By de Carvalho Bezerra S., Tindel S.

During this notice, we reflect on a SK (Sherrington-Kirkpatrick)-type version on ℤ d for d≥1, weighted through a functionality permitting to any unmarried spin to engage with a small share of the opposite ones. within the thermodynamical restrict, we examine the equivalence of this version with the standard SK spin method, throughout the learn of the fluctuations of the unfastened strength.

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1 there is a direct correlation between annual rainfalls and mean denudation rates. The combination of high rainfalls and dense plant covers in the islands and mainland of South-East Asia create optimum conditions for limestone dissolution. These areas therefore have the most spectacular karst, the largest caves, the largest sinkholes and the greatest engineering geohazards. In contrast, plant cover is constrained in the high latitudes and altitudes, as well as in the arid deserts (Jennings, 1983) ± which consequently have poorly developed karst, generally with a smaller scale of sinkhole development.

Most of the European chalks originated by pelagic sedimentation in temperate or tropical shelf seas with water depths of 100±300 m. Generally, chalk is a remarkably pure micritic limestone, containing over 95% CaCO3 , with >70% of grains composed almost entirely of coccolith skeletons that are < 40 mm in diameter. Chalk varies in hardness. In the soft chalks of south-east England, the individual particles are bound together at their points of contact by thin ®lms of calcite and Sec. 6 Chalk and its sinkholes 17 aragonite, and there are only minute amounts of these cements.

The mechanical properties of old, well-lithi®ed limestones cover a range of uncon®ned compressive strengths (UCS) of 30±100 MPa for the intact rock (Waltham and Fookes, 2003). 6 kN/m 3 and primary porosity < 2%. Groundwater ¯ow and dissolutional development are focused on fractures to create discrete conduits. These properties are largely dictated by tectonic history, but age of the limestone is irrelevant; major karst terrains lie on limestones that are Proterozoic in Brazil, Ordovician in Pennsylvania, Carboniferous in Great Britain, Permian in China, Mesozoic in Europe and Tertiary in Malaysia.

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A Central Limit Theorem for a Localized Version of the SK Model by de Carvalho Bezerra S., Tindel S.

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