Dimer states in atomic mixtures

A mixture of heavy atoms in a Mott state and light spin-1/2 fermionic atoms is studied in an optical lattice. Inelastic scattering processes between both atomic species excite the heavy atoms and renormalize the tunneling rate as well as the interaction of the light atoms. An effective Hamiltonian for the latter is derived that describes tunneling of single fermions, tunneling of fermionic pairs and an exchange of fermionic spins. Low energy states of this Hamiltonian are a N\'eel state for strong effective repulsion, dimer states for moderate interaction, and a density wave of paired fermions for strong effective attraction.Comment: 10 pages, 3 figure, extended versio

All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions

For Gorenstein quotient spaces $C^d/G$, a direct generalization of the classical McKay correspondence in dimensions $d\geq 4$ would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces which would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry.Comment: revised version of MPI-preprint 97/4, 35 pages, 13 figures, latex2e-file (preprint.tex), macro packages and eps-file

Construction and Analysis of Projected Deformed Products

We introduce a deformed product construction for simple polytopes in terms of lower-triangular block matrix representations. We further show how Gale duality can be employed for the construction and for the analysis of deformed products such that specified faces (e.g. all the k-faces) are ``strictly preserved'' under projection. Thus, starting from an arbitrary neighborly simplicial (d-2)-polytope Q on n-1 vertices we construct a deformed n-cube, whose projection to the last dcoordinates yields a neighborly cubical d-polytope. As an extension of thecubical case, we construct matrix representations of deformed products of(even) polygons (DPPs), which have a projection to d-space that retains the complete (\lfloor \tfrac{d}{2} \rfloor - 1)-skeleton. In both cases the combinatorial structure of the images under projection is completely determined by the neighborly polytope Q: Our analysis provides explicit combinatorial descriptions. This yields a multitude of combinatorially different neighborly cubical polytopes and DPPs. As a special case, we obtain simplified descriptions of the neighborly cubical polytopes of Joswig & Ziegler (2000) as well as of the ``projected deformed products of polygons'' that were announced by Ziegler (2004), a family of 4-polytopes whose ``fatness'' gets arbitrarily close to 9.Comment: 20 pages, 5 figure

Early-type Galaxies in the Cluster Abell 2390 at z=0.23

To examine the evolution of the early-type galaxy population in the rich cluster Abell 2390 at z=0.23 we have gained spectroscopic data of 51 elliptical and lenticular galaxies with MOSCA at the 3.5 m telescope on Calar Alto Observatory. This investigation spans both a broad range in luminosity (-19.3>M_B>-22.3) and uses a wide field of view of 10'x10', therefore the environmental dependence of different formation scenarios can be analysed in detail as a function of radius from the cluster centre. Here we present results on the surface brightness modelling of galaxies where morphological and structural information is available in the F814W filter aboard the Hubble Space Telescope (HST) and investigate for this subsample the evolution of the Fundamental Plane.Comment: 5 pages, 5 figures, to appear in "Carnegie Observatories Astrophysics Series, Vol. 3: Clusters of Galaxies: Probes of Cosmological Structure and Galaxy Evolution", ed. J. S. Mulchaey, A. Dressler, and A. Oemler (Pasadena: Carnegie Observatories, http://www.ociw.edu/ociw/symposia/series/symposium3/proceedings.html

Very high energy emission from the hard spectrum sources HESS J1641-463, HESS J1741-302 and HESS J1826-130

