High order symplectic integrators for perturbed Hamiltonian systems

A family of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form H=A+B was given in (McLachlan, 1995). We give here a constructive proof that for all integer p, such integrator exists, with only positive steps, and with a remainder of order O(^p + ²²), where is the stepsize of the integrator. Moreover, we compute the analytical expressions of the leading terms of the remainders at all orders. We show also that for a large class of systems, a corrector step can be performed such that the remainder becomes O(^p +⁴²). The performances of these integrators are compared for the simple pendulum and the planetary three-body problem of Sun–Jupiter–Saturn.     

Mid-Holocene hemlock decline and diatom communities in van Nostrand Lake, Ontario, Canada

Terrestrial ecosystem disturbances inferred from the fossil hemlock pollen decline (ca. 4,800 BP) and recovery (ca. 3,800 BP) affected van Nostrand Lake, including the diatom communities. Ecological models suggest the lake responded by eutrophying, reflecting higher nutrient influx resulting from increased erosion. A decline in lake productivity followed as the forest vegetation recovered and erosion slowed. Lastly, as the forest switched from early and middle successional species to mature species, lake productivity increased as erosion increased nutrient inflow, especially phosphorus. However, this eutrophication response was delayed or buffered, perhaps due to wetland development surrounding the lake. The lake never fully returned to its initial, pre-hemlock decline state, but oscillated between more eutrophic and more mesotrophic or oligotrophic stages, possibly reflecting other disturbances in the catchment and climatic change.     

Coordinated monitoring of the eccentric O-star binary Iota Orionis: optical spectroscopy and photometry

With the objective of investigating the windwind collision phenomenon and supporting contemporaneous X-ray observations, we have organized a large-scale, coordinated optical monitoring campaign of the massive, highly eccentric O9 III+B1 III binary Iota Orionis. Successfully separating the spectra of the components, we refine the orbital elements and confirm the rapid apsidal motion in the system. We also see strong interaction between the components during periastron passage and detect phase-locked variability in the spectrum of the secondary star. However, we find no unambiguous signs of the bow shock crashing on the surface of the secondary, despite the predictions of hydrodynamic simulations. Combining all available photometric data, we find rapid, phase-locked variations and model them numerically, thus restricting the orbital inclination to 50° i 70°.     

The Mid-Rivera-Transform Discordance: Morphology and Tectonic Development

To better define the morphotectonic elements and tectonic development of the Mid-Rivera-Transform Discordance, multibeam bathymetric, seafloor backscatter, multichannel seismic reflection and total field marine magnetic data were collected along the entire Rivera Transform west of 107°W during the BART and FAMEX campaigns of the N.O. L??Atalante conducted in 2002. These data show that, although the transform tectonized zone of the Rivera Transform west of 107°30??W is a single continuous morphologic basin, this basin consists of two distinct morphotectonic domains: an eastern domain which morphologically is a deep rhombochasm within which organized seafloor spreading has occurred, and a western ??leaky transform?? domain. These new data, in conjunction with the results of previous studies, support the idea that the Rivera-Pacific Euler pole is migrating southward towards the eastern half of the Rivera Transform, and further indicate a recent (<0.14?Ma), and most likely ongoing, clockwise reorganization of the principle transform displacement zones of the Rivera Transform west of 108°W. We propose that the Mid-Rivera-Transform Discordance owes its origin to this eastward progressing, clockwise reorganization of the transform segments that is occurring in response to recent changes in Rivera-Pacific relative plate motion.     

Variable self‐similar sinuosity properties within simulated river networks

River networks have been shown to obey power scaling laws and to follow self‐organization principles. Their self‐similar (fractal) properties open a path to relate small scale and large scale hydrological processes, such as erosion, deposition or geological movements. However, the existence of a self‐similar dimension has only been checked using either the whole channel network or, on the contrary, a single channel link. No study has explicitly addressed the possible spatial variation of the self‐similar properties between these two extreme geomorphologic objects. Here, a new method based on self‐similarity maps (SSM) is proposed to spatially explore the stream length self‐similar dimension D_l within a river network. The mapping principle consists in computing local self‐similar dimensions deduced from a fit of stream length estimations using increasing divider sizes. A local uncertainty related to the fit quality is also computed and localized on every stream. To assess the efficiency of the approach, contrasted river networks are simulated using optimal channel networks (OCN), where each network is characterized by an exponent γ conditioning its overall topology. By building SSM of these networks, it is shown that deviations from uniform self‐similarity across space occur. Depending on the type of network (γ parameter), these deviations are or are not related to Strahler's order structure. Finally, it is found numerically that the structural averaged stream length self‐similar dimension D_l is closely related to the more functional γ parameter. Results form a bridge between the studies on river sinuosity (single channel) and growth of channel networks (watershed). As for every method providing spatial information where they were lacking before, the SSM may soon help to accurately interpret natural networks and help to simulate more realistic channel networks. Copyright © 2011 John Wiley & Sons, Ltd.     

Using differential SAR interferometry to map land subsidence: a case study in the Pingtung Plain of SW Taiwan

Synthetic aperture radar (SAR) interferometry (InSAR) is a geodetic tool widely applied in the studies of earth-surface deformation. This technique has the benefits of high spatial resolution and centimetre-scale accuracy. Differential SAR interferometry (DInSAR) is used to measure ground deformation with repeat-pass SAR images. This study applied DInSAR and persistent scatterers InSAR (PSInSAR) for detecting land subsidence in the Pingtung Plain, southern Taiwan, between 1995 and 2000. In recent years, serious land subsidence occurred along coastal regions of Taiwan as a consequence of over-pumping of underground water. Results of this study revealed that the critical subsidence region is located on the coast near the estuary of Linpien River. It is also found that subsidence was significantly higher during the dry season than the wet season. The maximum annual subsidence rate of the dry season is up to −11.51 cm/year in critical subsidence region and the vertical land movement rate is much slower during the wet season. The average subsidence rates in wet and dry seasons are −0.31 and −3.37 cm/year, respectively. As a result, the subsidence rate in dry seasons is about 3 cm larger than in wet seasons.