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"Semi-Lagrangian Advection Methods and Their Applications in Geoscience provides a much-needed resource on semi-Lagrangian theory, methods, and application. Covering a variety of applications, the book brings together developments of the semi-Lagrangian in one place and offers a comparison of semi-Lagrangian methods with Eulerian-based approaches. It also includes a chapter dedicated to difficulties of dealing with the adjoint of semi-Lagrangian methods and illustrates the behaviour of different schemes for different applications. This allows for a better understanding of which schemes are most efficient, stable, consistent, and likely to introduce the minimum model error into a given problem. Beneficial for students learning about numerical approximations to advection, researchers applying these techniques to geoscientific modeling, and practitioners looking for the best approach for modeling, Semi-Lagrangian Advection Methods and Their Applications in Geoscience fills a crucial gap in numerical modeling and data assimilation in geoscience. Provides a single resource for understanding semi-Lagrangian methods and what is involved in its application. Includes exercises and codes to supplement learning and create opportunities for practice Includes coverage of adjoints, examining the advantages and disadvantages of different approaches in multiple coordinate systems and different discretizations. Includes links to numerical datasets and animations to further enhance understanding"--

Earth sciences --- Mathematical models. --- Lagrange equations. --- Geosciences --- Environmental sciences --- Physical sciences --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion

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The rigorous mathematical theory of the Navier-Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier-Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier-Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Differential equations, Partial. --- Navier-Stokes equations. --- Lagrange equations. --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Partial differential equations

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Devoted to the subject of shape charge design using numerical methods, this book offers the defense and commercial industries unique material not contained in any other single volume. The coverage of the Lagrangian and Eulerian methods as well as the equation of state provides first hand help to engineers working on shape charge problems.The book includes detailed descriptions of oil-well perforation not available from any other sources and, coupled with the material flow physics discussed in Chapters 2 and 3 and Appendix B, readers can design the fuel rod configurations for a nuclear reactor

Shaped charges --- Flow visualization --- Penetration mechanics --- Lagrange equations. --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Ballistics --- Fracture mechanics --- Impact --- Mechanics, Applied --- Visualization of flow --- Fluid dynamics --- Cavity charges --- Hollow charges (Explosives) --- Munroe charges --- Explosives --- Computer simulation. --- Mathematical models.

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The aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.

Hamiltonian systems. --- Lagrange equations. --- Mathematical physics. --- Physical mathematics --- Physics --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Mathematics --- Mechanics. --- Statistical physics. --- Classical Mechanics. --- Complex Systems. --- Classical Electrodynamics. --- Statistical Physics and Dynamical Systems. --- Mathematical statistics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Statistical methods --- Dynamical systems. --- Optics. --- Electrodynamics. --- Light --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics

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Dynamics --- Lagrange equations --- Dynamique --- Lagrange, Equations de --- 531 --- 517 --- dynamica --- lagrange --- euler --- Hamilton --- mechanica --- wiskunde --- D'Alembert equation --- Equations, Euler-Lagrange --- Equations, Lagrange --- Euler-Lagrange equations --- Lagrangian equations --- Differential equations --- Equations of motion --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- General mechanics. Mechanics of solid and rigid bodies --- Analysis --- Dynamics. --- Lagrange equations. --- 517 Analysis --- 531 General mechanics. Mechanics of solid and rigid bodies