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Twinning in Intermetallic Compounds Are Long Shear Vectors and/or shuffles Really Necessary?

Journal of Materials Science & Technology 1993年第5期9卷 313-321页

作者： F.M.Chu David P.Pope Dept.of Materials Science and Engineering,University of Pennsylvania,Philadelphia,PA 19104,USA

In this paper the geometric description and general theory of mechanical twinning are reviewed, the twins in general lattices and superlattices are summarized, and the kinetic process by which mechanical twins form is revisited. A case study of mechanical twinning of HfV2+Nb, (cubic) Laves phase, is presented and the synchroshear of selected atomic layers is proposed to explain the physical process of twin formation. If the twins form in this way, then long shear vectors and / or atomicshuffles are not really necessary.

关键词： twin intermetallic compounds shear vector shuffles

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Progressive Randomization of a Deck of Playing Cards: Experimental Tests and Statistical Analysis of the Riffle Shuffle

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Open Journal of Statistics 2019年第2期9卷 268-298页

作者： M. P. Silverman Department of Physics Trinity College Hartford CT USA

The question of how many shuffles are required to randomize an initially ordered deck of cards is a problem that has fascinated mathematicians, scientists, and the general public. The two principal theoretical approaches to the problem, which differed in how each defined randomness, has led to statistically different threshold numbers of shuffles. This paper reports a comprehensive experimental analysis of the card randomization problem for the purposes of determining 1) which of the two theoretical approaches made the more accurate prediction, 2) whether different statistical tests yield different threshold numbers of randomizing shuffles, and 3) whether manual or mechanical shuffling randomizes a deck more effectively for a given number of shuffles. Permutations of 52-card decks, each subjected to sets of 19 successive riffle shuffles executed manually and by an auto-shuffling device were recorded sequentially and analyzed in respect to 1) the theory of runs, 2) rank ordering, 3) serial correlation, 4) theory of rising sequences, and 5) entropy and information theory. Among the outcomes, it was found that: 1) different statistical tests were sensitive to different patterns indicative of residual order;2) as a consequence, the threshold number of randomizing shuffles could vary widely among tests;3) in general, manual shuffling randomized a deck better than mechanical shuffling for a given number of shuffles;and 4) the mean number of rising sequences as a function of number of manual shuffles matched very closely the theoretical predictions based on the Gilbert-Shannon-Reed (GSR) model of riffle shuffles, whereas mechanical shuffling resulted in significantly fewer rising sequences than predicted.

关键词： Randomization of Cards Number of Riffle shuffles Rising Sequences GSR Model Entropy and Information

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