Long-term orbital lifetime predictions

Long-term orbital lifetime predictions are analyzed. Predictions were made for three satellites: the Solar Max Mission (SMM), the Long Duration Exposure Facility (LDEF), and the Pegasus Boiler Plate (BP). A technique is discussed for determining an appropriate ballistic coefficient to use in the lifetime prediction. The orbital decay rate should be monitored regularly. Ballistic coefficient updates should be done whenever there is a significant change in the actual decay rate or in the solar activity prediction

Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein we: show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.Comment: 19 page

A Limited Habitable Zone for Complex Life

The habitable zone (HZ) is commonly defined as the range of distances from a host star within which liquid water, a key requirement for life, may exist on a planet's surface. Substantially more CO2 than present in Earth's modern atmosphere is required to maintain clement temperatures for most of the HZ, with several bars required at the outer edge. However, most complex aerobic life on Earth is limited by CO2 concentrations of just fractions of a bar. At the same time, most exoplanets in the traditional HZ reside in proximity to M dwarfs, which are more numerous than Sun-like G dwarfs but are predicted to promote greater abundances of gases that can be toxic in the atmospheres of orbiting planets, such as carbon monoxide (CO). Here we show that the HZ for complex aerobic life is likely limited relative to that for microbial life. We use a 1D radiative-convective climate and photochemical models to circumscribe a Habitable Zone for Complex Life (HZCL) based on known toxicity limits for a range of organisms as a proof of concept. We find that for CO2 tolerances of 0.01, 0.1, and 1 bar, the HZCL is only 21%, 32%, and 50% as wide as the conventional HZ for a Sun-like star, and that CO concentrations may limit some complex life throughout the entire HZ of the coolest M dwarfs. These results cast new light on the likely distribution of complex life in the universe and have important ramifications for the search for exoplanet biosignatures and technosignatures.Comment: Revised including additional discussion. Published Gold OA in ApJ. 9 pages, 5 figures, 5 table

Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II

The strong convergence of Wong-Zakai approximations of the solution to the reflecting stochastic differential equations was studied in [2]. We continue the study and prove the strong convergence under weaker assumptions on the domain.Comment: To appear in "Stochastic Analysis and Applications 2014-In Honour of Terry Lyons", Springer Proceedings in Mathematics and Statistic

Adaptive constraints for feature tracking

In this paper extensions to an existing tracking algorithm are described. These extensions implement adaptive tracking constraints in the form of regional upper-bound displacements and an adaptive track smoothness constraint. Together, these constraints make the tracking algorithm more flexible than the original algorithm (which used fixed tracking parameters) and provide greater confidence in the tracking results. The result of applying the new algorithm to high-resolution ECMWF reanalysis data is shown as an example of its effectiveness

A requirement for bone morphogenetic protein-7 during development of the mammalian kidney and eye.

BMP-7/OP-1, a member of the transforming growth factor-beta (TGF-beta) family of secreted growth factors, is expressed during mouse embryogenesis in a pattern suggesting potential roles in a variety of inductive tissue interactions. The present study demonstrates that mice lacking BMP-7 display severe defects confined to the developing kidney and eye. Surprisingly, the early inductive tissue interactions responsible for establishing both organs appear largely unaffected. However, the absence of BMP-7 disrupts the subsequent cellular interactions required for their continued growth and development. Consequently, homozygous mutant animals exhibit renal dysplasia and anophthalmia at birth. Overall, these findings identify BMP-7 as an essential signaling molecule during mammalian kidney and eye development