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Stochastic processes --- Stochastic analysis. --- Stochastic differential equations. --- Analyse stochastique --- Equations différentielles stochastiques --- Stochastic analysis --- Flows (Differentiable dynamical systems) --- Stochastic differential equations --- Equations différentielles stochastiques

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This book aims to provide a self-contained introduction to the local geometry of the stochastic flows. It studies the hypoelliptic operators, which are written in Hörmander's form, by using the connection between stochastic flows and partial differential equations. The book stresses the author's view that the local geometry of any stochastic flow is determined very precisely and explicitly by a universal formula referred to as the Chen-Strichartz formula. The natural geometry associated with the Chen-Strichartz formula is the sub-Riemannian geometry, and its main tools are introduced throughou

Stochastic geometry. --- Flows (Differentiable dynamical systems) --- Stochastic differential equations. --- Differentiable dynamical systems --- Differential equations --- Fokker-Planck equation --- Geometry --- Equations différentielles stochastiques --- Géométrie stochastique

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This book is the first monograph providing an introduction to and an overview of numerical methods for the simulation of two-phase incompressible flows. The Navier-Stokes equations describing the fluid dynamics are examined in combination with models for mass and surfactant transport. The book pursues a comprehensive approach: important modeling issues are treated, appropriate weak formulations are derived, level set and finite element discretization techniques are analyzed, efficient iterative solvers are investigated, implementational aspects are considered and the results of numerical experiments are presented. The book is aimed at M Sc and PhD students and other researchers in the fields of Numerical Analysis and Computational Engineering Science interested in the numerical treatment of two-phase incompressible flows.

Flows (Differentiable dynamical systems). --- Numerical analysis. --- Viscous flow --- Navier-Stokes equations --- Fluid mechanics --- Numerical analysis --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematics - General --- Mathematical models --- Numerical solutions --- Flows (Differentiable dynamical systems) --- Mathematics. --- Computer mathematics. --- Applied mathematics. --- Engineering mathematics. --- Fluid mechanics. --- Mechanical engineering. --- Computational Mathematics and Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- Engineering Fluid Dynamics. --- Mechanical Engineering. --- Mathematical analysis --- Differentiable dynamical systems --- Computer science --- Hydraulic engineering. --- Mathematical and Computational Engineering. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Engineering, Hydraulic --- Hydraulics --- Shore protection --- Engineering analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Hydromechanics --- Continuum mechanics

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This book presents several new findings in the field of turbulent duct flows, which are important for a range of industrial applications. It presents both high-quality experiments and cutting-edge numerical simulations, providing a level of insight and rigour rarely found in PhD theses. The scientific advancements concern the effect of the Earth’s rotation on large duct flows, the experimental confirmation of marginal turbulence in a pressure-driven square duct flow (previously only predicted in simulations), the identification of similar marginal turbulence in wall-driven flows using simulations (for the first time by any means) and, on a separate but related topic, a comprehensive experimental study on the phenomenon of drag reduction via polymer additives in turbulent duct flows. In turn, the work on drag reduction resulted in a correlation that provides a quantitative prediction of drag reduction based on a single, measurable material property of the polymer solution, regardless of the flow geometry or concentration. The first correlation of its kind, it represents an important advancement from both a scientific and practical perspective.

Flows (Differentiable dynamical systems) --- Differentiable dynamical systems --- Hydraulic engineering. --- Fluid- and Aerodynamics. --- Engineering Fluid Dynamics. --- Materials Engineering. --- Numerical and Computational Physics, Simulation. --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Fluids. --- Fluid mechanics. --- Engineering—Materials. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Hydromechanics --- Continuum mechanics --- Mechanics --- Physics --- Hydrostatics --- Permeability

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The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

Chaotic behavior in systems -- Mathematics. --- Flows (Differentiable dynamical systems). --- Mathematics. --- Flows (Differentiable dynamical systems) --- Chaotic behavior in systems --- Physics --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Atomic Physics --- Geometry --- Applied Mathematics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Physics. --- Geophysics. --- Continuum physics. --- Fluids. --- Statistical physics. --- Dynamical systems. --- Statistical Physics, Dynamical Systems and Complexity. --- Classical Continuum Physics. --- Geophysics/Geodesy. --- Fluid- and Aerodynamics. --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Physical geography. --- Complex Systems. --- Classical and Continuum Physics. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Geography --- Statistical methods --- Hydraulics --- Mechanics --- Hydrostatics --- Permeability --- Geological physics --- Terrestrial physics --- Earth sciences --- Classical field theory --- Continuum physics --- Continuum mechanics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics