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- W2033071092 abstract "By extending the theory of Kurtz and Carpay, a detailed statistical theory of normal grain growth has been developed. The theory utilizes their concept of multiple distributions, i.e. the division of grains into topological classes (14 planar, 34 spatial) but unlike their treatment it does not require the individual distributions of each class to be lognormal. An alternate multiple distribution of grain sizes, where the grains are classified according to a given value of size, rather than a given value of sides, or faces is also proposed. The overall distributions (both in grain shapes and sizes) are then obtained by summing the individual distributions, and are shown to be approximately lognormal. Alternate origins of lognormality are also discussed. A partir de la théorie de Kurtz et Carpay, nous avons développé une théorie statistique complète de la croissance normale du grain. Notre théorie utilise leur concept de distributions multiples, c'est-à-dire le classement des grains en modes topologiques (14 modes plans et 34 modes spatiaux), mais au contraire de leur traitement, il n'est pas nécessaire que les distributions individuelles de chaque mode soient lognormales. Nous proposons également une autre distribution multiple des tailles de grain, dans laquelle nous classons les grains en fonction d'une valeur donnée de la taille plutôt que d'une valeur donnée des côtés ou des faces. Nous obtenons alors les distributions globales (à la fois en forme et en taille de grain) en additionnant les distributions individuelles; elles sont en première approximation lognormales. Nous discutons d'autres causes pour la répartition lognormale. Eine ausführliche statisticche Theorie des normalen Kornwachstums wird entwickelt, indem die Theorie von Kurtz und Carpay erweitert wird. Die Theorie benutzt deren Konzept der multiplen Verteilungen, d.h. der Aufteilung der Körner in topologische Klassen (14 planare, 34 räumliche); im Gegensatz zu deren Behandlung erfordert die vorgelegte Theorie nicht, daß die individuellen Verteilungen lognormal (= Gaußverteilung des Logarithmus der Kenngröße) sind. Eine andere multiple Verteilung der Korngrößen, in der die Körner nach einem vorgegebenen Wert der Größe statt der Seiten oder Flächen klassifiziert werden, wird auch vorgeschlagen. Die Gesamtverteilungen (von Kornform und -größen) werden danach erhalten, indem die individuellen Verteilungen aufsummiert werden; es wird gezeigt, daß diese etwa lognormal sind. Andere Ursachen für Lognormalität werden auch diskutiert." @default.
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- W2033071092 date "1988-08-01" @default.
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- W2033071092 title "A statistical theory of grain growth" @default.
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