9,116 research outputs found
On the Red-Green-Blue Model
We experimentally study the red-green-blue model, which is a sytem of loops
obtained by superimposing three dimer coverings on offset hexagonal lattices.
We find that when the boundary conditions are ``flat'', the red-green-blue
loops are closely related to SLE_4 and double-dimer loops, which are the loops
formed by superimposing two dimer coverings of the cartesian lattice. But we
also find that the red-green-blue loops are more tightly nested than the
double-dimer loops. We also investigate the 2D minimum spanning tree, and find
that it is not conformally invariant.Comment: 4 pages, 7 figure
Ground states and formal duality relations in the Gaussian core model
We study dimensional trends in ground states for soft-matter systems.
Specifically, using a high-dimensional version of Parrinello-Rahman dynamics,
we investigate the behavior of the Gaussian core model in up to eight
dimensions. The results include unexpected geometric structures, with
surprising anisotropy as well as formal duality relations. These duality
relations suggest that the Gaussian core model possesses unexplored symmetries,
and they have implications for a broad range of soft-core potentials.Comment: 7 pages, 1 figure, appeared in Physical Review E (http://pre.aps.org
Factorizations of Elements in Noncommutative Rings: A Survey
We survey results on factorizations of non zero-divisors into atoms
(irreducible elements) in noncommutative rings. The point of view in this
survey is motivated by the commutative theory of non-unique factorizations.
Topics covered include unique factorization up to order and similarity, 2-firs,
and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and
Jordan and generalizations thereof. We recall arithmetical invariants for the
study of non-unique factorizations, and give transfer results for arithmetical
invariants in matrix rings, rings of triangular matrices, and classical maximal
orders as well as classical hereditary orders in central simple algebras over
global fields.Comment: 50 pages, comments welcom
Spherical codes, maximal local packing density, and the golden ratio
The densest local packing (DLP) problem in d-dimensional Euclidean space Rd
involves the placement of N nonoverlapping spheres of unit diameter near an
additional fixed unit-diameter sphere such that the greatest distance from the
center of the fixed sphere to the centers of any of the N surrounding spheres
is minimized. Solutions to the DLP problem are relevant to the realizability of
pair correlation functions for packings of nonoverlapping spheres and might
prove useful in improving upon the best known upper bounds on the maximum
packing fraction of sphere packings in dimensions greater than three. The
optimal spherical code problem in Rd involves the placement of the centers of N
nonoverlapping spheres of unit diameter onto the surface of a sphere of radius
R such that R is minimized. It is proved that in any dimension, all solutions
between unity and the golden ratio to the optimal spherical code problem for N
spheres are also solutions to the corresponding DLP problem. It follows that
for any packing of nonoverlapping spheres of unit diameter, a spherical region
of radius less than or equal to the golden ratio centered on an arbitrary
sphere center cannot enclose a number of sphere centers greater than one more
than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of
Mathematical Physic
Dimers on two-dimensional lattices
We consider close-packed dimers, or perfect matchings, on two-dimensional
regular lattices. We review known results and derive new expressions for the
free energy, entropy, and the molecular freedom of dimers for a number of
lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6),
kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its
dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase
transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43
A Factorization Algorithm for G-Algebras and Applications
It has been recently discovered by Bell, Heinle and Levandovskyy that a large
class of algebras, including the ubiquitous -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -algebra, with minor assumptions on the underlying field.
Moreover, the property of being an FFD, in combination with the factorization
algorithm, enables us to propose an analogous description of the factorized
Gr\"obner basis algorithm for -algebras. This algorithm is useful for
various applications, e.g. in analysis of solution spaces of systems of linear
partial functional equations with polynomial coefficients, coming from
. Additionally, it is possible to include inequality constraints
for ideals in the input
Nucleotide sequence of the luxA gene of Vibrio harveyi and the complete amino acid sequence of the alpha subunit of bacterial luciferase
The nucleotide sequence of the 1.85-kilobase EcoRI fragment from Vibrio harveyi that was cloned using a mixed-sequence synthetic oligonucleotide probe (Cohn, D. H., Ogden, R. C., Abelson, J. N., Baldwin, T. O., Nealson, K. H., Simon, M. I., and Mileham, A. J. (1983) Proc. Natl. Acad. Sci. U.S.A. 80, 120-123) has been determined. The alpha subunit-coding region (luxA) was found to begin at base number 707 and end at base number 1771. The alpha subunit has a calculated molecular weight of 40,108 and comprises a total of 355 amino acid residues. There are 34 base pairs separating the start of the alpha subunit structural gene and a 669-base open reading frame extending from the proximal EcoRI site. At the 3' end of the luxA coding region there are 26 bases between the end of the structural gene and the start of the luxB structural gene. Approximately two-thirds of the alpha subunit was sequenced by protein chemical techniques. The amino acid sequence implied by the DNA sequence, with few exceptions, confirmed the chemically determined sequence. Regions of the alpha subunit thought to comprise the active center were found to reside in two discrete and relatively basic regions, one from around residues 100-115 and the second from around residues 280-295
Faint X-ray Sources in the Globular Cluster Terzan 5
We report our analysis of a Chandra X-ray observation of the rich globular
cluster Terzan 5, in which we detect 50 sources to a limiting 1.0-6 keV X-ray
luminosity of 3*10^{31} ergs/s within the half-mass radius of the cluster.
Thirty-three of these have L_X>10^{32} ergs/s, the largest number yet seen in
any globular cluster. In addition to the quiescent low-mass X-ray binary (LMXB,
identified by Wijnands et al.), another 12 relatively soft sources may be
quiescent LMXBs. We compare the X-ray colors of the harder sources in Terzan 5
to the Galactic Center sources studied by Muno and collaborators, and find the
Galactic Center sources to have harder X-ray colors, indicating a possible
difference in the populations. We cannot clearly identify a metallicity
dependence in the production of low-luminosity X-ray binaries in Galactic
globular clusters, but a metallicity dependence of the form suggested by Jordan
et al. for extragalactic LMXBs is consistent with our data.Comment: 15 pages, 10 figures (3 color). Resubmitted to ApJ after
incorporating referee comments. v2: Added references to introductio
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