Fertility and post-reproductive longevity

Journal ArticleWe examine the effects of reproduction on longevity among mothers and fathers after age 60. This study is motivated by evolutionary theories of aging and theories predicting social benefits and costs of children to older parents. We use the Utah Population Database, that includes a large genealogical database from the Utah Family History Library. Cox proportional hazard models based on 13,987 couples married between 1860-1899 indicate that women with fewer children as well as those bearing children late in life live longer post-reproductive lives. As the burdens of motherhood increase, the relative gains in longevity of late fertile women increase compared to their non-late fertile counterparts. Husbands' longevity is less sensitive to reproductive history, although husbands have effects that are similar to those of their wives during the latter marriage cohort. We find some support for predictions based on evolutionary principles, but we also find evidence that implicates a role for shared marital environments

Development of scenarios for land cover, population density, impervious cover, and conservation in New Hampshire, 2010–2100

Future changes in ecosystem services will depend heavily on changes in land cover and land use, which, in turn, are shaped by human activities. Given the challenges of predicting long-term changes in human behaviors and activities, scenarios provide a framework for simulating the long-term consequences of land-cover change on ecosystem function. As input for process-based models of terrestrial and aquatic ecosystem function, we developed scenarios for land cover, population density, and impervious cover for the state of New Hampshire for 2020–2100. Key drivers of change were identified through information gathered from six sources: historical trends, existing plans relating to New Hampshire’s land-cover future, surveys, existing population scenarios, key informant interviews with diverse stakeholders, and input from subject-matter experts. Scenarios were developed in parallel with information gathering, with details added iteratively as new questions emerged. The final scenarios span a continuum from spatially dispersed development with a low value placed on ecosystem services (Backyard Amenities) to concentrated development with a high value placed on ecosystem services (the Community Amenities family). The Community family includes two population scenarios (Large Community and Small Community), to be combined with two scenarios for land cover (Protection of Wildlands and Promotion of Local Food), producing combinations that bring the total number of scenarios to six. Between Backyard Amenities and Community Amenities is a scenario based on linear extrapolations of current trends (Linear Trends). Custom models were used to simulate decadal change in land cover, population density, and impervious cover. We present raster maps and proportion of impervious cover for HUC10 watersheds under each scenario and discuss the trade-offs of our translation and modeling approach within the context of contemporary scenario projects

On the effectiveness of mixing in violent relaxation

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasi-stationary states (QSS), i.e. long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation". The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure

Relaxation to thermal equilibrium in the self-gravitating sheet model

We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly detected and characterized by following the evolution of order parameters defined by appropriately normalized moments of the phase space distribution which probe its entanglement in space and velocity coordinates. For a class of quasi-stationary states which result from the violent relaxation of rectangular waterbag initial conditions, characterized by their virial ratio R_0, we show that relaxation occurs on a time scale which (i) scales approximately linearly in the particle number N, and (ii) shows also a strong dependence on R_0, with quasi-stationary states from colder initial conditions relaxing much more rapidly. The temporal evolution of the order parameter may be well described by a stretched exponential function. We study finally the correlation of the relaxation times with the amplitude of fluctuations in the relaxing quasi-stationary states, as well as the relation between temporal and ensemble averages.Comment: 37 pages, 24 figures; some additional discussion of previous literature and other minor modifications, final published versio

A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method

A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary orbits back to t=0. To make this procedure feasible, a self-consistent field (SCF) method for solving Poisson's equation is adopted to compute the orbits of arbitrary stars. As an example, for the violent relaxation of a uniform-density sphere, the phase-space evolution which the current method generates is compared to that obtained with a phase-space method for integrating the collisionless Boltzmann equation, on the assumption of spherical symmetry. Then, excellent agreement is found between the two methods if an optimal basis set for the SCF technique is chosen. Since this reproduction method requires only the functional form of initial DFs but needs no assumptions about symmetry of the system, the success in reproducing the phase-space evolution implies that there would be no need of directly solving the collisionless Boltzmann equation in order to access phase space even for systems without any special symmetries. The effects of basis sets used in SCF simulations on the reproduced phase space are also discussed.Comment: 16 pages w/4 embedded PS figures. Uses aaspp4.sty (AASLaTeX v4.0). To be published in ApJ, Oct. 1, 1997. This preprint is also available at http://www.sue.shiga-u.ac.jp/WWW/prof/hozumi/papers.htm

