tied directly to theoretical predictions of clumping in CO₂, regardless of the laboratory’s primary research field (carbonate thermometry or CO₂ biogeochemistry); it explicitly accounts for mass spectrometric artifacts rather than convolving (and potentially confusing) them with chemical fractionations associated with sample preparation; and it is based on a thermodynamic equilibrium that can be experimentally established in any suitably equipped laboratory using commonly available materials.By analyzing CO₂ gases that have been subjected to established laboratory procedures known to promote isotopic equilibrium (i.e., heated gases and water-equilibrated CO₂), and by reference to thermodynamic predictions of equilibrium isotopic distributions, it is possible to construct an empirical transfer function that is applicable to data with unknown clumped isotope signatures. This transfer function empirically accounts for the fragmentation and recombination reactions that occur in electron impact ionization sources and other mass spectrometric artifacts. We describe the protocol necessary to construct such a reference frame, the method for converting gases with unknown clumped isotope compositions to this reference frame, and suggest a protocol for ensuring that all reported isotopic compositions (e.g., Δ₄₇ values; [Eiler and Schauble, 2004] and [Eiler, 2007]) can be compared among different laboratories and instruments, independent of laboratory-specific analytical or methodological differences. We then discuss the use of intra-laboratory secondary reference frames (e.g., based on carbonate standards) that can be more easily used to track the evolution of each laboratory’s empirical transfer function. Finally, we show inter-laboratory reproducibility on the order of ±0.010 (1σ) for four carbonate standards, and present revised paleotemperature scales that should be used to convert carbonate clumped isotope signatures to temperature when using the absolute reference frame described here. Even when using the reference frame, small discrepancies remain between two previously published synthetic carbonate calibrations. We discuss possible reasons for these discrepancies, and highlight the need for additional low temperature (<15 °C) synthetic carbonate experiments.