Distribution of volumes and coordination number in jammed matter: mesoscopic ensemble

We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an exponential distribution of the orientational volumes for random close packings and random loose packings. A comparison with computer generated packings reveals deviations from the theoretical prediction in the volume distribution, which can be better modeled by a compressed exponential function. On the other hand, the average of the volumes is well reproduced by the theory leading to good predictions of the limiting densities of RCP and RLP. We discuss a more exact theory to capture the volume distribution in its entire range. The available data suggests a plausible order/disorder transition defining random close packings. Finally, we consider an extended ensemble to calculate the coordination number distribution which is shown to be of an exponential and inverse exponential form for coordinations larger and smaller than the average, respectively, in reasonable agreement with the simulated data.Comment: 20 pages, 6 figures, accepted by JSTA

LTR retrotransposon landscape in Medicago truncatula: more rapid removal than in rice

<p>Abstract</p> <p>Background</p> <p>Long terminal repeat retrotransposons (LTR elements) are ubiquitous Eukaryotic TEs that transpose through RNA intermediates. Accounting for significant proportion of many plant genomes, LTR elements have been well established as one of the major forces underlying the evolution of plant genome size, structure and function. The accessibility of more than 40% of genomic sequences of the model legume <it>Medicago truncatula </it>(<it>Mt</it>) has made the comprehensive study of its LTR elements possible.</p> <p>Results</p> <p>We use a newly developed tool LTR_FINDER to identify LTR retrotransposons in the <it>Mt </it>genome and detect 526 full-length elements as well as a great number of copies related to them. These elements constitute about 9.6% of currently available genomic sequences. They are classified into 85 families of which 64 are reported for the first time. The majority of the LTR retrotransposons belong to either Copia or Gypsy superfamily and the others are categorized as TRIMs or LARDs by their length. We find that the copy-number of Copia-like families is 3 times more than that of Gypsy-like ones but the latter contribute more to the genome. The analysis of PBS and protein-coding domain structure of the LTR families reveals that they tend to use only 4–5 types of tRNAs and many families have quite conservative ORFs besides known TE domains. For several important families, we describe in detail their abundance, conservation, insertion time and structure. We investigate the amplification-deletion pattern of the elements and find that the detectable full-length elements are relatively young and most of them were inserted within the last 0.52 MY. We also estimate that more than ten million bp of the <it>Mt </it>genomic sequences have been removed by the deletion of LTR elements and the removal of the full-length structures in <it>Mt </it>has been more rapid than in rice.</p> <p>Conclusion</p> <p>This report is the first comprehensive description and analysis of LTR retrotransposons in the <it>Mt </it>genome. Many important novel LTR families were discovered and their evolution is elucidated. Our results may outline the LTR retrotransposon landscape of the model legume.</p