TERMIUM Plus^®

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Despite its limited accuracy, the geostrophic momentum approximation reveals remarkable mathematical properties such as Hamiltonian structure, Legendre duality and contact structure, and its ability to represent contact discontinuities within the fluid enables it to describe subsynoptic phenomena such as fronts and jets.  2, record 1, English, - subsynoptic%20phenomenon

Record 1,  Textual support,  French

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Record 2,  Textual support,  English

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[A branch of statistical mechanics that is] based on the fundamental assumption that all possible configurations of a given system, which satisfy the given boundary conditions such as temperature, volume and number of particles, are equally likely to occur.  3, record 2, English, - equilibrium%20statisticals%20mecanics

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Equilibrium statistical mechanics provides the fundamental basis for the thermodynamics of a given system in terms of its Hamiltonian and the characteristics of its environment...  4, record 2, English, - equilibrium%20statisticals%20mecanics

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L'objectif de la thermodynamique statistique est de relier la description microscopique [...] d'un système à sa description macroscopique [...]  3, record 2, French, - thermodynamique%20statistique

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A non-Hamiltonian graph... is maximal if the addition of any edge transforms the graph into a Hamiltonian one.  2, record 3, English, - non%2DHamiltonian%20graph

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... a semi-Hamiltonian graph has a Hamiltonian path but no Hamiltonian cycle.  2, record 4, English, - semi%2DHamiltonian%20graph

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Un graphe semi-hamiltonien est un graphe qui contient des chaînes hamiltoniennes[, mais] pas de cycles hamiltoniens.  1, record 4, French, - graphe%20semi%2Dhamiltonien

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Se dice que un grafo [...] es semihamiltoniano si no es un grafo hamiltoniano pero admite un camino hamiltoniano.  1, record 4, Spanish, - grafo%20semihamiltoniano

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A Hamiltonian graph is a graph with a circuit – a path starting and ending at the same point – [that] visits each node exactly once.  2, record 5, English, - Hamiltonian%20graph

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Graphe hamiltonien. Un graphe est hamiltonien si l'on peut trouver un cycle passant une fois et une seule fois par tous les sommets.  2, record 5, French, - graphe%20hamiltonien

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Gráfico no dirigido con un ciclo simple a través de cada vértice.  1, record 5, Spanish, - gr%C3%A1fico%20hamiltoniano

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A quantum chemical computation procedure that explicitly includes all electrons and utilizes their full Hamiltonian operator; occasionally used to describe pseudopotential methods or other approaches with minimal semi-empirical input.  1, record 6, English, - ab%20initio%20method

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Les méthodes ab initio sont basées sur la résolution approchée de l'équation de Schrödinger. Elles ne nécessitent pas l'introduction de paramètres empiriques et sont en principe les plus proches des réalités physiques étudiées. En raison de leur difficulté de mise en œuvre, elles sont utilisées pour déterminer les caractéristiques physiques statiques de systèmes dans des configurations atomiques données. On peut utiliser les méthodes ab initio pour calculer des grandeurs comme des énergies de surface, des énergies de formation de défauts ponctuels ou de petits amas de défauts ponctuels, des barrières d'énergie pour la diffusion des défauts et par là même des atomes.  1, record 6, French, - m%C3%A9thode%20ab%20initio

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Record 7,  Textual support,  English

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A two-dimensional map used for the description of Hamiltonian nonlinear systems. The distortion engendered by this transformation is reminiscent of a maladjusted out-of-sync television set. The map is expanding in one direction and contracting in the orthogonal direction.  3, record 7, English, - Arnold%26rsquo%3Bs%20cat%20map

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Dr. Arnold’s math explanations also exhibited playfulness. In one of his books, he explained a simple algorithm that stretches and rearranges an image, shredding it into a chaotic mess. In the book, Dr. Arnold illustrated the idea with a sketch of a cat’s head that is now known as Arnold’s Cat Map.  4, record 7, English, - Arnold%26rsquo%3Bs%20cat%20map

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A word about spelling: we use "Arnold", as opposed to "Arnol’d"; the latter is closer to the Russian pronunciation, but Vladimir Arnold preferred the former (it is used in numerous translations of his books into English) ...  5, record 7, English, - Arnold%26rsquo%3Bs%20cat%20map

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Transformation discontinue inversible caractérisée par une conservation des aires : la contraction d'un facteur 1/2 le long de l'axe vertical est compensée par une dilatation d'un facteur 2 le long de l'axe horizontal.  1, record 7, French, - chat%20d%27Arnold

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La densité de spin sur les atomes de fer (et par différence sur les ligands) peut être déterminée dans des cas simples (spin 1/2). Il existe des modèles plus sophistiqués (hamiltonien de spin) pour les grands spins et les complexes à plusieurs spins.  2, record 8, French, - mod%C3%A8le%20hamiltonien%20de%20spin

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The Traveling Salesman Problem is to find a Hamiltonian cycle of a Hamiltonian graph(where every edge has length) with minimum total length.  1, record 9, English, - traveling%20salesman%20problem

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Le problème du voyageur de commerce est de parcourir un réseau en passant au moins une fois en chaque sommet et en minimisant la distance totale, étant donné que chaque arête a une certaine longueur.  2, record 9, French, - probl%C3%A8me%20du%20commis%20voyageur

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Problema muy conocido en la búsqueda de gráficos. El problema es hallar un ciclo de Hamilton de peso mínimo en un gráfico ponderado.  1, record 9, Spanish, - problema%20del%20agente%20viajero

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We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are negligible and the dressed electron is governed by an effective one-particle Hamiltonian.  2, record 11, English, - dressed%20electron

