A two-cocycle on the group of symplectic diffeomorphisms

We investigate a two-cocycle on the group of symplectic diffeomorphisms of an exact symplectic manifolds defined by Ismagilov, Losik, and Michor and investigate its properties. We provide both vanishing and non-vanishing results and applications to foliated symplectic bundles and to Hamiltonian actions of finitely generated groups.Comment: 16 pages, no figure

The Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey. I. The Survey Design and First Results on CL 0023+0423 at z = 0.84 and RX J1821.6+6827 at z = 0.82

We present the Observations of Redshift Evolution in Large-Scale Environments (ORELSE) Survey, a systematic search for structure on scales greater than 10 h^(–1)_70 Mpc around 20 well-known clusters at redshifts of 0.6 < z < 1.3. The goal of the survey is to examine a statistical sample of dynamically active clusters and large-scale structures in order to quantify galaxy properties over the full range of local and global environments. We describe the survey design, the cluster sample, and our extensive observational data covering at least 25' around each target cluster. We use adaptively smoothed red galaxy density maps from our wide-field optical imaging to identify candidate groups/clusters and intermediate-density large-scale filaments/walls in each cluster field. Because photometric techniques (such as photometric redshifts, statistical overdensities, and richness estimates) can be highly uncertain, the crucial component of this survey is the unprecedented amount of spectroscopic coverage. We are using the wide-field, multiobject spectroscopic capabilities of the Deep Multiobject Imaging Spectrograph to obtain 100-200+ confirmed cluster members in each field. Our survey has already discovered the Cl 1604 supercluster at z ≈ 0.9, a structure which contains at least eight groups and clusters and spans 13 Mpc × 100 Mpc. Here, we present the results on the large-scale environments of two additional clusters, Cl 0023+0423 at z = 0.84 and RX J1821.6+6827 at z = 0.82, which highlight the diversity of global properties at these redshifts. The optically selected Cl 0023+0423 is a four-way group-group merger with constituent groups having measured velocity dispersions between 206 and 479 km s^–1. The galaxy population is dominated by blue, star-forming galaxies, with 80% of the confirmed members showing [O II] emission. The strength of the Hδ line in a composite spectrum of 138 members indicates a substantial contribution from recent starbursts to the overall galaxy population. In contrast, the X-ray-selected RX J1821.6+6827 is a largely isolated, massive cluster with a measured velocity dispersion of 926 ± 77 km s^(–1). The cluster exhibits a well-defined red sequence with a large quiescent galaxy population. The results from these two targets, along with preliminary findings on other ORELSE clusters, suggest that optical selection may be more effective than X-ray surveys at detecting less-evolved, dynamically active systems at these redshifts

The scientific heritage of Richard Henry Dalitz, FRS (1925-2006)

Professor Richard H. Dalitz passed away on January 13, 2006. He was almost 81 years old and his outstanding contributions are intimately connected to some of the major breakthroughs of the 20th century in particle and nuclear physics. These outstanding contributions go beyond the Dalitz Plot, Dalitz Pair and CDD poles that bear his name. He pioneered the theoretical study of strange baryon resonances, of baryon spectroscopy in the quark model, and of hypernuclei, to all of which he made lasting contributions. His formulation of the "$\theta-\tau$ puzzle" led to the discovery that parity is not a symmetry of the weak interactions. A brief scientific evaluation of Dalitz's major contributions to particle and nuclear physics is hereby presented, followed by the first comprehensive list of his scientific publications, as assembled from several sources. The list is divided into two categories: the first, main part comprises Dalitz's research papers and reviews, including topics in the history of particle physics, biographies and reminiscences; the second part lists book reviews, public lectures and obituaries authored by Dalitz, and books edited by him. This provides the first necessary step towards a more systematic research of the Dalitz heritage in modern physics. The present 2016 edition updates the original 2006 edition, published in Nucl. Phys. A 771 (2006) 2-7, doi:10.1016/j.nuclphysa.2006.03.007, and 8-25, doi:10.1016/j.nuclphysa.2006.03.008, by including for the first time a dozen or so of publications, found recently in a list submitted to the Royal Society by Dalitz in 2004, that escaped our attention in the original version.Comment: updates the original edition by including several publications, mostly in category III, that were unknown to us in 200

Multi-Kˉ\bar{K} nuclei and kaon condensation

We extend previous relativistic mean-field (RMF) calculations of multi-$\bar K$ nuclei, using vector boson fields with SU(3) PPV coupling constants and scalar boson fields constrained phenomenologically. For a given core nucleus, the resulting $\bar K$ separation energy $B_{\bar K}$, as well as the associated nuclear and $\bar K$-meson densities, saturate with the number $\kappa$ of $\bar K$ mesons for $\kappa > \kappa_{\rm sat} \sim 10$. Saturation appears robust against a wide range of variations, including the RMF nuclear model used and the type of boson fields mediating the strong interactions. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is argued that multi-$\bar K$ nuclei do not compete with multihyperonic nuclei in providing the ground state of strange hadronic configurations and that kaon condensation is unlikely to occur in strong-interaction self-bound strange hadronic matter. Last, we explore possibly self-bound strange systems made of neutrons and ${\bar K}^0$ mesons, or protons and $K^-$ mesons, and study their properties.Comment: 21 pages, 8 figures, revised text and reference

Simulation model of erosion and deposition on a barchan dune

Erosion and deposition over a barchan dune near the Salton Sea, California, are modeled by bookkeeping the quantity of sand in saltation following streamlines of transport. Field observations of near surface wind velocity and direction plus supplemental measurements of the velocity distribution over a scale model of the dune are combined as input to Bagnold type sand transport formulas corrected for slope effects. A unidirectional wind is assumed. The resulting patterns of erosion and deposition compare closely with those observed in the field and those predicted by the assumption of equilibrium (downwind translation of the dune without change in size or geometry). Discrepancies between the simulated results and the observed or predicted erosional patterns appear to be largely due to natural fluctuations in the wind direction. The shape of barchan dunes is a function of grain size, velocity, degree of saturation of the oncoming flow, and the variability in the direction of the oncoming wind. The size of the barchans may be controlled by natural atmospheric scales, by the age of the dunes, or by the upwind roughness. The upwind roughness can be controlled by fixed elements or by sand in the saltation. In the latter case, dune scale is determined by grain size and wind velocity

Some aspects of mathematical and chemical modeling of complex chemical processes

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra