Stability of Nonlinear Control Systems

"Stochastic Methods for Flow in Porous Coping with Uncertainties" explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter.; As never seen before, this book includes key features such balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods; tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes; practical examples throughout the text; and exercises at the end of each chapter which reinforce specific concepts and techniques. For the reader who is interested in hands-on experience, a number of computer codes are included and discussed.