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This book provides an accessible introduction to a new set of methods for the analysis of Lagrangian motion in geophysical flows. These methods were originally developed in the abstract mathematical setting of dynamical systems theory, through a geometric approach to differential equations. Despite the recent developments in this field and the existence of a substantial body of work on geophysical fluid problems in the dynamical systems and geophysical literature, this is the first introductory text that presents these methods in the context of geophysical fluid flow. The book is organized into seven chapters; the first introduces the geophysical context and the mathematical models of geophysical fluid flow that are explored in subsequent chapters. The second and third cover the simplest case of steady flow, develop basic mathematical concepts and definitions, and touch on some important topics from the classical theory of Hamiltonian systems. The fundamental elements and methods of Lagrangian transport analysis in time-dependent flows that are the main subject of the book are described in the fourth, fifth, and sixth chapters. The seventh chapter gives a brief survey of some of the rapidly evolving research in geophysical fluid dynamics that makes use of this new approach. Related supplementary material, including a glossary and an introduction to numerical methods, is given in the appendices. This book will prove useful to graduate students, research scientists, and educators in any branch of geophysical fluid science in which the motion and transport of fluid, and of materials carried by the fluid, is of interest. It will also prove interesting and useful to the applied mathematicians who seek an introduction to an intriguing and rapidly developing area of geophysical fluid dynamics. The book was jointly authored by a geophysical fluid dynamicist, Roger M. Samelson of the College of Oceanic and Atmospheric Sciences at Oregon State University, USA and an applied mathematician, Stephen Wiggins of the School of Mathematics, University of Bristol, UK.

Geophysics --- Fluid dynamics. --- Lagrangian functions. --- Fluid models. --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization --- Fluid mechanics --- Fluid models in geophysics --- Rotating dishpan --- Differentiable dynamical systems. --- Geography. --- Dynamical Systems and Ergodic Theory. --- Earth Sciences, general. --- Classical and Continuum Physics. --- Cosmography --- Earth sciences --- World history --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Dynamics. --- Ergodic theory. --- Earth sciences. --- Continuum physics. --- Classical field theory --- Continuum physics --- Physics --- Continuum mechanics --- Geosciences --- Environmental sciences --- Physical sciences --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Dynamique des fluides --- Lagrange, Fonctions de --- Géophysique

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Remarkable progress has recently been made in the application of quantumtrajectories as the computational tool for solving quantum mechanical problems. This is the first book to present these developments in the broader context of the hydrodynamical formulation of quantum dynamics. In addition to a thorough discussion of the quantum trajectory equations of motion, there is considerable material that deals with phase space dynamics, adaptive moving grids, electronic energy transfer, and trajectories for stationary states. On the pedagogical side, a number of sections of this book will be accessible to students who have had an introductory quantum mechanics course. There is also considerable material for advanced researchers, and chapters in the book cover both methodology and applications. The book will be useful to students and researchers in physics, chemistry, applied math, and computational dynamics. "This excellent book covers a wide range of topics associated with Quantum Hydrodynamics. It's an excellent survey of the history, current state-of-the-field, and future research directions." Brian Kendrick,Theoretical Division, Los Alamos National Laboratory, Los Alamos,NM, USA The book is unique in that it addresses with equal expertise, computational methodology and theoretical connections at the interface between de Broglie-Bohm theory and phase space moment methods.A highly didactic text, to be recommended to graduate students and researchers in physics and chemistry. Irene Burghardt,Departement de chimie, Ecole Normale Superieure, Paris, France Wyatt shows how one can use the ideas drawn from Bohm's interpretation to develop new and efficient computational methods for both time dependent and time independent quantum mechanics.This is THE definitive text on practical Bohmian mechanics. Eric Bittner,Department of Chemistry, University of Houston, Tx, USA .

Hydrodynamics. --- Quantum trajectories. --- Lagrangian functions. --- Schrödinger equation. --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Equation, Schrödinger --- Schrödinger wave equation --- Differential equations, Partial --- Particles (Nuclear physics) --- Wave mechanics --- WKB approximation --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization --- Trajectories, Quantum --- Hydrodynamics --- Quantum field theory --- Fluid dynamics --- Computer science --- Quantum theory. --- Chemistry, Physical organic. --- Hydraulic engineering. --- Computational Mathematics and Numerical Analysis. --- Quantum Physics. --- Atomic, Molecular, Optical and Plasma Physics. --- Fluid- and Aerodynamics. --- Physical Chemistry. --- Engineering Fluid Dynamics. --- Mathematics. --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Chemistry, Physical organic --- Chemistry, Organic --- Chemistry, Physical and theoretical --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Computer mathematics. --- Quantum physics. --- Atoms. --- Physics. --- Fluids. --- Physical chemistry. --- Fluid mechanics. --- Hydromechanics --- Continuum mechanics --- Chemistry, Theoretical --- Physical chemistry --- Theoretical chemistry --- Chemistry --- Hydrostatics --- Permeability --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Matter --- Stereochemistry --- Constitution --- Schrodinger equation.