Oxygen Isotopic Constraints on the Number and Origin of Basaltic Achondrite Parent Bodies

Our data show that HED meteorites have a homogeneous oxygen isotopic composition consistent with a magma ocean on Vesta. Ibitira, Asuka 881394, Pasamonte, and NWA 1240 probably come from separate parent asteroids

Some symmetry classifications of hyperbolic vector evolution equations

Motivated by recent work on integrable flows of curves and 1+1 dimensional sigma models, several O(N)-invariant classes of hyperbolic equations $u_{tx} =f(u,u_t,u_x)$ for an $N$-component vector $u(t,x)$ are considered. In each class we find all scaling-homogeneous equations admitting a higher symmetry of least possible scaling weight. Sigma model interpretations of these equations are presented.Comment: Revision of published version, incorporating errata on geometric aspects of the sigma model interpretations in the case of homogeneous space

Three-dimensional Binary Superlattices of Oppositely-charged Colloids

We report the equilibrium self-assembly of binary crystals of oppositely-charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched between face-centered cubic, cesium chloride and sodium chloride. We interpret these transformations in terms of a competition between entropic and Coulombic forces

Representations of the Weyl group and Wigner functions for SU(3)

Bases for SU(3) irreps are constructed on a space of three-particle tensor products of two-dimensional harmonic oscillator wave functions. The Weyl group is represented as the symmetric group of permutations of the particle coordinates of these space. Wigner functions for SU(3) are expressed as products of SU(2) Wigner functions and matrix elements of Weyl transformations. The constructions make explicit use of dual reductive pairs which are shown to be particularly relevant to problems in optics and quantum interferometry.Comment: : RevTex file, 11 pages with 2 figure

Partitioning Complex Networks via Size-constrained Clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis

Highly nonclassical photon statistics in parametric down conversion

We use photon counters to obtain the joint photon counting statistics from twin-beam non-degenerate parametric down conversion, and we demonstrate directly, and with no auxiliary assumptions, that these twin beams are nonclassical