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Dans la théorie quantique des champs, électron en interaction avec lui-même et entouré d'un nuage de photons virtuels qu'il émet et réabsorbe immédiatement.  2, record 11, French, - %C3%A9lectron%20habill%C3%A9

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Record 12,  Textual support,  English

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Smooth ergodic theory, topological dynamics, Hamiltonian mechanics, and the qualitative theory of ordinary differential equations all developed as disciplines in their own right.  1, record 12, English, - Hamiltonian%20mechanics

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[...] on voit que l'énergie reste constante au cours du mouvement [...] Cette propriété range le pendule dans la classe des systèmes qualifiés de conservatifs (ou hamiltoniens), caractérisés précisément par cette invariance de l'énergie. Les systèmes conservatifs : [...] Le résultat auquel nous venons d'aboutir à propos du pendule simple est de portée beaucoup plus générale. La mécanique classique montre qu'il est en principe possible de décrire le comportement de tout système sans dissipation à l'aide d'une fonction de Hamilton H [...]  2, record 12, French, - m%C3%A9canique%20hamiltonienne

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Record 13,  Textual support,  English

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The energy operator that gives the energy eigenstates and that is a counterpart of the Hamiltonain function in classical mechanics.  2, record 13, English, - Hamiltonian

Record 13,  Textual support,  French

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Pour un système dynamique, opérateur agissant dans un espace hilbertien, qui représente la grandeur énergie.  1, record 13, French, - hamiltonien

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Du nom de W.R. Hamilton (1805-1865), mathématicien et physicien irlandais inventeur des quaternions.  1, record 13, French, - hamiltonien

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hamiltonien d'un mouvement, d'un système.  1, record 13, French, - hamiltonien

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A graph is called Eulerian if there exists a walk that traverses each edge of the graph exactly once, and is called Hamiltonian if there exists a path passing through each vertex only once.  1, record 14, English, - Hamiltonian%20path

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chemin passant une fois et une seule par chaque sommet du graphe.  1, record 14, French, - chemin%20hamiltonien

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Record 15,  Textual support,  English

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Conservation of surface and volume in phase space.  2, record 15, English, - area%20conservation

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The word "area" is generalized in the usual way to the measure of a two-dimensional space. The element of a given area will continue to occupy a surface of the same measure during evolution. This property of Hamiltonian systems is much more restrictive than simple conservation of energy or reversibility of equations of motion. It entails the conservation of volume in phase space.  2, record 15, English, - area%20conservation

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See conservative vs. dissipation system.  3, record 15, English, - area%20conservation

Record 15,  Textual support,  French

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Propriété d'un système dynamique en mouvement, qui lui permet de garder la surface des conditions initiales, mais pas nécessairement la même forme, quel que soit le temps.  2, record 15, French, - conservation%20des%20aires

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La conservation des aires subsiste par renversement du temps.  2, record 15, French, - conservation%20des%20aires

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Record 16,  Textual support,  English

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A property of dissipative systems whose surface given by initial conditions shrinks in time.  3, record 16, English, - area%20contraction

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Clearly any contraction is a continuous mapping. The ratio of the contraction is the infinum value for which the inequality ... holds. A contraction that transforms every subset of an n-dimensional euclidean space into a geometrically similar set is called a similitude.  4, record 16, English, - area%20contraction

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Contrast with area conservation characteristic of Hamiltonian systems. See also dilation and divergence.  3, record 16, English, - area%20contraction

Record 16,  Textual support,  French

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Propriété distinctive d'un système dissipatif dont la surface des conditions initiales diminue en moyenne au cours du temps.  3, record 16, French, - contraction%20des%20aires

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On dit, par exemple, que le flot «contracte» les aires dans l'espace des phases. En modélisation fractale, une image peut être soumise à une contraction isotrope c'est-à-dire, appliquée simultanément dans toutes les directions. Dérivés attestés : contractivité, contractant (adjectif).  3, record 16, French, - contraction%20des%20aires

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contraction des aires anisotrope, isotrope, radiale.  3, record 16, French, - contraction%20des%20aires

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facteur, divergence de contraction des aires.  3, record 16, French, - contraction%20des%20aires

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Record 17,  Textual support,  English

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... the KAM theory defines the conditions of the conservation of invariant tori in a Hamiltonian system affected by a small perturbation. According to one of the key concepts of this theory, the measure of destroyed tori is small and, what is more, small regions containing destroyed tori are clamped between invariant tori.  2, record 17, English, - KAM%20theory

Record 17,  Textual support,  French

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[...] la théorie KAM montre que, pour certaines valeurs des conditions initiales, les mouvements sont quasi périodiques, comme dans le cas intégrable, mais pour d'autres conditions initiales arbitrairement proches, il apparaît des zones d'instabilité (ou zones chaotiques) où la dynamique est beaucoup plus compliquée, et dans lesquelles les méthodes de perturbation ne sont plus du tout applicables.  1, record 17, French, - th%C3%A9orie%20KAM

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Record 18,  Textual support,  French

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Système dynamique caractérisé par l'invariance d'énergie, la réversibilité des équations du mouvement et la conservation des aires et des volumes dans l'espace des phases.  3, record 18, French, - syst%C3%A8me%20conservatif

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Chemin simple qui passe une seule fois par chaque sommet d'un graphe.  1, record 20, French, - circuit%20hamiltonien

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Record 21,  Textual support,  English

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... it is this property of invariance of the Hamiltonian coupled with some properties of the Shrdinger equation....  2, record 21, English, - invariance%20of%20the%20Hamiltonian

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[...] le lien entre les fonctions d'onde d'une molécule et les symétries de la molécule est une conséquence de l'invariance de l'hamiltonien [...]  2, record 21, French, - invariance%20de%20l%27hamiltonien

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