Fermat's principle of least time in the presence of uniformly moving boundaries and media

The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: a) the material half-space is moving parallel to the interface; b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtained refraction formula is provided, and in the latter case, an intriguing backward refraction of light is noticed and thoroughly discussed. The results confirm the validity of Fermat's principle when the optical media and the boundaries between them are moving at relativistic speeds.Comment: 11 pages, 6 figures, RevTeX 4, comments welcome; V2: revised, Fig. 7 added; V3: several typos corrected, accepted for publication in European Journal of Physics (online at: http://stacks.iop.org/EJP/28/933

Hierarchical model for the scale-dependent velocity of seismic waves

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.Comment: 7 pages including 3 figure

Ecological goods and services and agroforestry : the benefits for farmers and the interests for society

Paper presented at the 11th North American Agroforesty Conference, which was held May 31-June 3, 2009 in Columbia, Missouri.In Gold, M.A. and M.M. Hall, eds. Agroforestry Comes of Age: Putting Science into Practice. Proceedings, 11th North American Agroforestry Conference, Columbia, Mo., May 31-June 3, 2009.The main objective of this project is to estimate the social value of environmental goods and services (EG&S) generated by agroforestry practices and to evaluate the profitability of these practices for agricultural producers and for society. Two agroforestry practices are considered: riparian buffer zones and windbreaks. Moreover, the situations in two representative agricultural watersheds serve our analysis (Chateauguay and Fouquette watersheds). Among the numerous EG&S that are provided through agroforestry practices, nine have been chosen for this study: agriculture-related odors, aestheticism of the landscape, terrestrial biodiversity, surface water quality, carbon sequestration, road accidents, clearing snow from roads, treatment of drinking water and wild pollinating insects. Several economic valuation methods have been used, such as hedonic pricing value, benefit transfer, productivity method or experimental economics.Jean Nolet (1), Claude Sauve_ (1), Maria Olar (1), Maribel Hernandez (1), Marjolaine Mondon (1), Caroline Simard (1), Louis-Samuel Jacques (1), Andr� V�zina (2), Nathan De Baets (2), Maud Ablain (3), and Pierre Etcheverry (3) ; 1. EcoRessources Consultants, 825, rue Raoul-Jobin, Qu�bec, QC, Canada, G1N 1S6. 2. Activa Environnement Inc., 106, rue Industrielle, New Richmond (Qu�bec), G0C 2B0. 3. Centre d'expertise sur les produits agroforestiers (CEPAF), 235, route 230 ouest, La Pocati�re, QC, Canada, G0R 1Z0.try pIncludes bibliographical references

Characterization of an Ionization Readout Tile for nEXO

A new design for the anode of a time projection chamber, consisting of a charge-detecting "tile", is investigated for use in large scale liquid xenon detectors. The tile is produced by depositing 60 orthogonal metal charge-collecting strips, 3~mm wide, on a 10~\si{\cm} $\times$ 10~\si{\cm} fused-silica wafer. These charge tiles may be employed by large detectors, such as the proposed tonne-scale nEXO experiment to search for neutrinoless double-beta decay. Modular by design, an array of tiles can cover a sizable area. The width of each strip is small compared to the size of the tile, so a Frisch grid is not required. A grid-less, tiled anode design is beneficial for an experiment such as nEXO, where a wire tensioning support structure and Frisch grid might contribute radioactive backgrounds and would have to be designed to accommodate cycling to cryogenic temperatures. The segmented anode also reduces some degeneracies in signal reconstruction that arise in large-area crossed-wire time projection chambers. A prototype tile was tested in a cell containing liquid xenon. Very good agreement is achieved between the measured ionization spectrum of a $^{207}$Bi source and simulations that include the microphysics of recombination in xenon and a detailed modeling of the electrostatic field of the detector. An energy resolution $\sigma/E$=5.5\% is observed at 570~\si{keV}, comparable to the best intrinsic ionization-only resolution reported in literature for liquid xenon at 936~V/\si{cm}.Comment: 18 pages, 13 figures, as publishe

Sensitivity and discovery potential of the proposed nEXO experiment to neutrinoless double beta decay

The next-generation Enriched Xenon Observatory (nEXO) is a proposed experiment to search for neutrinoless double beta ($0\nu\beta\beta$) decay in $^{136}$Xe with a target half-life sensitivity of approximately $10^{28}$ years using $5\times10^3$ kg of isotopically enriched liquid-xenon in a time projection chamber. This improvement of two orders of magnitude in sensitivity over current limits is obtained by a significant increase of the $^{136}$Xe mass, the monolithic and homogeneous configuration of the active medium, and the multi-parameter measurements of the interactions enabled by the time projection chamber. The detector concept and anticipated performance are presented based upon demonstrated realizable background rates.Comment: v2 as publishe

How and when plume zonation appeared during the 132 Myr evolution of the Tristan Hotspot

Increasingly, spatial geochemical zonation, present as geographically distinct, subparallel trends, is observed along hotspot tracks, such as Hawaii and the Galapagos. The origin of this zonation is currently unclear. Recently zonation was found along the last B70 Myr of the Tristan-Gough hotspot track. Here we present new Sr–Nd–Pb–Hf isotope data from the older parts of this hotspot track (Walvis Ridge and Rio Grande Rise) and re-evaluate published data from the Etendeka and Parana flood basalts erupted at the initiation of the hotspot track. We show that only the enriched Gough, but not the less-enriched Tristan, component is present in the earlier (70–132 Ma) history of the hotspot. Here we present a model that can explain the temporal evolution and origin of plume zonation for both the Tristan-Gough and Hawaiian hotspots, two end member types of zoned plumes, through processes taking place in the plume sources at the base of the lower mantle