An Exactly Conservative Integrator for the n-Body Problem

The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n > 2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem, and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and center of mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators.Comment: 17 pages, 3 figures; to appear in J. Phys. A.: Math. Ge

Association of Lifestyle Factors With Abdominal Subcutaneous and Visceral Adiposity: The Framingham Heart Study

OBJECTIVE— The purpose of this study was to assess the relationship between lifestyle factors and abdominal subcutaneous adipose tissue (SAT) and visceral adipose tissue (VAT) in a community-based setting

Foreign policy beliefs and support for Stephen Harper and the Conservative Party

Similar to other recent Canadian elections, foreign policy did not feature prominently in the 2011 federal election campaign. In fact, many doubt Canadian public opinion on international affairs is linked to the actions taken by recent Governments. In this paper, we examine Canadian public opinion toward a range of foreign policy issues and argue that the survey questions measure two latent dimensions —militarism and internationalism. Our survey evidence indicates the existence of an “issue public” which is prepared to endorse military action and is skeptical of human rights and overseas aid programs, and this group is far more supportive of Prime Minister Harper and the Conservative Party than other Canadians. The absence of an elite discussion, either among politicians or between media elites, about the direction of Canadian foreign policy does not prevent the Canadian voter from thinking coherently about questions pertaining to this issue domain and employing these beliefs to support or oppose political parties and their leaders

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam

State of the Carbon Cycle - Consequences of Rising Atmospheric CO2

The rise of atmospheric CO2, largely attributable to human activity through fossil fuel emissions and land-use change, has been dampened by carbon uptake by the ocean and terrestrial biosphere. We outline the consequences of this carbon uptake as direct and indirect effects on terrestrial and oceanic systems and processes for different regions of North America and the globe. We assess the capacity of these systems to continue to act as carbon sinks. Rising CO2 has decreased seawater pH; this process of ocean acidification has impacted some marine species and altered fundamental ecosystem processes with further effects likely. In terrestrial ecosystems, increased atmospheric CO2 causes enhanced photosynthesis, net primary production, and increased water-use efficiency. Rising CO2 may change vegetation composition and carbon storage, and widespread increases in water use efficiency likely influence terrestrial hydrology and biogeochemical cycling. Consequences for human populations include changes to ecosystem services including cultural activities surrounding land use, agricultural or harvesting practices. Commercial fish stocks have been impacted and crop production yields have been changed as a result of rising CO2. Ocean and terrestrial effects are contingent on, and feedback to, global climate change. Warming and modified precipitation regimes impact a variety of ecosystem processes, and the combination of climate change and rising CO2 contributes considerable uncertainty to forecasting carbon sink capacity in the ocean and on land. Disturbance regime (fire and insects) are modified with increased temperatures. Fire frequency and intensity increase, and insect lifecycles are disrupted as temperatures move out of historical norms. Changes in disturbance patterns modulate the effects of rising CO2 depending on ecosystem type, disturbance frequency, and magnitude of events. We discuss management strategies designed to limit the rise of atmospheric CO2 and reduce uncertainty in forecasts of decadal and centennial feedbacks of rising atmospheric CO2 on carbon storage

Bioreactors as engineering support to treat cardiac muscle and vascular disease

Cardiovascular disease is the leading cause of morbidity and mortality in the Western World. The inability of fully differentiated, load-bearing cardiovascular tissues to in vivo regenerate and the limitations of the current treatment therapies greatly motivate the efforts of cardiovascular tissue engineering to become an effective clinical strategy for injured heart and vessels. For the effective production of organized and functional cardiovascular engineered constructs in vitro, a suitable dynamic environment is essential, and can be achieved and maintained within bioreactors. Bioreactors are technological devices that, while monitoring and controlling the culture environment and stimulating the construct, attempt to mimic the physiological milieu. In this study, a review of the current state of the art of bioreactor solutions for cardiovascular tissue engineering is presented, with emphasis on bioreactors and biophysical stimuli adopted for investigating the mechanisms influencing cardiovascular tissue development, and for eventually generating suitable cardiovascular tissue replacements

Carbon cycling in the North American coastal ocean: a synthesis

A quantification of carbon fluxes in the coastal ocean and across its boundaries with the atmosphere, land, and the open ocean is important for assessing the current state and projecting future trends in ocean carbon uptake and coastal ocean acidification, but this is currently a missing component of global carbon budgeting. This synthesis reviews recent progress in characterizing these carbon fluxes for the North American coastal ocean. Several observing networks and high-resolution regional models are now available. Recent efforts have focused primarily on quantifying the net air–sea exchange of carbon dioxide (CO2). Some studies have estimated other key fluxes, such as the exchange of organic and inorganic carbon between shelves and the open ocean. Available estimates of air–sea CO2 flux, informed by more than a decade of observations, indicate that the North American Exclusive Economic Zone (EEZ) acts as a sink of 160±80&thinsp;Tg&thinsp;C&thinsp;yr−1, although this flux is not well constrained. The Arctic and sub-Arctic, mid-latitude Atlantic, and mid-latitude Pacific portions of the EEZ account for 104, 62, and −3.7&thinsp;Tg&thinsp;C&thinsp;yr−1, respectively, while making up 51&thinsp;%, 25&thinsp;%, and 24&thinsp;% of the total area, respectively. Combining the net uptake of 160±80&thinsp;Tg&thinsp;C&thinsp;yr−1 with an estimated carbon input from land of 106±30&thinsp;Tg&thinsp;C&thinsp;yr−1 minus an estimated burial of 65±55&thinsp;Tg&thinsp;C&thinsp;yr−1 and an estimated accumulation of dissolved carbon in EEZ waters of 50±25&thinsp;Tg&thinsp;C&thinsp;yr−1 implies a carbon export of 151±105&thinsp;Tg&thinsp;C&thinsp;yr−1 to the open ocean. The increasing concentration of inorganic carbon in coastal and open-ocean waters leads to ocean acidification. As a result, conditions favoring the dissolution of calcium carbonate occur regularly in subsurface coastal waters in the Arctic, which are naturally prone to low pH, and the North Pacific, where upwelling of deep, carbon-rich waters has intensified. Expanded monitoring and extension of existing model capabilities are required to provide more reliable coastal carbon budgets, projections of future states of the coastal ocean, and quantification of anthropogenic carbon contributions.</p

Late Winter Biogeochemical Conditions Under Sea Ice in the Canadian High Arctic

With the Arctic summer sea-ice extent in decline, questions are arising as to how changes in sea-ice dynamics might affect biogeochemical cycling and phenomena such as carbon dioxide (CO2) uptake and ocean acidification. Recent field research in these areas has concentrated on biogeochemical and CO2 measurements during spring, summer or autumn, but there are few data for the winter or winter–spring transition, particularly in the High Arctic. Here, we present carbon and nutrient data within and under sea ice measured during the Catlin Arctic Survey, over 40 days in March and April 2010, off Ellef Ringnes Island (78° 43.11′ N, 104° 47.44′ W) in the Canadian High Arctic. Results show relatively low surface water (1–10 m) nitrate (<1.3 µM) and total inorganic carbon concentrations (mean±SD=2015±5.83 µmol kg−1), total alkalinity (mean±SD=2134±11.09 µmol kg−1) and under-ice pCO2sw (mean±SD=286±17 µatm). These surprisingly low wintertime carbon and nutrient conditions suggest that the outer Canadian Arctic Archipelago region is nitrate-limited on account of sluggish mixing among the multi-year ice regions of the High Arctic, which could temper the potential of widespread under-ice and open-water phytoplankton blooms later in the season