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Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled "The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space-time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure. The result was the path

530.145 --- 530.145 Quantum theory --- Quantum theory --- Least action --- Lagrangian functions --- Quantum mechanics. Quantumfield theory --- Feynman, Richard P. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Variational principles --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization --- Acqui 2006

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The book presents advanced stochastic models and simulation methods for random flows and transport of particles by turbulent velocity fields and flows in porous media. Two main classes of models are constructed: (1) turbulent flows are modeled as synthetic random fields which have certain statistics and features mimicing those of turbulent fluid in the regime of interest, and (2) the models are constructed in the form of stochastic differential equations for stochastic Lagrangian trajectories of particles carried by turbulent flows. The book is written for mathematicians, physicists, and engineers studying processes associated with probabilistic interpretation, researchers in applied and computational mathematics, in environmental and engineering sciences dealing with turbulent transport and flows in porous media, as well as nucleation, coagulation, and chemical reaction analysis under fluctuation conditions. It can be of interest for students and post-graduates studying numerical methods for solving stochastic boundary value problems of mathematical physics and dispersion of particles by turbulent flows and flows in porous media.

Random fields. --- Lagrangian functions. --- Lagrange spectrum. --- Lagrange's spectrum --- Lagrangian spectrum --- Spectrum, Lagrange --- Spectrum, Lagrangian --- Diophantine approximation --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization --- Fields, Random --- Stochastic processes --- Footprint Function. --- Lagrangian Stochastic Model. --- Random Field. --- Stochastic Flow.

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This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed;

Gauge fields (Physics) --- Manifolds (Mathematics) --- Hamiltonian systems. --- Lagrangian functions. --- Relativistic mechanics. --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Geometry, Differential --- Topology --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Symmetry (Physics) --- Mechanics --- Relativity (Physics) --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization

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Classical mechanics. Field theory --- Differential geometry. Global analysis --- Mechanics, Analytic --- Lagrangian functions --- Hamiltonian systems --- Mécanique analytique --- Fonctions de Lagrange --- Systèmes hamiltoniens --- Textbooks --- Manuels d'enseignement supérieur --- 517.9 --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Mécanique analytique --- Systèmes hamiltoniens --- Manuels d'enseignement supérieur --- Functions, Lagrangian --- Calculus of variations --- Dynamics --- Mathematical optimization --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Analytical mechanics --- Kinetics --- Mechanics, Analytic - Textbooks --- Lagrangian functions - Textbooks --- Hamiltonian systems - Textbooks

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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.