Linear theory and violent relaxation in long-range systems: a test case

In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \rightarrow \infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times

Ejection of Supermassive Black Holes from Galaxy Cores

[Abridged] Recent numerical relativity simulations have shown that the emission of gravitational waves during the merger of two supermassive black holes (SMBHs) delivers a kick to the final hole, with a magnitude as large as 4000 km/s. We study the motion of SMBHs ejected from galaxy cores by such kicks and the effects on the stellar distribution using high-accuracy direct N-body simulations. Following the kick, the motion of the SMBH exhibits three distinct phases. (1) The SMBH oscillates with decreasing amplitude, losing energy via dynamical friction each time it passes through the core. Chandrasekhar's theory accurately reproduces the motion of the SMBH in this regime if 2 < ln Lambda < 3 and if the changing core density is taken into account. (2) When the amplitude of the motion has fallen to roughly the core radius, the SMBH and core begin to exhibit oscillations about their common center of mass. These oscillations decay with a time constant that is at least 10 times longer than would be predicted by naive application of the dynamical friction formula. (3) Eventually, the SMBH reaches thermal equilibrium with the stars. We estimate the time for the SMBH's oscillations to damp to the Brownian level in real galaxies and infer times as long as 1 Gyr in the brightest galaxies. Ejection of SMBHs also results in a lowered density of stars near the galaxy center; mass deficits as large as five times the SMBH mass are produced for kick velocities near the escape velocity. We compare the N-body density profiles with luminosity profiles of early-type galaxies in Virgo and show that even the largest observed cores can be reproduced by the kicks, without the need to postulate hypermassive binary SMBHs. Implications for displaced AGNs and helical radio structures are discussed.Comment: 18 pages, The Astrophysical Journal, in press. Replaced with revised versio

A coupled terrestrial and aquatic biogeophysical model of the Upper Merrimack River watershed, New Hampshire, to inform ecosystem services evaluation and management under climate and land-cover change

Accurate quantification of ecosystem services (ES) at regional scales is increasingly important for making informed decisions in the face of environmental change. We linked terrestrial and aquatic ecosystem process models to simulate the spatial and temporal distribution of hydrological and water quality characteristics related to ecosystem services. The linked model integrates two existing models (a forest ecosystem model and a river network model) to establish consistent responses to changing drivers across climate, terrestrial, and aquatic domains. The linked model is spatially distributed, accounts for terrestrial–aquatic and upstream–downstream linkages, and operates on a daily time-step, all characteristics needed to understand regional responses. The model was applied to the diverse landscapes of the Upper Merrimack River watershed, New Hampshire, USA. Potential changes in future environmental functions were evaluated using statistically downscaled global climate model simulations (both a high and low emission scenario) coupled with scenarios of changing land cover (centralized vs. dispersed land development) for the time period of 1980–2099. Projections of climate, land cover, and water quality were translated into a suite of environmental indicators that represent conditions relevant to important ecosystem services and were designed to be readily understood by the public. Model projections show that climate will have a greater influence on future aquatic ecosystem services (flooding, drinking water, fish habitat, and nitrogen export) than plausible changes in land cover. Minimal changes in aquatic environmental indicators are predicted through 2050, after which the high emissions scenarios show intensifying impacts. The spatially distributed modeling approach indicates that heavily populated portions of the watershed will show the strongest responses. Management of land cover could attenuate some of the changes associated with climate change and should be considered in future planning for the region