The modular geometry of Random Regge Triangulations

We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial quantum gravity. In particular, we discuss in detail an explicit bijection between the space of possible random Regge triangulations (of given genus g and with N vertices) and a suitable decorated version of the (compactified) moduli space of genus g Riemann surfaces with N punctures. Such an analysis allows us to associate a Weil-Petersson metric with the set of random Regge triangulations and prove that the corresponding volume provides the dynamical triangulation partition function for pure gravity.Comment: 36 pages corrected typos, enhanced introductio

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

Ternary transition-metal fluoride precursors for the fluorolytic sol-gel route: new insights into speciation and decomposition

The nanoscaled ternary transition-metal fluorides Li3MF6 (M = V, Fe, Mn) and Li2NiF4 are promising candidates for cathode materials in high-voltage lithium-ion batteries. The fluorolytic route to these compounds relies on thermal decomposition of a hitherto uncharacterised precursor mixture produced from acetylacetonates and hydrofluoric acid. By addition of pyridine, different cationic, electroneutral and anionic complexes containing the motifs [MFn]((3-n)+) (n = 0-4) have been trapped and characterised by single-crystal X-ray diffraction and IR spectroscopy. Based on the results, a model of successive and incomplete fluorination is proposed for the speciation and formation of the precursor. The decomposition of the latter has been monitored via thermogravimetry (TG) and differential scanning calorimetry (DSC)

Triangulations and volume form on moduli spaces of flat surfaces

In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some deformation of the moduli space of translation surfaces. Using geodesic triangulations, we define a volume form on this moduli space, and show that, in the well-known cases, this volume form agrees with usual ones, up to a multiplicative constant.Comment: 42 page

H(3)+ correlators from Liouville theory

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations between the structure constants of Liouville theory and the H(3)+ model. In the critical level limit, these results imply a direct link between eigenvectors of the Gaudin Hamiltonians and the problem of uniformization of Riemann surfaces. We also present an expression for correlation functions of the SL(2)/U(1) coset model in terms of correlation functions in Liouville theory.Comment: 24 pages, v3: minor changes, references adde

Crystal experiments on efficient beam extraction

Silicon crystal was channeling and extracting 70-GeV protons from the U-70 accelerator with efficiency of 85.3+-2.8% as measured for a beam of 10^12 protons directed towards crystals of 2 mm length in spills of 1-2 s duration. The experimental data follow very well the prediction of Monte Carlo simulations. This success is important to devise a more efficient use of the U-70 accelerator in Protvino and provides a crucial support for implementation of crystal-assisted collimation of gold ion beam in RHIC and slow extraction from AGS onto E952, now in preparation at Brookhaven Nat'l Lab. Future applications, spanning in the energy from sub-GeV (medical) to order of 1 GeV (scraping in the SNS, extraction from COSY) to order of 1 TeV and beyond (scraping in the Tevatron, LHC, VLHC), can benefit from these studies.Comment: 12pp. Presented at 19-th Intern. Conference on Atomic Collisions in Solids (ICACS-19: Paris, July 29 - August 3, 2001

Progress in crystal extraction and collimation

Recent IHEP Protvino experiments show efficiencies of crystal-assisted slow extraction and collimation of 85.3+-2.8%, at the intensities of the channeled beam on the order of 10^12 proton per spill of 2 s duration. The obtained experimental data well follows the theory predictions. We compare the measurements against theory and outline the theoretical potential for further improvement in the efficiency of the technique. This success is important for the efficient use of IHEP accelerator and for implementation of crystal-assisted collimation at RHIC and slow extraction from AGS onto E952, now in preparation. Future applications, spanning in the energy from order of 1 GeV (scraping in SNS, slow extraction from COSY and medical accelerators) to order of 1 TeV and beyond (scraping in Tevatron, LHC, VLHC), can benefit from these studies.Comment: 7pp. Presented at HEACC 2001 (Tsukuba, March 25-30

1,3,7,10,14,17,21,28,31,42,52,55-Dodeca­kis(trifluoro­meth­yl)- 1,3,7,10,14,17,21,28,31,42,52,55-dodeca­hydro­(C60–Ih)[5,6]fullerene

The title compound, C72F36, is one of four isomers of C60(CF3)12 for which crystal structures have been obtained. The fullerene mol­ecule has an idealized Ih C60 core with the 12 CF3 groups arranged in an asymmetric fashion on two ribbons of edge-sharing C6(CF3)2 hexa­gons, a para–meta–para–para–para–meta–para ribbon and a para–meta–para ribbon, giving an overall pmp 3 mp,pmp structure. There are no cage Csp 3—Csp 3 bonds. The F atoms of two CF3 groups are disordered over two positions; the site occupancy factors are 0.85/0.15 and 0.73/0.27. There are intra­molecular F⋯F contacts between pairs of CF3 groups on the same hexa­gon that range from 2.521 (3) to 2.738 (4) Å