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Written by a group of international experts in their field, this book is a review of Lagrangian observation, analysis and assimilation methods in physical and biological oceanography. This multidisciplinary text presents new results on nonlinear analysis of Lagrangian dynamics, the prediction of particle trajectories, and Lagrangian stochastic models. It includes historical information, up-to-date developments, and speculation on future developments in Lagrangian-based observations, analysis, and modeling of physical and biological systems. Containing contributions from experimentalists, theoreticians, and modellers in the fields of physical oceanography, marine biology, mathematics, and meteorology, this book will be of great interest to researchers and graduate students looking for both practical applications and information on the theory of transport and dispersion in physical systems, biological modelling, and data assimilation.

Ocean currents --- Lagrange equations. --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Currents, Oceanic --- Ocean circulation --- Water currents --- Ocean surface topography --- Mathematical models. --- Hydrodynamique --- Océanographie

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This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

Conservation laws (Mathematics) --- Lagrange equations. --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Mathematics. --- Partial differential equations. --- Computer mathematics. --- Computational Mathematics and Numerical Analysis. --- Partial Differential Equations. --- Computer science --- Differential equations, partial. --- Partial differential equations --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics --- Differential equations --- Equations of motion --- Differential equations, Hyperbolic

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The principle of least action originates in the idea that, if nature has a purpose, it should follow a minimum or critical path. This simple principle, and its variants and generalizations, applies to optics, mechanics, electromagnetism, relativity, and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics, and examines its history and fundamental role in science. It includes - with varying levels of mathematical sophistication - explanations from historical sources, discussion of classic papers, and original worked examples. The result is a story that is understandable to those with a modest mathematical background, as well as to researchers and students in physics and the history of physics.

Least action. --- Variational principles. --- Mechanics. --- Lagrange equations. --- Hamilton-Jacobi equations. --- Equations, Hamilton-Jacobi --- Equations, Jacobi-Hamilton --- Jacobi-Hamilton equations --- Calculus of variations --- Differential equations, Partial --- Hamiltonian systems --- Mechanics --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Extremum principles --- Minimal principles --- Variation principles --- Variational principles

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Differential equations --- Classical mechanics. Field theory --- Differentiable dynamical systems --- Lagrange equations --- Variational principles --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Equations of motion --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Lagrange equations. --- Lagrange, Équations de --- Differentiable dynamical systems. --- Systèmes dynamiques --- Variational principles. --- Principes variationnels --- Lagrange, Équations de. --- Systèmes dynamiques. --- Principes variationnels.

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This widely acclaimed introduction to N = 1 supersymmetry and supergravity is aimed at readers familiar with relativistic quantum field theory who wish to learn about the supersymmetry algebra. In this new volume Supersymmetry and Supergravity has been greatly expanded to include a detailed derivation of the most general coupling of super-symmetric gauge theory to supergravity. The final result is the starting point for phenomenological studies of supersymmetric theories. The book is distinguished by its pedagogical approach to supersymmetry. It develops several topics in advanced field theory as the need arises. It emphasizes the logical coherence of the subject and should appeal to physicists whose interests range from the mathematical to the phenomenological. In praise of the first edition: "A beautiful exposition of the original ideas of Wess and Zumino in formulating N = 1 supersymmetry and supergravity theories, couched in the language of superfields introduced by Strathdee and the reviewer.... [All] serious students of particle physics would do well to acquire a copy."--Abdus Salam, Nature "An excellent introduction to this exciting area of theoretical physics."--C. J. Isham, Physics Bulletin

Supersymmetry --- Supergravity --- Supersymétrie --- Supergravité --- Supersymétrie --- Supergravité --- Supergravity. --- Supersymmetry. --- Unified theories --- Particles (Nuclear physics) --- Symmetry (Physics) --- Superunified theories --- General relativity (Physics) --- Quantum theory --- ". --- "Coleman-Mandula theorem. --- Bianchi identities. --- Chiral superfields. --- Euler-Lagrange equations. --- Feynman rules. --- Gauge theories. --- Green's functions. --- Killing vectors. --- Kähler geometry. --- Lie algebra. --- Nonlinear transformations. --- Schwinger terms. --- Vectors. --- bracket structure. --- chiral dynamics. --- covariant derivatives. --- low-energy theorems. --- nonlinear realizations. --- polynomial. --- spinors algebra. --- standard realizations. --- supersymmetry.