On the Acoustic-Electromagnetic Analogy for the Reflection-Refraction Problem

The same mathematical theory can be used to describe physical phenomena of different nature. For instance, the wave equation and the related mathematical developments can be used to describe elastic and electromagnetic wave propagation, and it is also extensively used in quantum mechanics. Fresnel's equations are a classical example of the analogy between shear waves and light waves. George Green in the nineteenth century, used analogies to obtain the reflection coefficients for sound waves and light waves, before the advent of the electromagnetic theory of light.In this work, we investigate the mathematical analogy between elastic waves and electromagentic waves. We obtain a complete parallelism for the reflection and refraction problem, considering the most general situation, that is, the presence of anisotropy and attenuation—viscosity in the elastic case and conductivity in the electromagnetic case. The analogy is illustrated with Fresnel's equations, the Brewster and critical angles, the concept of reflectivity and transmissivity, and the corresponding duals fields. The analysis of the elastic-solid theory of reflection applied by Green to light waves, and a brief historical review of wave propagation through the ether, further illustrate the analogy.     

Phénomènes karstiques fossiles et actuels au sein des formations métamorphiques silico-alumineuses de la nappe pan-africaine de Yaoundé (Sud-Cameroun)Fossil and present-time karstic phenomena in silico-aluminous metamorphic formations of the Pan-African nappe of Yaoundé (South-Cameroon)

Numerous karstic features have been recognised in the non-carbonaceous micaschists and gneisses of the Yaoundé Pan-African nappe, south of Cameroon. It is shown that their formation was controlled by the structural features of the rocks. The wells and the pipes in the bedrock outcrops point out a current karstification process, resulting from the plagioclase dissolution by the acid rain waters. Hill wall alveoli and caves, of pre-Miocene age, are exhumed features that were done by dissolution in the aquiferous underground. To cite this article: J.-P. Vicat et al., C. R. Geoscience 334 (2002) 545–550.     

Microstructural evolution of the Seridó Belt, NE-Brazil: the effect of two tectonic events on development of c-axis preferred orientation in quartz

The polyphase evolution of the Seridó Belt (NE-Brazil) includes D₁ crust formation at 2.3–2.1 Ga, D₂ thrust tectonics at 1.9 Ga and crustal reworking by D₃ strike-slip shear zones at 600 Ma. Microstructural investigations within mylonites associated with D₂ and D₃ events were used to constrain the tectono-thermal evolution of the belt. D₂ shear zones commenced at deeper crustal levels and high amphibolite facies conditions (600–650 °C) through grain boundary migration, subgrain rotation and operation of quartz c-prism slip. Continued shearing and exhumation of the terrain forced the re-equilibration of high-T fabrics and the switching of slip systems from c-prism to positive and negative a-rhombs. During D₃, enhancement of ductility by dissipation of heat that came from syn-D₃ granites developed wide belts of amphibolite facies mylonites. Continued shearing, uplift and cooling of the region induced D₃ shear zones to act in ductile-brittle regimes, marked by fracturing and development of thinner belts of greenschist facies mylonites. During this event, switching from a-prism to a-basal slip indicates a thermal path from 600 to 350 °C. Therefore, microstructures and quartz c-axis fabrics in polydeformed rocks from the Seridó Belt preserve the record of two major events, which includes contrasting deformation mechanisms and thermal paths.     

Validation of Landslide Susceptibility Maps; Examples and Applications from a Case Study in Northern Spain

A procedure for validating landslide susceptibility maps wasapplied in a study area in northern Spain and the results obtained compared. Validationwas used to carry out sensitivity analysis for individual variables and combinationsof variables. The validity of different map-making methods was tested, as well as theutility of different types of Favourability Functions. The results obtained show thatvalidation is essential to determine the predictive value of susceptibility maps. Italso helps to better select the most suitable function and significant variables, thus improving the efficiency of the mapping process. Validation based on a temporal strategy makes it possible to derive hazard maps from susceptibility maps.     

Pressure-Dependence of Rare Earth Element Distribution in Amphibolite- and Granulite- Grade Garnets. A LA-ICP-MS Study

Using an excimer (KrF) laser ablation ICP-MS system, we studied the distribution of REE in garnets from metapelites and metabasites from Ivrea-Verbano (Western Alps, Italy) and from the Peña Negra Anatectic Complex (Central Iberia), finding systematic variations that correlate well with the metamorphic grade. Chondrite-normalized REE patterns of garnets from amphibolite-grade metapelites have lower-than-chondrite levels from La to Sm, a very small or no Eu anomaly, and a steep rise in the abundance of heavy REE as the atomic number increases. Metapelitic garnets from the amphibolite-granulite transition have a marked Eu negative anomaly and are enriched in MREE such that Sm is 10-15 times chondrite and the pattern is almost flat from Dy to Yb-Lu. In garnets from granulite-grade metapelites, the intensity of the Eu anomaly and the relative concentration of Nd, Sm, Gd and Tb increase, with almost flat chondrite-normalized patterns from Sm to Lu. Garnets from mafic granulites are remarkably similar to those of metapelitic garnets equilibrated at the same pressure, except for the Eu anomaly. The apparent paradox of enhanced uptake of larger REE ions with increasing pressure is attributed to the 3M²⁺ 2REE³⁺+ vacancy substitution, which produces a net decrease in the dimensions of the unit-cell of garnet. Variations in REE patterns depend essentially on the pressure and have little dependence on either temperature, bulk-composition of garnet, or REE whole-rock composition, so they could represent a new approach for geobarometric studies. The best numerical parameter to express pressure-related variations of REE distribution in garnets is the Gd/Dy ratio which does not seem perceptibly affected by disequilibrium partitioning. The regression equation between GASP pressure and the average Gd/Dy^garnet is P = 3.6 + 5.6 Gd/Dy. This equation seems to be reliable for garnets: (1)equilibrated within a pressure range of 4-9 kbar, (2) coexisting with modal monazite; and (3) with unit-cell dimensions under 11.46 Å.     

Effects of early season defoliation ofAnthyllis cytisoides(a Mediterranean browse species) on further herbivore attack

To determine if defoliation of a woody plant affects foraging by folivorous insects, we examined the infection rate (number of leaves damaged per total number of leaves sampled on marked stems) ofAnthyllis cytisoidesunder three experimental treatments: 10, 50 and 90% plant defoliation. Observations were made for three age classes, established by trunk base perimeter (equal to or lower than 11 cm, between 11 and 20 cm, larger than 20 cm). Plants respond positively to artificial defoliation by increasing total vegetative length of the stem and total inflorescence length. This response is most evident in young individuals.Response to herbivory was measured as overall infection rate and also as infection rate by different feeding guilds—chewing, mining, or sucking insects. We found that increased defoliation elicited increased resistance of leaves to insect attack. This was particularly evident in young plants. Different insect guilds respond in different ways. Attack by chewing insects declines with defoliation for all plant age classes; only sucking insects which feed on the oldest plants reduce feeding rate with plant defoliation. Finally, mining insects present the opposite trend in young and senescent plants.     

Comparison of Cu and Zn cycling in eutrophic lakes with oxic and anoxic hypolimnion

Data on the cycling of Cu and Zn in two eutrophic lakes are presented: Lake Greifen that becomes seasonally anoxic in its hypolimnion and Lake Sempach that is aerated during winter and oxygenated during summer. They suggest that hypolimnetic oxygenation 1) enhances the release of copper from the sediment but 2) also accelerates the entrapment and deposition of Cu and Zn by freshly formed Mn- and Fe-oxides.