Ebook: Mathematical Aspects of Weyl Quantization and Phase

This work concerns a rapidly developing area of science that deals with the behaviour of porous media saturated by fluids. Three basic aspects of this field are rather uniformly balanced in the book: namely, complex physical mechanisms of processes in porous media, new mathematical models, and numerical methods of process study. The following topics are included: homogenization and up-scaling of flow through heterogeneous media; micro-structural laws of complex flow at the pore scale; flow with phase transition and chemical reactions in porous media; wave propagation in saturated porous media; numerical model of flow in natural oil reservoirs; non-classical models of flow, percolation, fractals, foam flow; and multi-phase flow with free surface. The contributors are leading researchers in the field Part 1 Fundamentals: some remarks on classical mechanics; the bounded model; the smooth model; representations of the CCR; probability in quantum mechanics; dynamical systems; Weyl quantization. Part Quantization and phase: quantization in polar co-ordinates; phase operators; the laser model; Weyl dequantization; the moyal product; ordered quantization; asymptotics; measurements