A recent study of the diffuse $\gamma$-ray emission in the Central Molecular Zone using very high energy (VHE, E $>$ 0.1 TeV) H.E.S.S. data suggests that the Galactic Center (GC) is the most plausible supplier of Galactic ultra-relativistic cosmic-rays (CRs) up to the knee at about 10$^{15}$ eV (PeV). However, the GC might not be the only source capable to accelerate CRs up to PeV energies in the Galaxy. Here we present H.E.S.S. data analysis results and interpretation of three H.E.S.S. sources, with spectra extending beyond 10 TeV and relatively hard spectral indices compared with the average spectral index of H.E.S.S. sources, namely HESS J1641-463, HESS J1741-302 and HESS J1826-130. Although the nature of these VHE $\gamma$-ray sources is still open, their spectra suggest that the astrophysical objects producing such emission must be capable of accelerating the parental particle population up to energies of at least several hundreds of TeV. Assuming a hadronic scenario, dense gas regions can provide rich target material for accelerated particles to produce VHE $\gamma$-ray emission via proton-proton interactions followed by a subsequent $\pi^{0}$ decay. Thus, detailed investigations of the interstellar medium along the line of sight to all of these sources have been performed by using data from available atomic and molecular hydrogen surveys. The results point out the existence of dense interstellar gas structures coincident with the best fit positions of these sources. One can find possible hadronic models with CRs being accelerated close to the PeV energies to explain the $\gamma$-ray emission from all of these sources, which opens up the possibility that a population of PeV CR accelerators might be active in the Galaxy.Comment: 8 pages, 2 figures, in Proceedings of 35th ICRC, Busan (Korea) 201

Several examples of neigbourly polyhedra in co-dimension 4

In the article, a series of neigbourly polyhedra is constructed. They have $N=2d+4$ vertices and are embedded in $\mathbb R^{2d}$. Their (affine) Gale diagrams in $\mathbb R^2$ have $d+3$ black points that form a convex polygon. These Gale diagams can be enumerated using 3-trees (trees with some additional structure). Given $d$ and $m$, each of the constructed polyhedra in $\mathbb R^{2d}$ has a fixed number of faces of dimension $m$ that contain a vertex $A$. (This number depends on $d$ and $m$ does not depend on the polyhedron and the vertex $A$).Comment: In russian, 25 pages, 16 figure

Exploring Cluster Ellipticals as Cosmological Standard Rods

We explore the possibility to calibrate massive cluster ellipticals as cosmological standard rods using the Fundamental Plane relation combined with a correction for luminosity evolution. Though cluster ellipticals certainly formed in a complex way, their passive evolution out to redshifts of about 1 indicates that basically all major merging and accretion events took place at higher redshifts. Therefore, a calibration of their luminosity evolution can be attempted. We propose to use the Mg$-\sigma$ relation for that purpose because it is independent of distance and cosmology. We discuss a variety of possible caveats, ranging from dynamical evolution to uncertainties in stellar population models and evolution corrections to the presence of age spread. Sources of major random and systematic errors are analysed as well. We apply the described procedure to nine elliptical galaxies in two clusters at $z=0.375$ and derive constraints on the cosmological model. For the best fitting $\Lambda$-free cosmological model we obtain: $q_o \approx 0.1$, with 90% confidence limits being $0 < q_o < 0.7$ (the lower limit being due to the presence of matter in the Universe). If the inflationary scenario applies (i.e. the Universe has flat geometry), then, for the best fitting model, matter and $\Lambda$ contribute about equally to the critical cosmic density (i.e. $\Omega_m \approx \Omega_\Lambda \approx 0.5$). With 90% confidence $\Omega_\Lambda$ should be smaller than 0.9.Comment: 21 pages, including 5 eps-figures, Latex, uses aasms4.sty, accepted by ApJ main journa

Epic Human Failure on June 30, 2013

Nineteen Prescott Fire Department, Granite Mountain Hot Shot (GMHS) wildland firefighters and supervisors (WFF), perished on the June 2013 Yarnell Hill Fire (YHF) in Arizona. The firefighters left their Safety Zone during forecast, outflow winds, triggering explosive fire behavior in drought-stressed chaparral. Why would an experienced WFF Crew, leave ‘good black’ and travel downslope through a brush-filled chimney, contrary to their training and experience? An organized Serious Accident Investigation Team (SAIT) found, “… no indication of negligence, reckless actions, or violations of policy or protocol.” Despite this, many WFF professionals deemed the catastrophe, “… the final, fatal link, in a long chain of bad decisions with good outcomes.” This paper is a theoretical and realistic examination of plausible, faulty, human decisions with prior good outcomes; internal and external impacts, influencing the GMHS; and two explanations for this catastrophe: Individual Blame Logic and Organizational Function Logic, and proposed preventive mitigations