From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

Crystal Perfection Of HgI2 Studied By Neutron And Gamma-ray Diffraction

The crystalline perfection of wire sawn pieces of vapor grown single crystals of mercuric iodide was compared with the perfection of (00l) cleaved sections of the same crystal from which nuclear radiation detectors have been fabricated. The crystalline perfection was studied using neutron and gamma-ray diffraction rocking curves. Most of the gamma-ray data were obtained using a high intensity source of 153Sm gamma rays with a wavelength of λ = 0.12 Å. Some of the data were obtained using highly penetrating 198Au gamma rays with a shorter wavelength of λ = 0.03 Å. The neutrons had a wavelength of λ = 1.07 Å. It was found that, in terms of the mosaic spread of the crystals, the cleaved detector plates have a much lower crystalline perfection than the thicker uncleaved detector plates. At the same time, the results show that for detectors cut from the same crystal, the one with the lower spectral resolution for radiation detection will also have a lower perfection and larger width of the gamma-ray rocking curve. These results suggest consideration should be given to alternative fabrication procedures for HgI2 nuclear radiation detectors

Active Ground Patterns Near Mars' Equator in the Glen Torridon Region of Gale Crater

On Mars, near the equator, much of the terrain in Gale Crater consists of bedrock outcrops separated by relatively smooth, uniform regolith surfaces. In scattered sites, however, distinct patterns—in the form and texture of the ground surface—contrast sharply with the typical terrain and with eolian bedforms. This paper focuses on these diverse, intriguing ground patterns. They include ∼1 to >10 m-long linear disruptions of uniform regolith surfaces, alignments, and other arrangements of similar-sized rock fragments and shallow, ∼0.1 m-wide sandy troughs 1–10 m in length. Similar features were recognized early in the Mars Science Laboratory (MSL) mission, but they received only limited attention until Curiosity, the MSL rover, encountered striking examples in the Glen Torridon region. Herein, the ground patterns are illustrated with rover images. Potential mechanisms are briefly discussed in the context of the bedrock composition and atmospheric conditions documented by Curiosity. The evidence suggests that the patterns are active forms of spontaneous granular organization. It leads to the hypothesis that the patterns arise and develop from miniscule, inferred cyclic expansion and contraction of the bedrock and regolith, likely driven by oscillating transfers of energy and moisture between the atmosphere and the terrain. The hypothesis has significant implications for studies of contemporary processes on Mars on both sides of the atmosphere-lithosphere interface. The ground patterns, as well as ripples and dunes formed by the wind, constitute remarkable extra-terrestrial examples of granular self-organization, complex phenomena well known in diverse systems on Earth.A. G. Fairén was supported by the ERC-CoG #818602. M.-P. Zorzano has been partially funded by the Spanish State Research Agency (AEI) Project No. MDM-2017-0737 Unidad de Excelencia “María de Maeztu”-Centro de Astrobiología (INTA-CSIC) and by the Spanish Ministry of Science and Innovation (PID2019-104205GB-C21). Last but not least, B. Hallet and R. S. Sletten gratefully acknowledge sustained funding for their work through the MSL mission in a NASA grant awarded to MSSS

Polymer transport in random flow

The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and large arguments compared to the equilibrium length. The characteristic relaxation time is computed as a function of the Weissenberg number. In the stretched state the pdf is unstationary and exhibits multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow confirm the relevance of theoretical results obtained for the delta-correlated model.Comment: 28 pages, 6 figure

A demonstration of an affinity between pyrite and organic matter in a hydrothermal setting

One of the key-principles of the iron-sulphur world theory is to bring organic molecules close enough to interact with each other, using the surface of pyrite as a substrate in a hydrothermal setting. The present paper explores the relationship of pyrite and organic matter in a hydrothermal setting from the geological record; in hydrothermal calcite veins from Carboniferous limestones in central Ireland. Here, the organic matter is accumulated as coatings around, and through, pyrite grains. Most of the pyrite grains are euhedral-subhedral crystals, ranging in size from ca 0.1-0.5 mm in diameter, and they are scattered throughout the matrix of the vein calcite. The organic matter was deposited from a hydrothermal fluid at a temperature of at least 200°C, and gives a Raman signature of disordered carbon. This study points to an example from a hydrothermal setting in the geological record, demonstrating that pyrite can have a high potential for the concentration and accumulation of organic materials

Molecular evidence of Late Archean archaea and the presence of a subsurface hydrothermal biosphere

Author Posting. © National Academy of Sciences of the USA, 2007. This is the author's version of the work. It is posted here by permission of National Academy of Sciences of the USA for personal use, not for redistribution. The definitive version was published in Proceedings of the National Academy of Sciences 104 (2007): 14260-14265, doi:10.1073/pnas.0610903104.Highly cracked and isomerized archaeal lipids and bacterial lipids, structurally changed by thermal stress, are present in solvent extracts of 2,707-2,685 million year old (Ma) metasedimentary rocks from Timmins, Ontario, Canada. These lipids appear in conventional gas chromatograms as unresolved complex mixtures (UCMs) and include cyclic and acyclic biphytanes, C36-C39 derivatives of the biphytanes, and C31-C35 extended hopanes. Biphytane and extended hopanes are also found in high pressure catalytic hydrogenation (HPCH) products released from solvent-extracted sediments,indicating that archaea and bacteria were present in Late Archean sedimentary environments. Post-depositional, hydrothermal gold mineralization and graphite precipitation occurred prior to metamorphism (~2,665 Ma). Late Archean metamorphism significantly reduced the kerogen’s adsorptive capacity and severely restricted sediment porosity, limiting the potential for post-Archean additions of organic matter to the samples. Argillites exposed to hydrothermal gold mineralization have disproportionately high concentrations of extractable archaeal and bacterial lipids relative to what is releasable from their respective HPCH product and what is observed for argillites deposited away from these hydrothermal settings. The addition of these lipids to the sediments likely results from a Late Archean subsurface hydrothermal biosphere of archaea and bacteria.This project was supported by NASA Exobiology grant #NAG5-13446 to Fabien Kenig. SEM analysis was supported by NSF grant EAR 0318769 to Juergen Schieber. GC×GC analysis was supported by NSF grant IIS-0430835 and the Seaver Foundation to Christopher M. Reddy

Determination of the Michel Parameters rho, xi, and delta in tau-Lepton Decays with tau --> rho nu Tags

Using the ARGUS detector at the $e^+ e^-$ storage ring DORIS II, we have measured the Michel parameters $\rho$, $\xi$, and $\xi\delta$ for $\tau^{\pm}\to l^{\pm} \nu\bar\nu$ decays in $\tau$-pair events produced at center of mass energies in the region of the $\Upsilon$ resonances. Using $\tau^\mp \to \rho^\mp \nu$ as spin analyzing tags, we find $\rho_{e}=0.68\pm 0.04 \pm 0.08$, $\xi_{e}= 1.12 \pm 0.20 \pm 0.09$, $\xi\delta_{e}= 0.57 \pm 0.14 \pm 0.07$, $\rho_{\mu}= 0.69 \pm 0.06 \pm 0.08$, $\xi_{\mu}= 1.25 \pm 0.27 \pm 0.14$ and $\xi\delta_{\mu}= 0.72 \pm 0.18 \pm 0.10$. In addition, we report the combined ARGUS results on $\rho$, $\xi$, and $\xi\delta$ using this work und previous measurements.Comment: 10 pages, well formatted postscript can be found at http://pktw06.phy.tu-dresden.de/iktp/pub/desy97-194.p