The arctic circle boundary and the Airy process

We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond.Comment: Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Three-tangle for mixtures of generalized GHZ and generalized W states

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized GHZ state, a|000>+b|111>, and a generalized W state, c|001>+d|010>+f|100>. Using the methods introduced by Lohmayer et al. we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state

Electronic-structure-induced deformations of liquid metal clusters

Ab initio molecular dynamics is used to study deformations of sodium clusters at temperatures $500\cdots 1100$ K. Open-shell Na$_{14}$ cluster has two shape isomers, prolate and oblate, in the liquid state. The deformation is stabilized by opening a gap at the Fermi level. The closed-shell Na$_8$ remains magic also at the liquid state.Comment: REVTex, 11 pages, no figures, figures (2) available upon request (e-mail to hakkinen at jyfl.jyu.fi), submitted to Phys. Rev.

Millennial changes in North American wildfire and soil activity over the last glacial cycle

Climate changes in the North Atlantic region during the last glacial cycle were dominated by the slow waxing and waning of the North American ice sheet as well as by intermittent, millennial-scale Dansgaard-Oeschger climate oscillations. However, prior to the last deglaciation, the responses of North American vegetation and biomass burning to these climate variations are uncertain. Ammonium in Greenland ice cores, a product from North American soil emissions and biomass burning events, can help to fill this gap. Here we use continuous, high-resolution measurements of ammonium concentrations between 110,000 to 10,000 years ago from the Greenland NGRIP and GRIP ice cores to reconstruct North American wildfire activity and soil ammonium emissions. We find that on orbital timescales soil emissions increased under warmer climate conditions when vegetation expanded northwards into previously ice-covered areas. For millennial-scale interstadial warm periods during Marine Isotope Stage 3, the fire recurrence rate increased in parallel to the rapid warmings, whereas soil emissions rose more slowly, reflecting slow ice shrinkage and delayed ecosystem changes. We conclude that sudden warming events had little impact on soil ammonium emissions and ammonium transport to Greenland, but did result in a substantial increase in the frequency of North American wildfires

Diffusion of gold nanoclusters on graphite

We present a detailed molecular-dynamics study of the diffusion and coalescence of large (249-atom) gold clusters on graphite surfaces. The diffusivity of monoclusters is found to be comparable to that for single adatoms. Likewise, and even more important, cluster dimers are also found to diffuse at a rate which is comparable to that for adatoms and monoclusters. As a consequence, large islands formed by cluster aggregation are also expected to be mobile. Using kinetic Monte Carlo simulations, and assuming a proper scaling law for the dependence on size of the diffusivity of large clusters, we find that islands consisting of as many as 100 monoclusters should exhibit significant mobility. This result has profound implications for the morphology of cluster-assembled materials

Towards an effective potential for the monomer, dimer, hexamer, solid and liquid forms of hydrogen fluoride

We present an attempt to build up a new two-body effective potential for hydrogen fluoride, fitted to theoretical and experimental data relevant not only to the gas and liquid phases, but also to the crystal. The model is simple enough to be used in Molecular Dynamics and Monte Carlo simulations. The potential consists of: a) an intra-molecular contribution, allowing for variations of the molecular length, plus b) an inter-molecular part, with three charged sites on each monomer and a Buckingham "exp-6" interaction between fluorines. The model is able to reproduce a significant number of observables on the monomer, dimer, hexamer, solid and liquid forms of HF. The shortcomings of the model are pointed out and possible improvements are finally discussed.Comment: LaTeX, 24 pages, 2 figures. For related papers see also http://www.chim.unifi.it:8080/~valle

Density functional study of Aun_n (n=2-20) clusters: lowest-energy structures and electronic properties

We have investigated the lowest-energy structures and electronic properties of the Au$_n$(n=2-20) clusters based on density functional theory (DFT) with local density approximation. The small Au$_n$ clusters adopt planar structures up to n=6. Tabular cage structures are preferred in the range of n=10-14 and a structural transition from tabular cage-like structure to compact near-spherical structure is found around n=15. The most stable configurations obtained for Au$_{13}$ and Au$_{19}$ clusters are amorphous instead of icosahedral or fcc-like, while the electronic density of states sensitively depend on the cluster geometry. Dramatic odd-even alternative behaviors are obtained in the relative stability, HOMO-LUMO gaps and ionization potentials of gold clusters. The size evolution of electronic properties is discussed and the theoretical ionization potentials of Au$_n$ clusters compare well with experiments.Comment: 6 pages, 7 figure

Surface reconstruction induced geometries of Si clusters

We discuss a generalization of the surface reconstruction arguments for the structure of intermediate size Si clusters, which leads to model geometries for the sizes 33, 39 (two isomers), 45 (two isomers), 49 (two isomers), 57 and 61 (two isomers). The common feature in all these models is a structure that closely resembles the most stable reconstruction of Si surfaces, surrounding a core of bulk-like tetrahedrally bonded atoms. We investigate the energetics and the electronic structure of these models through first-principles density functional theory calculations. These models may be useful in understanding experimental results on the reactivity of Si clusters and their shape as inferred from mobility measurements.Comment: 9 figures (available from the author upon request) Submitted to Phys. Rev.

Density-functional-based predictions of Raman and IR spectra for small Si clusters

We have used a density-functional-based approach to study the response of silicon clusters to applied electric fields. For the dynamical response, we have calculated the Raman activities and infrared (IR) intensities for all of the vibrational modes of several clusters (SiN with N=3-8, 10, 13, 20, and 21) using the local density approximation (LDA). For the smaller clusters (N=3-8) our results are in good agreement with previous quantum-chemical calculations and experimental measurements, establishing that LDA-based IR and Raman data can be used in conjunction with measured spectra to determine the structure of clusters observed in experiment. To illustrate the potential of the method for larger clusters, we present calculated IR and Raman data for two low-energy isomers of Si10 and for the lowest-energy structure of Si13 found to date. For the static response, we compare our calculated polarizabilities for N=10, 13, 20, and 21 to recent experimental measurements. The calculated results are in rough agreement with experiment, but show less variation with cluster size than the measurements. Taken together, our results show that LDA calculations can offer a powerful means for establishing the structures of experimentally fabricated clusters and nanoscale systems