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

Pore geometry as a control on rock strength

This study was funded via RJW's University of Leicester start-up fund, as part of AAB's PhD project. We thank Don Swanson and Mike Poland at HVO, Hawai'i, for their help and advice during fieldwork planning and sample collection in the Koa'e fault system, and the National Park Service for granting a research permit to collect rock samples. Sergio Vinciguerra is thanked for access to the Rock Mechanics and Physics lab at the British Geological Survey and Audrey Ougier-Simonin is thanked for her help preparing samples and advice during testing. We thank Mike Heap (EOST Strasbourg) and an anonymous reviewer for their detailed and careful comments that greatly improved the manuscript.Peer reviewedPostprin

Singularities of the renormalization group flow for random elastic manifolds

We consider the singularities of the zero temperature renormalization group flow for random elastic manifolds. When starting from small scales, this flow goes through two particular points $l^{*}$ and $l_{c}$, where the average value of the random squared potential turnes negative ($l^{*}$) and where the fourth derivative of the potential correlator becomes infinite at the origin ($l_{c}$). The latter point sets the scale where simple perturbation theory breaks down as a consequence of the competition between many metastable states. We show that under physically well defined circumstances $l_{c} to negative values does not take place.Comment: RevTeX, 3 page

A molecular theory for two-photon and three-photon fluorescence polarization

In the analysis of molecular structure and local order in heterogeneous samples, multiphoton excitation of fluorescence affords chemically specific information and high-resolution imaging. This report presents the results of an investigation that secures a detailed theoretical representation of the fluorescence polarization produced by one-, two-, and three-photon excitations, with orientational averaging procedures being deployed to deliver the fully disordered limits. The equations determining multiphoton fluorescence response prove to be expressible in a relatively simple, generic form, and graphs exhibit the functional form of the multiphoton fluorescence polarization. Amongst other features, the results lead to the identification of a condition under which the fluorescence produced through the concerted absorption of any number of photons becomes completely unpolarized. It is also shown that the angular variation of fluorescence intensities is reliable indicator of orientational disorder

Distance-generalized Core Decomposition

The $k$-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least $k$ other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of $k$-core, which we refer to as the $(k,h)$-core, i.e., the maximal subgraph in which every vertex has at least $k$ other vertices at distance $\leq h$ within that subgraph. We study the properties of the $(k,h)$-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as $h$-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm

Porous silica spheres as indoor air pollutant scavengers

Porous silica spheres were investigated for their effectiveness in removing typical indoor air pollutants, such as aromatic and carbonyl-containing volatile organic compounds (VOCs), and compared to the commercially available polymer styrene-divinylbenzene (XAD-4). The silica spheres and the XAD-4 resin were coated on denuder sampling devices and their adsorption efficiencies for volatile organic compounds evaluated using an indoor air simulation chamber. Real indoor sampling was also undertaken to evaluate the affinity of the silica adsorbents for a variety of indoor VOCs. The silica sphere adsorbents were found to have a high affinity for polar carbonyls and found to be more efficient than the XAD-4 resin at adsorbing carbonyls in an indoor environment