Interim Report on Studies of the Mw ~7.9 Earthquake of 3 May 2006, Kingdom of Tonga

The very large and rare Mw ~7.9 Earthquake of 3 May 2006 in the Kingdom of Tonga aroused great interest among both Tongan scientists and their colleagues in Australia, New Zealand, and the United States. To investigate the earthquake we formed a collaborative research group of scientists from Australia, New Zealand, Tonga, and the United States. We brought in seven seismographs from Australia and the US to supplement the three-station network already in Tonga and eight GPS receivers primarily for the islands west of the earthquake epicenter. In addition, we made coastal observations to determine the regional pattern of subsidence associated with the earthquake. The GPS instruments can measure horizontal and vertical motion quite precisely, but only after the earthquake from the time of deployment onward, except for some sites on Tongatapu, Vava’u, and Lifuka that had been occupied by GPS receivers in the past. This report describes our efforts.Ministry of Lands and Survey, Kingdom of TongaGeoscience AustraliaGeological and Nuclear Sciences, New ZealandThe National Science Foundation, U.S.A.Institute for Geophysic

Accurate gravitational waveforms for binary-black-hole mergers with nearly extremal spins

Motivated by the possibility of observing gravitational waves from merging black holes whose spins are nearly extremal (i.e., 1 in dimensionless units), we present numerical waveforms from simulations of merging black holes with the highest spins simulated to date: (1) a 25.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.97 aligned with the orbital angular momentum; and (2) a previously reported 12.5-orbit inspiral, merger, and ringdown of two holes with equal masses and spins of magnitude 0.95 anti-aligned with the orbital angular momentum. First, we consider the horizon mass and spin evolution of the new aligned-spin simulation. During the inspiral, the horizon area and spin evolve in remarkably close agreement with Alvi's analytic predictions, and the remnant hole's final spin agrees reasonably well with several analytic predictions. We also find that the total energy emitted by a real astrophysical system with these parameters---almost all of which is radiated during the time included in this simulation---would be 10.952% of the initial mass at infinite separation. Second, we consider the gravitational waveforms for both simulations. After estimating their uncertainties, we compare the waveforms to several post-Newtonian approximants, finding significant disagreement well before merger, although the phase of the TaylorT4 approximant happens to agree remarkably well with the numerical prediction in the aligned-spin case. We find that the post-Newtonian waveforms have sufficient uncertainty that hybridized waveforms will require far longer numerical simulations (in the absence of improved post-Newtonian waveforms) for accurate parameter estimation of low-mass binary systems.Comment: 17 pages, 7 figures, submitted to Classical and Quantum Gravit

A mathematical model of systemic inhibition of angiogenesis in metastatic development

We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the influence of three processes: birth (dissemination of secondary tumors), growth and inhibition (through angiogenesis). The resulting model is a nonlinear partial differential transport equation with nonlocal boundary condition. The nonlinearity stands in the velocity through a nonlocal quantity of the model (the total metastatic volume). The asymptotic behavior of the model is numerically investigated and reveals interesting dynamics ranging from convergence to a steady state to bounded non-periodic or periodic behaviors, possibly with complex repeated patterns. Numerical simulations are performed with the intent to theoretically study the relative impact of potentiation or impairment of each process of the birth/growth/inhibition balance. Biological insights on possible implications for the phenomenon of "cancer without disease" are also discussed

Pulsar scintillations from corrugated reconnection sheets in the ISM

We show that surface waves along interstellar current sheets closely aligned with the line of sight lead to pulsar scintillation properties consistent with those observed. This mechanism naturally produces the length and density scales of the ISM scattering lenses that are required to explain the magnitude and dynamical spectrum of the scintillations. In this picture, the parts of warm ionized interstellar medium that are responsible for the scintillations are relatively quiescent, with scintillation and scattering resulting from weak waves propagating along magnetic domain boundary current sheets, which are both expected from helicity conservation and have been observed in numerical simulations. The model statistically predicts the spacing and amplitudes of inverted parabolic arcs seen in Fourier-transformed dynamical spectra of strongly scintillating pulsars with only 3 parameters. Multi-frequency, multi-epoch low frequency VLBI observations can quantitatively test this picture. If successful, in addition to mapping the ISM, this may open the door to precise nanoarcsecond pulsar astrometry, distance measurements, and emission studies using these 10AU interferometers in the sky.Comment: 9 pages, 10 figures, accepted in MNRA

Urban Growth Drivers and Spatial Inequalities: Europe - a case with geographically sticky people

We try to combine theory with empirical analysis to investigate the drivers of spatial growth processes, welfare and disparities in a context in which people are markedly immobile. Drawing on two of our recent papers (Cheshire and Magrini, 2006 and 2008), we review the evidence on the drivers of differential urban growth in the EU both in terms of population and output growth. The main conclusion from our findings is that one cannot reasonably maintain the assumption of full spatial equilibrium in a European context. This has a number of wider implications. It suggests that i. differences in real incomes in Europe - and more generally where populations are relatively immobile - are likely to persist and indicate real differences in welfare; ii. there is no evidence of a unified European urban system but rather of a set of national systems; iii. there are significant but theoretically consistent, differences in the drivers of population compared to economic growth.Growth, urban system, spatial equilibrium