Stress concentrations around voids in three dimensions : The roots of failure

Funding This work forms part of a NERC New Investigator award for DH (NE/I001743/1), which is gratefully acknowledged. Acknowledgments The authors would like to acknowledge the reviewers, Elizabeth Ritz and Phillip Resor. Their reviews were very constructive, both helping to improve the manuscripts consistency and highlighting a number of errors in the initial submission. The authors would also like to thank Lydia Jagger's keen eye and patience, she helped greatly in removing a number of grammatical errors from the initial draft.Peer reviewedPublisher PD

N-Benzyl-2-(3-chloro-4-hy­droxy­phen­yl)acetamide

The title compound, C15H14ClNO2, was synthesized as part of a project to generate a combinatorial library based on the fungal natural product 2-(3-chloro-4-hy­droxy­phen­yl)acetamide. It crystallizes as non-planar discrete mol­ecules [the peripheral 3-chloro-4-hy­droxy­phenyl and benzyl groups are twisted out of the plane of the central acetamide group, with N—C—C—C and C—C—C—C torsion angles of −58.8 (3) and 65.0 (2)°, respectively] linked by inter­molecular N—H⋯O and O—H⋯O hydrogen bonds

2-(3-Chloro-4-hydroxy­phen­yl)-N-(3,4-dimethoxy­pheneth­yl)acetamide

The title compound, C18H20ClNO4, was synthesized during the generation of a combinatorial library based on the fungal natural product 3-chloro-4-hydroxy­phenyl­acetamide. It crystallizes as discrete mol­ecules linked by inter­molecular C(9) chains of N—H⋯O and O—H⋯O hydrogen bonds which in turn combine to form chains of R 2 2(20) rings

Slip on wavy frictional faults : Is the 3rd dimension a sticking point?

Funding T.D. has been funded by the DFG-ICDP, grant agreement N. RI 2782/3-1. Acknowledgements We thank both reviewers for the constructive reviews which resulted in improvements to the manuscript, the editor Cees Passchier and lastly, Lydia Jagger who helped improve the language of the initial draft. The work here was funded through the Deutsche Forschungsgemeinschaft/International Continental Scientific Drilling Program, grant agreement N. RI 2782/3-1.Peer reviewedPostprin

Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background (CMB) data, such as the imprint of topological defects, in particular cosmic strings, and for their reconstruction after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for publication in MNRAS. Version 3 (identical to version 2) posted for code release announcement - "Steerable scale discretised wavelets on the sphere" - S2DW code available for download at http://www.mrao.cam.ac.uk/~jdm57/software.htm

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Prediction of Large Events on a Dynamical Model of a Fault

We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events to establish a benchmark for predictability in the model. In comparison, intermediate term prediction techniques, analogous to the pattern recognition algorithms CN and M8 introduced and studied by Keilis-Borok et al., are more effective at predicting coming large events. We consider the implications of several different quality functions Q which can be used to optimize the algorithms with respect to features such as space, time, and magnitude windows, and find that our results are not overly sensitive to variations in these algorithm parameters. We also study the intrinsic uncertainties associated with seismicity catalogs of restricted lengths.Comment: 33 pages, plain.tex with special macros include