Linear multistep methods for integrating reversible differential equations

This paper studies multistep methods for the integration of reversible dynamical systems, with particular emphasis on the planar Kepler problem. It has previously been shown by Cano & Sanz-Serna that reversible linear multisteps for first-order differential equations are generally unstable. Here, we report on a subset of these methods -- the zero-growth methods -- that evade these instabilities. We provide an algorithm for identifying these rare methods. We find and study all zero-growth, reversible multisteps with six or fewer steps. This select group includes two well-known second-order multisteps (the trapezoidal and explicit midpoint methods), as well as three new fourth-order multisteps -- one of which is explicit. Variable timesteps can be readily implemented without spoiling the reversibility. Tests on Keplerian orbits show that these new reversible multisteps work well on orbits with low or moderate eccentricity, although at least 100 steps/radian are required for stability.Comment: 31 pages, 9 figures, in press at The Astronomical Journa

A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems

Symplectic integration algorithms are well-suited for long-term integrations of Hamiltonian systems because they preserve the geometric structure of the Hamiltonian flow. However, this desirable property is generally lost when adaptive timestep control is added to a symplectic integrator. We describe an adaptive-timestep symplectic integrator that can be used if the Hamiltonian is the sum of kinetic and potential energy components and the required timestep depends only on the potential energy (e.g. test-particle integrations in fixed potentials). In particular, we describe an explicit, reversible, symplectic, leapfrog integrator for a test particle in a near-Keplerian potential; this integrator has timestep proportional to distance from the attracting mass and has the remarkable property of integrating orbits in an inverse-square force field with only "along-track" errors; i.e. the phase-space shape of a Keplerian orbit is reproduced exactly, but the orbital period is in error by O(1/N^2), where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors in equations and one figure correcte

A summary of the Department of Fisheries, Western Australia invertebrate research at Cocos (Keeling) Islands 2006-2011

The Cocos (Keeling) Islands are located in the Indian Ocean (12° 12” S, 96° 54” E). The group is comprised of two separate coral atolls, consisting of 27 islands. The southern atoll consists of 26 islands, surrounding a shallow lagoon, two of which are inhabited with a total population of approximately 600 people. Management of the Cocos (Keeling) Islands’ fish resources is conducted by the Department of Fisheries Western Australia (DoF), on behalf of the Commonwealth Government, under a Service Delivery Agreement (SDA). Between 2006 and 2011 DoF has conducted annual risk assessments to focus research and management objectives for the Cocos (Keeling) Islands. This report summarises the research on three invertebrate groups (holothurians, Lambis lambis and giant clams) that were highlighted as high-risk, either due to lack of knowledge and/or current/potential fishing pressure. The key findings of the research projects are discussed below

Mapping shallow water habitats of the Wallabi Group, Houtman Abrolhos Islands, using remote sensing techniques

The use of mapping techniques to identify and quantify habitats is becoming an increasingly important tool for the effective management of marine resources. With a multitude of techniques such as remote sensing, acoustic surveys and towed video all commonly used, the decision on the methodology to use depends on the resolution of output data required to answer the objectives of the survey, the spatial extent and location of survey site as well as the associated costs of surveyin

Ocean acidification in the surface waters of the Pacific-Arctic boundary regions

Author Posting. © The Oceanography Society, 2015. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 28, no. 2 (2015): 122-135, doi:10.5670/oceanog.2015.36.The continental shelves of the Pacific-Arctic Region (PAR) are especially vulnerable to the effects of ocean acidification (OA) because the intrusion of anthropogenic CO2 is not the only process that can reduce pH and carbonate mineral saturation states for aragonite (Ωarag). Enhanced sea ice melt, respiration of organic matter, upwelling, and riverine inputs have been shown to exacerbate CO2 -driven ocean acidification in high-latitude regions. Additionally, the indirect effect of changing sea ice coverage is providing a positive feedback to OA as more open water will allow for greater uptake of atmospheric CO2 . Here, we compare model-based outputs from the Community Earth System Model with a subset of recent ship-based observations, and take an initial look at future model projections of surface water Ωarag in the Bering, Chukchi, and Beaufort Seas. We then use the model outputs to define benchmark years when biological impacts are likely to result from reduced Ωarag. Each of the three continental shelf seas in the PAR will become undersaturated with respect to aragonite at approximately 30-year intervals, indicating that aragonite undersaturations gradually progress upstream along the flow path of the waters as they move north from the Pacific Ocean. However, naturally high variability in Ωarag may indicate higher resilience of the Bering Sea ecosystem to these low-Ωarag conditions than the ecosystems of the Chukchi and the Beaufort Seas. Based on our initial results, we have determined that the annual mean for Ωarag will pass below the current range of natural variability in 2025 for the Beaufort Sea and 2027 for the Chukchi Sea. Because of the higher range of natural variability, the annual mean for Ωarag for the Bering Sea does not pass out of the natural variability range until 2044. As Ωarag in these shelf seas slips below the present-day range of large seasonal variability by mid-century, the diverse ecosystems that support some of the largest commercial and subsistence fisheries in the world may be under tremendous pressure.This project was funded by the National Science Foundation (PLR- 1041102 and AGS-1048827)

Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations

We study the fully nonlinear elliptic equation $F(D^2u,Du,u,x) = f$ in a smooth bounded domain $\Omega$, under the assumption the nonlinearity $F$ is uniformly elliptic and positively homogeneous. Recently, it has been shown that such operators have two principal "half" eigenvalues, and that the corresponding Dirichlet problem possesses solutions, if both of the principal eigenvalues are positive. In this paper, we prove the existence of solutions of the Dirichlet problem if both principal eigenvalues are negative, provided the "second" eigenvalue is positive, and generalize the anti-maximum principle of Cl\'{e}ment and Peletier to homogeneous, fully nonlinear operators.Comment: 32 page

Switching ferroelectric domain configurations using both electric and magnetic fields in Pb(Zr,Ti)O3–Pb(Fe,Ta)O3 single-crystal lamellae

Thin single-crystal lamellae cut from Pb(Zr,Ti)O(3)–Pb(Fe,Ta)O(3) ceramic samples have been integrated into simple coplanar capacitor devices. The influence of applied electric and magnetic fields on ferroelectric domain configurations has been mapped, using piezoresponse force microscopy. The extent to which magnetic fields alter the ferroelectric domains was found to be strongly history dependent: after switching had been induced by applying electric fields, the susceptibility of the domains to change under a magnetic field (the effective magnetoelectric coupling parameter) was large. Such large, magnetic field-induced changes resulted in a remanent domain state very similar to the remanent state induced by an electric field. Subsequent magnetic field reversal induced more modest ferroelectric switching

The Pathways for Intelligible Speech: Multivariate and Univariate Perspectives

An anterior pathway, concerned with extracting meaning from sound, has been identified in nonhuman primates. An analogous pathway has been suggested in humans, but controversy exists concerning the degree of lateralization and the precise location where responses to intelligible speech emerge. We have demonstrated that the left anterior superior temporal sulcus (STS) responds preferentially to intelligible speech (Scott SK, Blank CC, Rosen S, Wise RJS. 2000. Identification of a pathway for intelligible speech in the left temporal lobe. Brain. 123:2400-2406.). A functional magnetic resonance imaging study in Cerebral Cortex used equivalent stimuli and univariate and multivariate analyses to argue for the greater importance of bilateral posterior when compared with the left anterior STS in responding to intelligible speech (Okada K, Rong F, Venezia J, Matchin W, Hsieh IH, Saberi K, Serences JT,Hickok G. 2010. Hierarchical organization of human auditory cortex: evidence from acoustic invariance in the response to intelligible speech. 20: 2486-2495.). Here, we also replicate our original study, demonstrating that the left anterior STS exhibits the strongest univariate response and, in decoding using the bilateral temporal cortex, contains the most informative voxels showing an increased response to intelligible speech. In contrast, in classifications using local "searchlights” and a whole brain analysis, we find greater classification accuracy in posterior rather than anterior temporal regions. Thus, we show that the precise nature of the multivariate analysis used will emphasize different response profiles associated with complex sound to speech processin

Manipulating Ferroelectric Domains in Nanostructures Under Electron Beams

Freestanding BaTiO3 nanodots exhibit domain structures characterized by distinct quadrants of ferroelastic 90{\deg} domains in transmission electron microscopy (TEM) observations. These differ significantly from flux-closure domain patterns in the same systems imaged by piezoresponse force microscopy. Based upon a series of phase field simulations of BaTiO3 nanodots, we suggest that the TEM patterns result from a radial electric field arising from electron beam charging of the nanodot. For sufficiently large charging, this converts flux-closure domain patterns to quadrant patterns with radial net polarizations. Not only does this explain the puzzling patterns that have been observed in TEM studies of ferroelectric nanodots, but also suggests how to manipulate ferroelectric domain patterns via electron beams.Comment: 5 pages, 6 figure