The Effect of Encounters on the Eccentricity of Binaries in Clusters

We derive analytical expressions for the change in the orbital eccentricity of a binary following a distant encounter with a third star on a hyperbolic or parabolic orbit. To establish the accuracy of these expressions, we present detailed comparisons with the results of direct numerical integrations of the equations of motion for the three bodies. We treat with particular care the difficult case of a binary with zero initial eccentricity. In this case, we show that the eccentricity $\delta e$ induced by the encounter declines in general as a power-law, \delta e\propto (a/\rp)^{5/2}, where $a$ is the binary semi-major axis and \rp is the periastron distance of the encounter. This power-law arises from the octupole-level secular perturbation of the binary. In contrast, non-secular quadrupole-level perturbations induce an eccentricity change that declines exponentially with \rp. These non-secular effects can become dominant at sufficiently small \rp, for a sufficiently high relative velocity, or for a sufficiently massive perturber. We also derive cross sections for eccentricity change and compare our results with those of previous studies based on numerical scattering experiments. Our results have important implications for a number of astrophysical problems including, in particular, the evolution of binary millisecond pulsars in globular clusters.Comment: final version with minor revisions, uses MNRAS TeX macros, 23 pages, to appear in MNRAS, also available from http://ensor.mit.edu/~rasio/papers

Smoothed Particle Hydrodynamics Calculations of Stellar Interactions

Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar interactions, including collisions between main sequence stars and the coalescence of compact binaries.Comment: 21 pages, invited review paper to appear in Journal of Computational and Applied Mathematics (JCAM). Fig. 2 is available from the authors in hardcopy form only. Revised, slightly abbreviated versio

Sustainable landfill leachate treatment using refuse and pine bark as a carbon source for biodenitrification

Raw and 10-week composted commercial garden refuse (CGR) materials and pine bark (PB) mulch were evaluated for their potential use as alternative and sustainable sources of carbon for landfill leachate bio-denitrification. Dynamic batch tests using synthetic nitrate solutions of 100, 500 and 2000 mg NO3 L−1 were used to investigate the substrate performance at increasing nitrate concentrations under optimal conditions. Further to this, sequential batch tests using genuine nitrified landfill leachate with a concentration of 2000 mg NO3 L−1 were carried out to evaluate substrates behaviour in the presence of a complex mixture of chemicals present in leachate. Results showed that complete denitrification occurred in all conditions, indicating that raw and composted CGR and PB can be used as sustainable and efficient media for landfill leachate bio-denitrification. Of the three substrates, raw garden refuse yields the fastest denitrification rate followed by 10-week composted CGR and PB. However, the efficiency of the raw CGR was lower when using genuine leachate, indicating the inhibitory effect of components of the leachate on the denitrification process. Ten-week composted CGR performed optimally at low nitrate concentrations, while poor nitrate removal ability was found at higher nitrate concentrations (2000 mg L−1). In contrast, the PB performance was 3.5 times faster than that of the composted garden refuse at higher nitrate concentrations. Further to this, multi-criteria analysis of the process variables provided an easily implementable framework for the use of waste materials as an alternative and sustainable source of carbon for denitrification

Semiclassical analysis for the Kramers-Fokker-Planck equation

We study some accurate semiclassical resolvent estimates for operators that are neither selfadjoint nor elliptic, and applications to the Cauchy problem. In particular we get a precise description of the spectrum near the imaginary axis and precise resolvent estimates inside the pseudo-spectrum. We apply our results to the Kramers-Fokker-Planck operator

Low-temperature thermochronology and thermokinematic modeling of deformation, exhumation, and development of topography in the central Southern Alps, New Zealand

Apatite and zircon (U-Th)/He and fission track ages were obtained from ridge transects across the central Southern Alps, New Zealand. Interpretation of local profiles is difficult because relationships between ages and topography or local faults are complex and the data contain large uncertainties, with poor reproducibility between sample duplicates. Data do form regional patterns, however, consistent with theoretical systematics and corroborating previous observations: young Neogene ages occur immediately southeast of the Alpine Fault (the main plate boundary structure on which rocks are exhumed); partially reset ages occur in the central Southern Alps; and older Mesozoic ages occur further toward the southeast. Zircon apparent ages are older than apatite apparent ages for the equivalent method. Three-dimensional thermokinematic modeling of plate convergence incorporates advection of the upper Pacific plate along a low-angle detachment then up an Alpine Fault ramp, adopting a generally accepted tectonic scenario for the Southern Alps. The modeling incorporates heat flow, evolving topography, and the detailed kinetics of different thermochronometric systems and explains both complex local variations and regional patterns. Inclusion of the effects of radiation damage on He diffusion in detrital apatite is shown to have dramatic effects on results. Geometric and velocity parameters are tuned to fit model ages to observed data. Best fit is achieved at 9 mm a−1 plate convergence, with Pacific plate delamination on a gentle 10°SE dipping detachment and more rapid uplift on a 45–60° dipping Alpine Fault ramp from 15 km depth. Thermokinematic modeling suggests dip-slip motion on reverse faults within the Southern Alps should be highest ∼22 km from the Alpine Fault and much lower toward the southeast

Consistency Conditions for Brane Worlds in Arbitrary Dimensions

We consider ``brane world sum rules'' for compactifications involving an arbitrary number of spacetime dimensions. One of the most striking results derived from such consistency conditions is the necessity for negative tension branes to appear in five--dimensional scenarios. We show how this result is easily evaded for brane world models with more than five dimensions. As an example, we consider a novel realization of the Randall--Sundrum scenario in six dimensions involving only positive tension branes.Comment: 18 pages, LaTex, refs. adde

Flow studies in close-coupled ventral nozzles for STOVL aircraft

Flow in a generic ventral nozzle system was studied experimentally and analytically with the PARC3D computational fluid dynamics program in order to evaluate the program's ability to predict system performance and internal flow patterns. A generic model of a tailpipe with a rectangular ventral nozzle, about 1/3 of full size, was tested with unheated air at steady state pressure ratios up to 4.0. The end of the tailpipe was closed to simulate a blocked exhaust nozzle. Flow behavior into and through the ventral duct is discussed and illustrated with paint streak flow visualization photographs. PARC3D graphic images are shown for comparison with the experimental photographs. The program successfully predicted internal flow patterns; it also computed thrust and discharge coefficients within 1 pct. of measured values

Experimental and analytical study of close-coupled ventral nozzles for ASTOVL aircraft

Flow in a generic ventral nozzle system was studied experimentally and analytically with a block version of the PARC3D computational fluid dynamics program (a full Navier-Stokes equation solver) in order to evaluate the program's ability to predict system performance and internal flow patterns. For the experimental work a one-third-size model tailpipe with a single large rectangular ventral nozzle mounted normal to the tailpipe axis was tested with unheated air at steady-state pressure ratios up to 4.0. The end of the tailpipe was closed to simulate a blocked exhaust nozzle. Measurements showed about 5 1/2 percent flow-turning loss, reasonable nozzle performance coefficients, and a significant aftward axial component of thrust due to flow turning loss, reasonable nozzle performance coefficients, and a significant aftward axial component of thrust due to flow turning more than 90 deg. Flow behavior into and through the ventral duct is discussed and illustrated with paint streak flow visualization photographs. For the analytical work the same ventral system configuration was modeled with two computational grids to evaluate the effect of grid density. Both grids gave good results. The finer-grid solution produced more detailed flow patterns and predicted performance parameters, such as thrust and discharge coefficient, within 1 percent of the measured values. PARC3D flow visualization images are shown for comparison with the paint streak photographs. Modeling and computational issues encountered in the analytical work are discussed