Experimental and theoretical porosity profiles in a two-dimensional gas-fluidized bed with a central jet

A light transmission technique has been developed for measurement of the local porosity in two-dimensional gas-fluidized beds. The principles of liquid-solid fluidization and vibrofluidization were employed to perform the necessary calibration. Time-averaged porosity profiles have been measured in a thin two-dimensional gas-fluidized bed with a central rectangular jet. These profiles were predicted satisfactorily with a previously developed first principles hydrodynamic model, without the use of any fitted parameters. The hydrodynamic model is based on a two-fluid model approach in which both phases are considered to be continuous and fully interpenetratin

Densest local packing diversity. II. Application to three dimensions

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N = 348. We analyze the properties and characteristics of the densest local packings in R3 and employ knowledge of the Rmin(N), using methods applicable in any d, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In R3, we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of N spheres near a central sphere to minimal-energy configurations of N+1 points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12-6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in R3 (the Barlow packings) and find that the densest local packings are almost always most similar, as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the FCC Barlow packing. We additionally observe that the densest local packings are dominated by the spheres arranged with centers at precisely distance Rmin(N) from the fixed sphere's center.Comment: 45 pages, 18 figures, 2 table

Distribution of P1(D1) wart disease resistance in potato germplasm and GWAS identification of haplotype-specific SNP markers

Key message: A Genome-Wide Association Study using 330 commercial potato varieties identified haplotype specific SNPmarkers associated with pathotype 1(D1) wart disease resistance. Abstract: Synchytrium endobioticum is a soilborne obligate biotrophic fungus responsible for wart disease. Growing resistant varieties is the most effective way to manage the disease. This paper addresses the challenge to apply molecular markers in potato breeding. Although markers linked to Sen1 were published before, the identification of haplotype-specific single-nucleotide polymorphisms may result in marker assays with high diagnostic value. To identify hs-SNP markers, we performed a genome-wide association study (GWAS) in a panel of 330 potato varieties representative of the commercial potato gene pool. SNP markers significantly associated with pathotype 1 resistance were identified on chromosome 11, at the position of the previously identified Sen1 locus. Haplotype specificity of the SNP markers was examined through the analysis of false positives and false negatives and validated in two independent full-sib populations. This paper illustrates why it is not always feasible to design markers without false positives and false negatives for marker-assisted selection. In the case of Sen1, founders could not be traced because of a lack of identity by descent and because of the decay of linkage disequilibrium between Sen1 and flanking SNP markers. Sen1 appeared to be the main source of pathotype 1 resistance in potato varieties, but it does not explain all the resistance observed. Recombination and introgression breeding may have introduced new, albeit rare haplotypes involved in pathotype 1 resistance. The GWAS approach, in such case, is instrumental to identify SNPs with the best possible diagnostic value for marker-assisted breeding.</p

The strong thirteen spheres problem

The thirteen spheres problem is asking if 13 equal size nonoverlapping spheres in three dimensions can touch another sphere of the same size. This problem was the subject of the famous discussion between Isaac Newton and David Gregory in 1694. The problem was solved by Schutte and van der Waerden only in 1953. A natural extension of this problem is the strong thirteen spheres problem (or the Tammes problem for 13 points) which asks to find an arrangement and the maximum radius of 13 equal size nonoverlapping spheres touching the unit sphere. In the paper we give a solution of this long-standing open problem in geometry. Our computer-assisted proof is based on a enumeration of the so-called irreducible graphs.Comment: Modified lemma 2, 16 pages, 12 figures. Uploaded program packag

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference

Basic Understanding of Condensed Phases of Matter via Packing Models

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298