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Percolation theory Teoria da percolação em redes نظرية التخلل 渗流理论 Teoria della percolazione Теорія протікання Perkolationstheorie Teoría de la percolación Théorie de la percolation Теория перколяции
rdfs:comment
渗流理论(英語:Percolation theory)是数学和统计物理领域中研究随机图上簇的性质的一套理论。举例来说,假设有一多孔材料,求问液体能否从顶端贯穿该材料直至到达底部。渗流理论将此抽象成以下数学问题:建立一有n × n × n个顶点的三维网格模型,相邻顶点的边有p的概率是连接的,或者说有(1-p)的概率是不连接的,每条边连接与否相互独立。渗流理论的基本问题是,当n很大以至于体系可以近似为无限网格时,求问至少存在一条贯穿整个网格的路径(称为渗流)对应的p的范围。这一p的下界,pc,称为。该问题由布罗德本特和汉默斯利于1957年提出,其后相关问题被广泛研究。 上述问题称为边渗流或键渗流(英語:Bond percolation),是渗流理论两种主要的渗流形式之一。另外一种是点渗流(英語:Site percolation),与边渗流不同的是,每个顶点有p的概率是“占有”的;相应有(1-p)的概率是“空缺”的,如果相邻两个顶点皆属于占有则它们之间是连接的。而问题相同:求给定p值时,整个图是否渗流。 Теорія протікання або теорія перколяції (англ. percolation theory) — математична теорія, яка описує властивості зв'язаних кластерів на випадковому графі. Теорія знайшла застосування в описі явища перколяції в статистичній фізиці та матеріалознавстві. في الرياضيات، تصف نظرية التخلل أو نظرية التطعيم (بالإنجليزية: Percolation theory)‏ سلوك العقد المتصلة في عشوائي. تشمل تطبيقات هذه النظرية بشكل أساسي مجال علوم المواد الهندسية (طالع تخلل) وبالإضافة إلى مجالات أخرى تتعلق بالترشيح. و ترتبط هذه النظرية بالنظرية الكسيرية. In fisica statistica e matematica, la teoria della percolazione descrive il comportamento di una rete quando vengono rimossi nodi o collegamenti. Questo è un caso di transizione di fase geometrica, poiché per valore critico della frazione rimossa la rete si rompe in cluster connessi significativamente più piccoli. Tale teoria è nata nel tentativo di descrivere matematicamente il fenomeno chimico-fisico della percolazione. Em física estatística e matemática, a teoria de percolação descreve o comportamento de uma rede quando nós ou links são removidos. Este é um tipo geométrico de transição de fase, pois em uma fração crítica de remoção a rede se divide em clusters conectados significativamente menores. As aplicações da teoria da percolação à ciência dos materiais e em muitas outras disciplinas são discutidas aqui e nos artigos de teoria de redes e percolação. En física estadística y matemáticas, la teoría de la percolación describe el comportamiento de una red cuando se agregan nodos o enlaces. Este es un tipo geométrico de transición de fase, ya que en una fracción crítica de la adición, la red de grupos pequeños desconectados se fusiona formando una estructura conectada significativamente más grande, el llamado grupo de expansión. Las aplicaciones de la teoría de la percolación a la ciencia de materiales y en muchas otras disciplinas se discuten aquí y en los artículos dedicados al análisis de redes y a la percolación. La théorie de la percolation est une branche de la physique statistique et mathématique qui s'intéresse aux caractéristiques des milieux aléatoires, plus précisément aux ensembles de sommets connectés dans un graphe aléatoire. Cette théorie s'applique notamment en science des matériaux pour formaliser les propriétés d'écoulement dans les milieux poreux et pour la modélisation de phénomènes naturels, comme les incendies. Теория перколяции (теория протекания или теория просачивания) — математическая теория, используемая в физике, химии и других областях для описания возникновения связных структур в случайных средах (кластеров), состоящих из отдельных элементов. Die Perkolationstheorie (lat. percolare – durchsickern) ist ein Teilgebiet der Stochastik und der statistischen Physik und beschreibt das Ausbilden zusammenhängender Gebiete (Cluster) bei zufallsbedingtem Besetzen von Strukturen (Gittern). Unterarten sind die Punktperkolation, bei der Gitterpunkte mit einer bestimmten Wahrscheinlichkeit besetzt werden, und die Kantenperkolation, bei der besetzte Punkte untereinander verbunden werden. Man kann sich beliebige zufällig erzeugte Objekte, z. B. Tröpfchen, vorstellen, die untersucht werden. In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation.
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Em física estatística e matemática, a teoria de percolação descreve o comportamento de uma rede quando nós ou links são removidos. Este é um tipo geométrico de transição de fase, pois em uma fração crítica de remoção a rede se divide em clusters conectados significativamente menores. As aplicações da teoria da percolação à ciência dos materiais e em muitas outras disciplinas são discutidas aqui e nos artigos de teoria de redes e percolação. Теория перколяции (теория протекания или теория просачивания) — математическая теория, используемая в физике, химии и других областях для описания возникновения связных структур в случайных средах (кластеров), состоящих из отдельных элементов. Простейшие задачи теории перколяции формулируются для дискретных решеток. Задаётся вероятность (концентрация) , с которой узел решетки будет занятым. Соответственно, вероятность того, что узел будет свободным, равна . В простейшем случае все узлы считаются независимыми, то есть занятость одного узла не влияет на занятость других. Два узла считаются принадлежащими к одному кластеру, если их можно соединить непрерывной цепочкой соседних занятых узлов. При увеличении значения параметра всё большее количество узлов будет занято, и, как следствие, будут появляться кластеры всё большего размера. При некотором критическом значении в системе образуется стягивающий (перколяционный) кластер, соединяющий один конец системы с другим — произойдет критический переход, аналогичный фазовому переходу второго рода. Описанная постановка задачи соответствует так называемой задаче узлов. Можно сформулировать и другую задачу, в которой с вероятностью будут заняты не сами узлы, а связи между — задача связей. Подобный подход позволяет использовать аппарат теории перколяции во множестве областей, например, при описании пористых материалов, проводимости, полимеризации, биологической эволюции, формирования галактик и множества других. La théorie de la percolation est une branche de la physique statistique et mathématique qui s'intéresse aux caractéristiques des milieux aléatoires, plus précisément aux ensembles de sommets connectés dans un graphe aléatoire. Cette théorie s'applique notamment en science des matériaux pour formaliser les propriétés d'écoulement dans les milieux poreux et pour la modélisation de phénomènes naturels, comme les incendies. 渗流理论(英語:Percolation theory)是数学和统计物理领域中研究随机图上簇的性质的一套理论。举例来说,假设有一多孔材料,求问液体能否从顶端贯穿该材料直至到达底部。渗流理论将此抽象成以下数学问题:建立一有n × n × n个顶点的三维网格模型,相邻顶点的边有p的概率是连接的,或者说有(1-p)的概率是不连接的,每条边连接与否相互独立。渗流理论的基本问题是,当n很大以至于体系可以近似为无限网格时,求问至少存在一条贯穿整个网格的路径(称为渗流)对应的p的范围。这一p的下界,pc,称为。该问题由布罗德本特和汉默斯利于1957年提出,其后相关问题被广泛研究。 上述问题称为边渗流或键渗流(英語:Bond percolation),是渗流理论两种主要的渗流形式之一。另外一种是点渗流(英語:Site percolation),与边渗流不同的是,每个顶点有p的概率是“占有”的;相应有(1-p)的概率是“空缺”的,如果相邻两个顶点皆属于占有则它们之间是连接的。而问题相同:求给定p值时,整个图是否渗流。 Теорія протікання або теорія перколяції (англ. percolation theory) — математична теорія, яка описує властивості зв'язаних кластерів на випадковому графі. Теорія знайшла застосування в описі явища перколяції в статистичній фізиці та матеріалознавстві. في الرياضيات، تصف نظرية التخلل أو نظرية التطعيم (بالإنجليزية: Percolation theory)‏ سلوك العقد المتصلة في عشوائي. تشمل تطبيقات هذه النظرية بشكل أساسي مجال علوم المواد الهندسية (طالع تخلل) وبالإضافة إلى مجالات أخرى تتعلق بالترشيح. و ترتبط هذه النظرية بالنظرية الكسيرية. En física estadística y matemáticas, la teoría de la percolación describe el comportamiento de una red cuando se agregan nodos o enlaces. Este es un tipo geométrico de transición de fase, ya que en una fracción crítica de la adición, la red de grupos pequeños desconectados se fusiona formando una estructura conectada significativamente más grande, el llamado grupo de expansión. Las aplicaciones de la teoría de la percolación a la ciencia de materiales y en muchas otras disciplinas se discuten aquí y en los artículos dedicados al análisis de redes y a la percolación. In fisica statistica e matematica, la teoria della percolazione descrive il comportamento di una rete quando vengono rimossi nodi o collegamenti. Questo è un caso di transizione di fase geometrica, poiché per valore critico della frazione rimossa la rete si rompe in cluster connessi significativamente più piccoli. Tale teoria è nata nel tentativo di descrivere matematicamente il fenomeno chimico-fisico della percolazione. In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters. The applications of percolation theory to materials science and in many other disciplines are discussed here and in the articles network theory and percolation. Die Perkolationstheorie (lat. percolare – durchsickern) ist ein Teilgebiet der Stochastik und der statistischen Physik und beschreibt das Ausbilden zusammenhängender Gebiete (Cluster) bei zufallsbedingtem Besetzen von Strukturen (Gittern). Die Perkolationstheorie eignet sich zur Modellierung von physikalischer Phänomenen, die bei Phasenübergängen entstehen. Des Weiteren eignet sie sich zur Beschreibung der elektrischen Leitfähigkeit von Legierungen, der Ausbreitung von Epidemien und Waldbränden, sowie zur Beschreibung von Wachstumsmodelle. In der Geologie und Hydrologie beschreibt die Perkolation einfache Modelle zur Ausbreitung von Flüssigkeiten in porösem Gestein (siehe Perkolation (Technik)), die als anschauliche Beispiele der unten beschriebenen Clusterbildung dienen. Unterarten sind die Punktperkolation, bei der Gitterpunkte mit einer bestimmten Wahrscheinlichkeit besetzt werden, und die Kantenperkolation, bei der besetzte Punkte untereinander verbunden werden. Man kann sich beliebige zufällig erzeugte Objekte, z. B. Tröpfchen, vorstellen, die untersucht werden.
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