The relationship between beachface slope and sand grain size has been established based on multiple observations of beach characteristics in many parts of the world. We show that this observational result may be understood in the light of the Constructal Law (Bejan, 1997). A model of wave run-up and run-down along the beachface (swash) was developed to account for superficial flows together with flows through the porous sand bed of average porosity 0.35, the permeability of which may be related to grain diameter and sphericity (0.9 for sand grains) through the Kozeny-Carmán equation. Then, by using the Constructal Law, we minimized the time for completing a swash cycle, under fixed wave height and sand grain diameter. As the result, a relationship involving sand grain size, beachface slope and open ocean wave height has been obtained, and then discussed and validated against experimental data. In addition, this relationship has also been used to illuminate beachface dynamic processes, namely the reshaping of sandy beachfaces in response to changes in wave height. Though the model used in this work may be improved further, the results appear to show, as with other natural systems, that beachface morphing in time may be understood based on a unifying principle -the Constructal Law.

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In the Iberian Variscan Belt, polyphasic deformation has been recognized as comprising an early phase of crustal thickening, followed by an intermediate phase of crustal extension and doming, and a later phase of shortening. The Évora Massif is a gneiss dome of the westernmost domains of the Ossa-Morena Zone (SW Iberia), which provides a remarkable insight into the late Paleozoic deep crustal structure of the Variscan continental crust of northern Gondwana. In this study, we bring new structural and geochronological U-Pb data for the northern hanging-wall of the Évora Massif. We describe the existence of low-dipping D 2 extensional shear zones associated with Buchan-type metamorphism (M 2); this enables three tectono-metamorphic units to be distinguished: the Lower Gneiss Unit, the Intermediate Schist Unit, and the Upper Slate Unit. D 2-M 2 structures experienced subhorizontal shortening (D 3) and were transposed by low-plunging folding, thrusting and strike-slip faulting. Zircon grains extracted from Pavia quartz-feldspathic gneiss of the Lower Gneiss Unit yielded a crystallization age of ca. 521 Ma (Cambrian Stage 2-3), which establishes a correlation with tectono-metamorphic units of the footwall and southern hanging-wall of the Évora Massif. U-Pb zircon dating of Divôr foliated quartz-diorite (339 ± 7 Ma), Malarranha weakly foliated biotite-rich granite (322 ± 3 Ma), and undeformed porphyritic granite of the Pavia pluton (314 ± 4 Ma) constrain the timing of emplacement of granitic magmas synchronously with doming. Carboniferous magmatism initiated with doming (ME 1-ca. 343-335 Ma), continued through D 2-M 2 (ME 2-ca. 328-319 Ma), and lasted until the waning stage of crustal extension (ME 3-ca. 317-313 Ma). The Évora Massif gneiss dome probably formed as result of the combined effect of gravitational collapse of the thickened crust and buoyancy-driven gravitational instability developed in the partially molten continental crust influenced by the transfer of heat from rising mantle-derived (i.e. dioritic-gabbroic) magmas rocks found in the footwall of the Évora Massif.

formed during magmatic crystallization and subsequent solid-state deformation. Field relationships suggest contemporaneity between the ca. 319-317 Ma old magmatism of the study area and the switch from late D 2 extensional deformation to early D 3 contractional deformation. Inherited zircon cores are well preserved in these late D 2 -early D 3 S-type granite plutons. U-Pb ages of inherited zircon cores range from ca. 2576 to ca. 421 Ma. The spectra of inherited cores overlap closely the range of detrital and magmatic zircon grains displayed by the Ediacaran to Silurian metasedimentary and metaigneous rocks of the Iberian autochthonous and parautochthonous domains. This is evidence of a genetic relationship between S-type granites and the host metamorphic rocks. There is no substantial evidence for the addition of mantle-derived material in the genesis of these late D 2 -early D 3 S-type granitic rocks. The εNd arrays of heterogeneous crustal anatectic melts may be just inherited from the source, probably reflecting mixing of a range of crustal materials with different ages and primary isotopic signatures. The generation of the Bashkirian S-type granites has been dominated by continental crust recycling, rather than the addition of new material from mantle sources.

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