Optimal Packings of Superballs

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|^2p + |x2|^2p + |x3|^2p <= 1) provide a versatile family of convex particles (p >= 0.5) with both cubic- and octahedral-like shapes as well as concave particles (0 < p < 0.5) with octahedral-like shapes. In this paper, we provide analytical constructions for the densest known superball packings for all convex and concave cases. The candidate maximally dense packings are certain families of Bravais lattice packings. The maximal packing density as a function of p is nonanalytic at the sphere-point (p = 1) and increases dramatically as p moves away from unity. The packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two-dimensional "superdisk" counterparts, and are distinctly different from that of ellipsoid packings. Our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems, which should deepen our understanding of the statistical thermodynamics of nonspherical-particle systems.Comment: 28 pages, 16 figure

A gene-derived SNP-based high resolution linkage map of carrot including the location of QTL conditioning root and leaf anthocyanin pigmentation

Purple carrots accumulate large quantities of anthocyanins in their roots and leaves. These flavonoid pigments possess antioxidant activity and are implicated in providing health benefits. Informative, saturated linkage maps associated with well characterized populations segregating for anthocyanin pigmentation have not been developed. To investigate the genetic architecture conditioning anthocyanin pigmentation we scored root color visually, quantified root anthocyanin pigments by high performance liquid chromatography in segregating F2, F3 and F4 generations of a mapping population, mapped quantitative trait loci (QTL) onto a dense gene-derived single nucleotide polymorphism (SNP)-based linkage map, and performed comparative trait mapping with two unrelated populations. Results: Root pigmentation, scored visually as presence or absence of purple coloration, segregated in a pattern consistent with a two gene model in an F2, and progeny testing of F3-F4 families confirmed the proposed genetic model. Purple petiole pigmentation was conditioned by a single dominant gene that co-segregates with one of the genes conditioning root pigmentation. Root total pigment estimate (RTPE) was scored as the percentage of the root with purple color. Conclusions: This study generated the first high resolution gene-derived SNP-based linkage map in the Apiaceae. Two regions of chromosome 3 with co-localized QTL for all anthocyanin pigments and for RTPE, largely condition anthocyanin accumulation in carrot roots and leaves. Loci controlling root and petiole anthocyanin pigmentation differ across diverse carrot genetic backgrounds.Fil: Cavagnaro, Pablo Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. University of Wisconsin; Estados Unidos. Universidad Nacional de Cuyo. Facultad de Ciencias Agrarias; ArgentinaFil: Iorizzo, Massimo. University of Wisconsin; Estados UnidosFil: Yildiz, Mehtap. Yuzuncu Yil University; TurquíaFil: Senalik, Douglas. University of Wisconsin; Estados UnidosFil: Parsons, Joshua. University of Wisconsin; Estados UnidosFil: Ellison, Shelby. University of Wisconsin; Estados UnidosFil: Simon, Philipp W.. University of Wisconsin; Estados Unido

A classification of separable Rosenthal compacta and its applications

The present work consists of three parts. In the first one we determine the prototypes of separable Rosenthal compacta and we provide a classification theorem. The second part concerns an extension of a theorem of S. Todorcevic. The last one is devoted to applications.Comment: 55 pages, no figure