A note on multi-dimensional Camassa-Holm type systems on the torus

We present a $2n$-component nonlinear evolutionary PDE which includes the $n$-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as well as their partially averaged variations. Our goal is to apply Arnold's [V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de dimension infinie et ses applications \`a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general equation in order to obtain results on well-posedness, conservation laws or stability of its solutions. Following the line of arguments of the paper [M. Kohlmann, The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present geometric aspects of a two-dimensional periodic $\mu$-$b$-equation on the diffeomorphism group of the torus in this context.Comment: 14 page

Structure of Polyelectrolytes in Poor Solvent

We present simulations on charged polymers in poor solvent. First we investigate in detail the dilute concentration range with and without imposed extension constraints. The resulting necklace polymer conformations are analyzed in detail. We find strong fluctuations in the number of pearls and their sizes leading only to small signatures in the form factor and the force-extension relation. The scaling of the peak in the structure factor with the monomer density shows a pertinent different behavior from good solvent chains.Comment: 7 pages, 5 figures. submitted to EP

Multiband superconductivity in the heavy fermion compound PrOs4Sb12

The thermal conductivity of the heavy fermion superconductor PrOs4Sb12 was measured down to Tc/40 throughout the vortex state. At lowest temperatures and for magnetic fields H ~ 0.07Hc2, already 40% of the normal state thermal conductivity is restored. This behaviour (similar to that observed in MgB2) is a clear signature of multiband superconductivity in this compound.Comment: 12pages, version #1 20\_06\_200

Vore Kapellers Varmeforsyning i denne Vinter

Intet resumé

Regge Calculus in Teleparallel Gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller an smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra

Multi-elemental speciation analysis of barley genotypes diering in tolerance to cadmium toxicity using SEC-ICP-MS and ESI-TOF-MS

Plants respond to Cd exposure by synthesizing heavy-metal-binding oligopeptides, called phytochelatins (PCs). These peptides reduce the activity of Cd2+ ions in the plant tissues by forming Cd chelates. The main objective of the present work was to develop an analytical technique, which allowed identication of the most prominent Cd species in plant tissue by SEC-ICP-MS and ESI-TOF-MS. An integrated part of the method development was to test the hypothesis that dierential Cd tolerance between two barley genotypes was linked to dierences in Cd speciation. Only one fraction of Cd species, ranging from 7001800 Da, was detected in the shoots of both genotypes. In the roots, two additional fractions ranging from 29004600 and 670015 000 Da were found. The Cd-rich SEC fractions were heart-cut, de-salted and demetallized using reversed-phase chromatography (RPC), followed by ESI-MS-TOF to identify the ligands. Three dierent families of PCs, viz. (gGlu-Cys)n-Gly (PCn), (gGlu-Cys)n-Ser (iso-PCn) and Cys-(gGlu-Cys)n-Gly (des-gGlu-PCn), the last lacking the N-terminal amino acid, were identied. The PCs induced by Cd toxicity also bound several essential trace elements in plants, including Zn, Cu, and Ni, whereas no Mn species were detected. Zn, Cu and Ni-species were distributed between the 7001800 Da and 670015 000 Da fractions, whereas only Cd species were found in the 29004600 Da fraction dominated by PC3 ligands. Although the total tissue concentration of Cd was similar for the two species, the tolerant barley genotype synthesized signicantly more CdPC3 species with a high Cd specicity than the intolerant genotype, clearly indicating a correlation between Cd tolerance and the CdPC speciation

Mean-Field HP Model, Designability and Alpha-Helices in Protein Structures

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with large number of switch backs between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha-helices.Comment: 4 pages, 2 figure

Power-law correlations and orientational glass in random-field Heisenberg models

Monte Carlo simulations have been used to study a discretized Heisenberg ferromagnet (FM) in a random field on simple cubic lattices. The spin variable on each site is chosen from the twelve [110] directions. The random field has infinite strength and a random direction on a fraction x of the sites of the lattice, and is zero on the remaining sites. For x = 0 there are two phase transitions. At low temperatures there is a [110] FM phase, and at intermediate temperature there is a [111] FM phase. For x > 0 there is an intermediate phase between the paramagnet and the ferromagnet, which is characterized by a |k|^(-3) decay of two-spin correlations, but no true FM order. The [111] FM phase becomes unstable at a small value of x. At x = 1/8 the [110] FM phase has disappeared, but the power-law correlated phase survives.Comment: 8 pages, 12 Postscript figure

Torsion pairs and rigid objects in tubes

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte