39 research outputs found

    Random Convex Hulls and Extreme Value Statistics

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    In this paper we study the statistical properties of convex hulls of NN random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of nn independent random walks. In the continuum time limit this reduces to nn independent planar Brownian trajectories for which we compute exactly, for all nn, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

    Magnetic Properties

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    The necessity of obtaining accurate thermodynamic quantities for the actinideelements and their compounds was recognized at the outset of the Manhattan Project, when a dedicated team of scientists and engineers initiated the program to exploit nuclear energy for military purposes. Since the end of World War II, both fundamental and applied objectives have motivated a great deal of further study of actinide thermodynamics. This chapter brings together many research papers and critical reviews on this subject. It also seeks to assess, to systematize, and to predict important properties of the actinide elements, ions, and compounds, especially for species in which there is significant interest and for which there is an experimental basis for the prediction. Many experimental and theoretical studies of thermochemical and thermophysical properties of thorium, uranium, and plutonium species were undertaken by Manhattan Project investigators. To find more information please see the attachment.JRC.E.6-Actinides researc
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