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

Nonclassical rotational inertia for a supersolid under rotation

As proposed by Leggett [4], the supersolidity of a crystal is characterized by the Non Classical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau and Rica [5], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the inertia momentum. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity

Quaternions, octonions and Bell-type inequalities

Multipartite Bell-type inequalities are derived for general systems. They involve up to eight observables with arbitrary spectra on each site. These inequalities are closely related to the algebras of quaternions and octonions.Comment: 4 pages, no figure

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

Euler angles for G2

We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.Comment: 21 pages, 2 figures, some misprints correcte

Preliminary design and cost of a 1-megawatt solar-pumped iodide laser space-to-space transmission station

A preliminary conceptual design of a space-based solar pumped iodide laser emitting 1 megawatt of laser power for space-to-space power transmission is described. A near parabolic solar collector focuses sunlight onto the t-C4F9I (perfluoro-t butyl iodide) lasant within a transverse flow optical cavity. Using waste heat, a thermal system was designed to supply compressor and auxiliary power. System components were designed with weight and cost estimates assigned. Although cost is very approximate, the cost comparison of individual system components leads to valuable insights for future research. In particular, it was found that laser efficiency was not a dominant cost or weight factor, the dominant factor being the laser cavity and laser transmission optics. The manufacturing cost was approx. two thirds of the total cost with transportation to orbit the remainder. The flowing nonrenewable lasant comprised 20% of the total life cycle cost of the system and thus was not a major cost factor. The station mass was 92,000 kg without lasant, requiring approx. four shuttle flights to low Earth orbit where an orbital transfer vehicle will transport it to the final altitude of 6378 km

On the Response of an OST to a Point-like Heat Source

A new technique of superconducting cavity diagnostics has been introduced by D. Hartrill at Cornell University, Ithaca, USA. Oscillating Superleak Transducers (OST) detect the heat transferred from a cavity's quench point via "Second Sound" through the superfluid He bath, needed to cool the superconducting cavity. The observed response of an OST is a complex, but reproducible pattern of oscillations. A small helium evaporation cryostat was built which allows the investigation of the response of an OST in greater detail. The distance between a point-like electrical heater and the OST can be varied. The OST can be mounted either parallel or perpendicular to the plate, housing the heat source. If the artificial quench-point releases an amount of energy compatible to a real quench spot on a cavity's surface, the OST signal starts with a negative pulse, which is usually strong enough to allow automatic detection. Furthermore, the reflection of the Second Sound on the wall is observed. A reflection coefficient R = 0.39 +- 0.05 of the glass wall is measured. This excludes a strong influence of multiple reflections in the complex OST response. Fourier analyses show three main frequencies, found in all OST spectra. They can be interpreted as modes of an oscillating circular membrane.Comment: 10 pages, 16 figure

Does the Swedish Interactive Threshold Algorithm (SITA) accurately map visual field loss attributed to vigabatrin?

Purpose Vigabatrin (VGB) is an anti-epileptic medication which has been linked to peripheral constriction of the visual field. Documenting the natural history associated with continued VGB exposure is important when making decisions about the risk and benefits associated with the treatment. Due to its speed the Swedish Interactive Threshold Algorithm (SITA) has become the algorithm of choice when carrying out Full Threshold automated static perimetry. SITA uses prior distributions of normal and glaucomatous visual field behaviour to estimate threshold sensitivity. As the abnormal model is based on glaucomatous behaviour this algorithm has not been validated for VGB recipients. We aim to assess the clinical utility of the SITA algorithm for accurately mapping VGB attributed field loss. Methods The sample comprised one randomly selected eye of 16 patients diagnosed with epilepsy, exposed to VGB therapy. A clinical diagnosis of VGB attributed visual field loss was documented in 44% of the group. The mean age was 39.3 years ± 14.5 years and the mean deviation was -4.76 dB ±4.34 dB. Each patient was examined with the Full Threshold, SITA Standard and SITA Fast algorithm. Results SITA Standard was on average approximately twice as fast (7.6 minutes) and SITA Fast approximately 3 times as fast (4.7 minutes) as examinations completed using the Full Threshold algorithm (15.8 minutes). In the clinical environment, the visual field outcome with both SITA algorithms was equivalent to visual field examination using the Full Threshold algorithm in terms of visual inspection of the grey scale plots , defect area and defect severity. Conclusions Our research shows that both SITA algorithms are able to accurately map visual field loss attributed to VGB. As patients diagnosed with epilepsy are often vulnerable to fatigue, the time saving offered by SITA Fast means that this algorithm has a significant advantage for use with VGB recipients

The Mathieu group M-12 and its pseudogroup extension M-13

We study a construction of the Mathieu group M-12 using a game reminiscent of Loyd's "15-puzzle." The elements of M-12 are realized as permutations on 12 of the 13 points of the finite projective plane of order 3. There is a natural extension to a "pseudogroup" M-13 acting on all 13 points, which exhibits a limited form of sextuple transitivity. Another corollary of the construction is a metric, akin to that induced by a Cayley graph, on both M-12 and M-13. We develop these results, and extend them to the double covers and automorphism groups of M-12 and M-13, using the ternary Golay code and 12 x 12 Hadamard matrices. In addition, we use experimental data on the quasi-Cayley metric to gain some insight into the structure of these groups and pseudogroups.Mathematic