The Annual Banquet, Held at the Hotel Cecil, London, W.C., on Friday, April 29th, 1921

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On the Coherence of Ground Motion in the San Fernando Valley

We present an analysis of the coherence of seismic ground motion recorded on alluvial sediments in the San Fernando Valley, California. Using aftershocks of the 17 January 1994 M_w6.7 earthquake recorded at a quasi-dense array of portable stations, we analyze the coherence of three well-recorded magnitude 3.7 to 4.0 events over the frequency range 0.5 to 15 Hz and a distance range of 0.5 to 5.3 km. All stations are located at sites with broadly similar near-site geology, characterized by medium to fine-grain Quaternary alluvial sediments. On average, relatively high values of coherence are observed for distances up to 3 to 4 km and frequencies up to 2 to 3 Hz; coherence drops sharply at frequencies near and above 3 Hz. Although average coherence functions are described reasonably well by a log-linear relationship with frequency, the curves at all distances exhibit a flattening at low frequencies that is not consistent with previous observations of coherence at hardrock sites. The distance decay of coherence is also markedly less strong, with high coherence values observed over station separations corresponding to multiple wavelengths. This may reflect fundamental differences in shallow-wave propagation in the two environments, with high-frequency scattering relatively more dominant in regions of hard-rock near-surface geology. Within a sedimentary basin or valley, the site response itself generally reflects a resonance phenomenon that may tend to give rise to more uniform ground motions. However, previous studies have demonstrated the existence of pathological focusing and amplification effects within complex sedimentary basin environments such as the greater Los Angeles region; our results undoubtedly do not quantify the full range of ground-motion variability at all sites, but rather represent the level of that variability that can be expected, and quantified, for typical source/receiver paths

Resonance bifurcations from robust homoclinic cycles

We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions for asymptotic stability using transition matrix techniques which make explicit use of the geometry of the group action. Secondly, through an explicit computation of the global parts of the Poincare map near the cycle we show that, generically, the resonance bifurcations from the cycles are supercritical: a unique branch of asymptotically stable period orbits emerges from the resonance bifurcation and exists for coefficient values where the cycle has lost stability. This calculation is the first to explicitly compute the criticality of a resonance bifurcation, and answers a conjecture of Field and Swift in a particular limiting case. Moreover, we are able to obtain an asymptotically-correct analytic expression for the period of the bifurcating orbit, with no adjustable parameters, which has not proved possible previously. We show that the asymptotic analysis compares very favourably with numerical results.Comment: 24 pages, 3 figures, submitted to Nonlinearit

Fitting Precision Electroweak Data with Exotic Heavy Quarks

The 1999 precision electroweak data from LEP and SLC persist in showing some slight discrepancies from the assumed standard model, mostly regarding $b$ and $c$ quarks. We show how their mixing with exotic heavy quarks could result in a more consistent fit of all the data, including two unconventional interpretations of the top quark.Comment: 7 pages, no figure, 2 typos corrected, 1 reference update

Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations

During the transition from a neutral to a fully reionized universe, scattering of cosmic microwave background (CMB) photons via free-electrons leads to a new anisotropy contribution to the temperature distribution. If the reionization process is inhomogeneous and patchy, the era of reionization is also visible via brightness temperature fluctuations in the redshifted 21 cm line emission from neutral Hydrogen. Since regions containing electrons and neutral Hydrogen are expected to trace the same underlying density field, the two are (anti) correlated and this is expected to be reflected in the anisotropy maps via a correlation between arcminute-scale CMB temperature and the 21 cm background. In terms of the angular cross-power spectrum, unfortunately, this correlation is insignificant due to a geometric cancellation associated with second order CMB anisotropies. The same cross-correlation between ionized and neutral regions, however, can be studied using a bispectrum involving large scale velocity field of ionized regions from the Doppler effect, arcminute scale CMB anisotropies during reionization, and the 21 cm background. While the geometric cancellation is partly avoided, the signal-to-noise ratio related to this bispectrum is reduced due to the large cosmic variance related to velocity fluctuations traced by the Doppler effect. Unless the velocity field during reionization can be independently established, it is unlikely that the correlation information related to the relative distribution of ionized electrons and regions containing neutral Hydrogen can be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure

The use (and misuse) of sediment traps in coral reef environments : theory, observations, and suggested protocols

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Coral Reefs 30 (2011): 23-38, doi:10.1007/s00338-010-0705-3.Sediment traps are commonly used as standard tools for monitoring “sedimentation” in coral reef environments. In much of the literature where sediment traps were used to measure the effects of “sedimentation” on corals, it is clear from deployment descriptions and interpretations of the resulting data that information derived from sediment traps has frequently been misinterpreted or misapplied. Despite their widespread use in this setting, sediment traps do not provide quantitative information about “sedimentation” on coral surfaces. Traps can provide useful information about the relative magnitude of sediment dynamics if trap deployment standards are used. This conclusion is based first on a brief review of the state of knowledge of sediment trap dynamics, which has primarily focused on traps deployed high above the seabed in relatively deep water, followed by our understanding of near-bed sediment dynamics in shallow-water environments that characterize coral reefs. This overview is followed by the first synthesis of near-bed sediment trap data collected with concurrent hydrodynamic information in coral reef environments. This collective information is utilized to develop nine protocols for using sediment traps in coral reef environments, which focus on trap parameters that researchers can control such as trap height (H), trap mouth diameter (D), the height of the trap mouth above the substrate (z o ), and the spacing between traps. The hydrodynamic behavior of sediment traps and the limitations of data derived from these traps should be forefront when interpreting sediment trap data to infer sediment transport processes in coral reef environments

Collective patterns arising out of spatio-temporal chaos

We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under a periodic boundary condition. Thus the spatial inhomogeneity of the statistical state arises through a spontaneous symmetry breaking. The transition from a state of homogeneous spatio-temporal chaos to one exhibiting spatial order is explained by introducing a collective viscosity which relates the averaged pattern with a correlation of the fluctuations.Comment: 11 pages (Revtex) + 5 figures (postscript