Toward the Jamming Threshold of Sphere Packings: Tunneled Crystals

We have discovered a new family of three-dimensional crystal sphere packings that are strictly jammed (i.e., mechanically stable) and yet possess an anomalously low density. This family constitutes an uncountably infinite number of crystal packings that are subpackings of the densest crystal packings and are characterized by a high concentration of self-avoiding "tunnels" (chains of vacancies) that permeate the structures. The fundamental geometric characteristics of these tunneled crystals command interest in their own right and are described here in some detail. These include the lattice vectors (that specify the packing configurations), coordination structure, Voronoi cells, and density fluctuations. The tunneled crystals are not only candidate structures for achieving the jamming threshold (lowest-density rigid packing), but may have substantially broader significance for condensed matter physics and materials science.Comment: 19 pages, 5 figure

Probing the pc- and kpc-scale environment of the powerful radio galaxy Hercules A

We present the kpc-scale behaviour of the powerful extragalactic radio source Hercules A and the behaviour of the intracluster gas in which the radio source is situated. We have found that Hercules A exhibits a strong Laing-Garrington effect. The X-ray observations have revealed an extended X-ray emission elongated along the radio galaxy axis. The estimated temperature of the cluster is kT = 2.45 keV and the central electron density is no~7.8 x 10^(-3) cm^(-3) which reveals a hot, dense environment in which Hercules A is situated. From the combined study of the radio and X-ray data we have estimated a central value of 3<Bo (muG)<9. We also present the most recent results from the analysis of the radio data on the pc-scale structure of the radio galaxy, observed at 18 cm by the EVN-MERLIN array. A faint but compact radio source, coincident with the optical centre of Hercules A was detected by the EVN at 18 mas resolution. The total flux density of the EVN core is 14.6 mJy. Its angular size is 18 x 7 mas with a position angle of ~139 degrees. There is also evidence for extended emission in the NW-SE direction, most probably from the eastern pc-scale jet. If this is true then there is a misalignment between the direction of the pc-eastern and the aligned kpc-scale jets of ~35 degrees.Comment: 7 pages, 2 figures, Submitted to PAS

Fluid/solid transition in a hard-core system

We prove that a system of particles in the plane, interacting only with a certain hard-core constraint, undergoes a fluid/solid phase transition

Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in $d$-dimensional Euclidean space $\mathbb{R}^d$, it is most suitable and natural to solve the corresponding ASC optimization problem using sequential linear programming (SLP) techniques. We implement an SLP solution to produce robustly a wide spectrum of jammed sphere packings in $\mathbb{R}^d$ for $d=2,3,4,5$ and $6$ with a diversity of disorder and densities up to the maximally densities. This deterministic algorithm can produce a broad range of inherent structures besides the usual disordered ones with very small computational cost by tuning the radius of the {\it influence sphere}. In three dimensions, we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range $[0.6, 0.7408...]$. We also apply the algorithm to generate various disordered packings as well as the maximally dense packings for $d=2,3, 4,5$ and 6. Compared to the LS procedure, our SLP protocol is able to ensure that the final packings are truly jammed, produces disordered jammed packings with anomalously low densities, and is appreciably more robust and computationally faster at generating maximally dense packings, especially as the space dimension increases.Comment: 34 pages, 6 figure

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

Achieving Good Angular Resolution in 3D Arc Diagrams

We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to a given 2D straight-line drawing of the input graph. Our methods make use of various graph coloring algorithms, including an algorithm for a new coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on Graph Drawing (GD 2013

Gene expression profiling of oxidative stress response of C. elegans aging defective AMPK mutants using massively parallel transcriptome sequencing

<p>Abstract</p> <p>Background</p> <p>A strong association between stress resistance and longevity in multicellular organisms has been established as many mutations that extend lifespan also show increased resistance to stress. AAK-2, the <it>C. elegans </it>homolog of an alpha subunit of AMP-activated protein kinase (AMPK) is an intracellular fuel sensor that regulates cellular energy homeostasis and functions in stress resistance and lifespan extension.</p> <p>Findings</p> <p>Here, we investigated global transcriptional responses of <it>aak-2 </it>mutants to oxidative stress and in turn identified potential downstream targets of AAK-2 involved in stress resistance in <it>C. elegans</it>. We employed massively parallel Illumina sequencing technology and performed comprehensive comparative transcriptome analysis. Specifically, we compared the transcriptomes of <it>aak-2 </it>and wild type animals under normal conditions and conditions of induced oxidative stress. This research has presented a snapshot of genome-wide transcriptional activities that take place in <it>C. elegans </it>in response to oxidative stress both in the presence and absence of AAK-2.</p> <p>Conclusions</p> <p>The analysis presented in this study has enabled us to identify potential genes involved in stress resistance that may be either directly or indirectly under the control of AAK-2. Furthermore, we have extended our current knowledge of general defense responses of <it>C. elegans </it>against oxidative stress supporting the function for AAK-2 in inhibition of biosynthetic processes, especially lipid synthesis, under oxidative stress and transcriptional regulation of genes involved in reproductive processes.</p

Images of an equatorial outflow in SS433

We have imaged the X-ray binary SS433 with unprecedented Fourier-plane coverage at 6cm using simultaneously the VLBA, MERLIN, and the VLA, and also at 20cm with the VLBA. At both wavelengths we have securely detected smooth, low-surface brightness emission having the appearance of a `ruff' or collar attached perpendicularly to the well-studied knotty jets in this system, extending over at least a few hundred AU. We interpret this smooth emission as a wind-like outflow from the binary, and discuss its implications for the present evolutionary stage of this system.Comment: Accepted by ApJ Letter