We consider SL(2,R)-valued cocycles over rotations of the circle and prove that they are likely to have Lyapunov exponents ≈ ± logλ if the norms of all of the matrices are ≈ λ. This is proved for λ sufficiently large. The ubiquity of elliptic behavior is also observed. Consider an area preserving diffeomorphism f of a compact surface. Assume that f is not uniformly hyperbolic, but that it has o...

Abstract. The crystalline basement is considered a ubiquitous and almost inexhaustible source of geothermal energy in the Upper Rhine Graben (URG) other regions worldwide. hydraulic properties basement, which are one key factors productivity power plants, primarily controlled by hydraulically active faults fractures. While most accurate situ information about general fracture network obtained f...

Abstract The modelling of discontinuities in rock mass is undertaken with different measurement techniques and used to determine the situ block size distribution (IBSD). Two monitoring are employed: televiewer logging boreholes photogrammetry highwall faces a quarry bench; performs at borehole diameter scale, while surveys entire bench scale. Ground sampling distances were, respectively, about ...

To simulate the propagation law of hydraulic fractures in deep Coal Bed Methane (CBM) reservoirs Qin-shui basin, a 3D numerical model is established using continuous-discontinuous algorithm, and discrete fracture network (DFN) included to increase its heterogeneity. The control variable method was employed study effects situ stress, random number, fracturing fluid flow viscosity on propagation....

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity geological formations and availability different types data that are typically affected by uncertainties. In case geologically complex depositional environments, such as fractured reservoirs, uncertainties involved in process demand accurate analysis quantification order provide reliable conf...

The present paper gives a brief description of the Math-Net project which is carried out by nine mathematical institutions in Germany, supported by Deutsches Forschungsnetz (DFN) and Deutsche Telekom. The project aims at setting up the technical and organizational infrastructure for eecient, inexpensive and user-driven information services for mathematics. With the aid of active (structured ret...

Fluid flow modeling of naturally fractured reservoirs remains a challenge because the complex nature fracture systems controlled by various chemical and physical phenomena. A discrete network (DFN) model represents an approach to capturing relationship fractures in system. Topology connectivity aspect planes, which have fundamental role simulation geomaterials involving rock matrix. Therefore, ...