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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 --- Lagrange equations. --- Mathematical models.
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Number theory --- algebra --- Lagrange, Joseph-Louis --- Galois, Evariste
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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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Classical mechanics. Field theory --- Hamiltonian systems --- Lagrange equations --- Mathematical physics --- Systèmes hamiltoniens --- Lagrange, Equations de --- Physique mathématique --- Hamiltonian systems. --- Lagrange equations. --- Mathematical physics. --- Systèmes hamiltoniens --- Physique mathématique --- Mechanics, Analytic --- Lagrange, Équations de --- Study and teaching (Higher) --- Numerical solutions --- Étude et enseignement (supérieur) --- Solutions numériques --- Étude et enseignement (supérieur)
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Mathematical physics --- 51 --- Mathematics --- Lagrange equations. --- Laplacian operator. --- Sound-waves --- Wave equation. --- Scattering. --- 51 Mathematics --- Equations aux derivees partielles --- Scattering
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This is a rare book on a rare topic : it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains : why an optimization principle underlies physics, what action is, what the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired.
Hamiltonian systems --- Lagrange equations --- Mechanics, Analytic --- Force and energy --- Variational principles --- Systèmes hamiltoniens --- Lagrange, Équations de --- Dynamique --- Mécanique analytique --- Énergie --- Principes variationnels --- Lanczos, Cornelius, --- Criticism and interpretation --- Critique et interprétation --- Least action. --- Mathematical physics. --- Physical mathematics --- Physics --- Mechanics --- Mathematics --- 531 --- 531 General mechanics. Mechanics of solid and rigid bodies --- General mechanics. Mechanics of solid and rigid bodies --- Systèmes hamiltoniens. --- Lagrange, Équations de. --- Dynamique. --- Mécanique analytique. --- Énergie. --- Principes variationnels. --- Mathematical physics --- Lanczos, Cornelius --- Criticism and interpretation. --- Critique et interprétation. --- Classical mechanics. Field theory
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Law --- Discrimination --- Droit --- Lagrange, Emérentienne de --- France --- Politics and government --- Politique et gouvernement --- Law and legislation --- Lagrange, Emérentienne de --- 347 <082> --- -France --- -Law --- -347 <44> --- 32 --- Acts, Legislative --- Enactments, Legislative --- Laws (Statutes) --- Legislative acts --- Legislative enactments --- Jurisprudence --- Legislation --- Bias --- Interpersonal relations --- Minorities --- Toleration --- Burgerlijk recht. Privaatrecht--Feestbundels. Festschriften --- -Politics and government --- Politiek. Staatskunde. Staatswetenschappen --(algemeen) --- Lagrange, Emerentienne de --- 32 Politiek. Staatskunde. Staatswetenschappen --(algemeen) --- 347 <082> Burgerlijk recht. Privaatrecht--Feestbundels. Festschriften --- 347 <44> --- Lagrange, Emérentienne de. --- Politics and government. --- 32 Politics --- Politics --- Law - France --- Discrimination - Law and legislation - France --- France - Politics and government
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