Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes

Gravitational waves from coalescences of neutron stars or stellar-mass black holes into intermediate-mass black holes (IMBHs) of $\gtrsim 100$ solar masses represent one of the exciting possible sources for advanced gravitational-wave detectors. These sources can provide definitive evidence for the existence of IMBHs, probe globular-cluster dynamics, and potentially serve as tests of general relativity. We analyse the accuracy with which we can measure the masses and spins of the IMBH and its companion in intermediate-mass ratio coalescences. We find that we can identify an IMBH with a mass above $100 ~ M_\odot$ with $95\%$ confidence provided the massive body exceeds $130 ~ M_\odot$. For source masses above $\sim200 ~ M_\odot$, the best measured parameter is the frequency of the quasi-normal ringdown. Consequently, the total mass is measured better than the chirp mass for massive binaries, but the total mass is still partly degenerate with spin, which cannot be accurately measured. Low-frequency detector sensitivity is particularly important for massive sources, since sensitivity to the inspiral phase is critical for measuring the mass of the stellar-mass companion. We show that we can accurately infer source parameters for cosmologically redshifted signals by applying appropriate corrections. We investigate the impact of uncertainty in the model gravitational waveforms and conclude that our main results are likely robust to systematics.Comment: 9 pages, 11 figure

Jamming in finite systems: stability, anisotropy, fluctuations and scaling

Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.Comment: 20 pages, 12 figure

Some fine-tuning for dominant diagonal matrices

Given a linear system Ax = b, where A is a dominant diagonal matrix with positive diagonals and non-positive off-diagonals, but b has both positive and negative components, necessary and sufficient conditions on bj are derived to guarantee that xj is positive.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27774/1/0000168.pd

A bound for the fixed-point index of an area-preserving map with applications to mechanics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46598/1/222_2005_Article_BF01418948.pd

The geometry of reaction norms yields insights on classical fitness functions for Great Lakes salmon.

Life history theory examines how characteristics of organisms, such as age and size at maturity, may vary through natural selection as evolutionary responses that optimize fitness. Here we ask how predictions of age and size at maturity differ for the three classical fitness functions-intrinsic rate of natural increase r, net reproductive rate R0, and reproductive value Vx-for semelparous species. We show that different choices of fitness functions can lead to very different predictions of species behavior. In one's efforts to understand an organism's behavior and to develop effective conservation and management policies, the choice of fitness function matters. The central ingredient of our approach is the maturation reaction norm (MRN), which describes how optimal age and size at maturation vary with growth rate or mortality rate. We develop a practical geometric construction of MRNs that allows us to include different growth functions (linear growth and nonlinear von Bertalanffy growth in length) and develop two-dimensional MRNs useful for quantifying growth-mortality trade-offs. We relate our approach to Beverton-Holt life history invariants and to the Stearns-Koella categorization of MRNs. We conclude with a detailed discussion of life history parameters for Great Lakes Chinook Salmon and demonstrate that age and size at maturity are consistent with predictions using R0 (but not r or Vx) as the underlying fitness function

Addendum to: A bound for the fixed-point index of an area-preserving map with applications to mechanics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46599/1/222_2005_Article_BF01389772.pd

Decentralized dynamic processes for finding equilibrium

This paper describes a class of decentralized dynamic processes designed to converge to equilibrium when the equilibrium equations are linear. These processes can also be viewed as distributed algorithms for solving systems of linear equations, or as learning algorithms. The class includes processes that use a message space larger by one binary digit than the space in which the equilibrium exists. However, memory and time requirements increase exponentially with the number of agents (equations).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30135/1/0000512.pd

Characterization of optima in smooth Pareto economic systems

Simple techniques of calculus and geometry are used to study and characterize the optima of pure exchange economies in which the utility functions are smooth but not necessarily convex. It is also shown how one can reduce the problem of optimizing p functions on the manifold of states to that of maximizing a single function on a submanifold of this space. Two models are described: one in which a person cannot trade to an optimum unless he starts at one; and one in which a person cannot even get near a local Pareto optimum along continuous `trade curves' from most initial distributions. Finally, the set of optima is described for a generic set of utility mappings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22045/1/0000463.pd

Electoral and welfare consequences of political manipulation of the economy

This paper examines the long-term electoral and welfare consequences of repeated strategies whereby a political office-holder induces cycles in economic variables to maximize his chances of re-election. Unlike other studies of political business cycles, we focus on questions of the desirability of these cyclical patterns and on the long-run properties of these political economic models. Noting that the welfare costs of vote maximizing in a single term extend beyond that term, we examine in detail the properties of the `long-run equilibrium path' to which such cycles converge. If the economy starts above this path, vote maximizing can lead to increased social welfare and vote margins. However, if the economy starts below this path, vote-maximizing in the present can cause reduced votes and electocal defeat in subsequent terms. This possibility should lead a far-sighted, enlightened politician or political party to eschew vote-maximizing tactics and the political business cycles which accompany them and thus canhelp explain why empirical studies have not found convincing evidence of the existence of such cycles. This paper also quantifies the dependence of this long-run equilibrium path on the important political and economic parameters of the model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25648/1/0000200.pd