Spectral properties of zero temperature dynamics in a model of a compacting granular column

The compacting of a column of grains has been studied using a one-dimensional Ising model with long range directed interactions in which down and up spins represent orientations of the grain having or not having an associated void. When the column is not shaken (zero 'temperature') the motion becomes highly constrained and under most circumstances we find that the generator of the stochastic dynamics assumes an unusual form: many eigenvalues become degenerate, but the associated multi-dimensional invariant spaces have but a single eigenvector. There is no spectral expansion and a Jordan form must be used. Many properties of the dynamics are established here analytically; some are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table

Mitochondrial Genetic Differentiation of Spirlin (Actinopterigii: Cyprinidae) in the South Caspian Sea basin of Iran

Background Knowledge about Alburnoides remains lacking relative to many other species, resulting in a lack of a systematic position and taxonomic diagnosis. Basic biological information for Alburnoides has been constructed, and it is necessary to understand further and obtain more information about this species. Its phylogenetic relationships are still debated and no molecular data have been used to study this taxon in Iran. A holistic approach for genetic methods was adopted to analyze possible spirlin population differences at selected centers in the south Caspian Sea basin of Iran. Methods The phylogenetic relationships were determined based on 774 base pairs of the mitochondrial cytochrome b gene of 32 specimens of spirlin from nine locations in the south Caspian Sea drainage basin of Iran. The nucleotide sequences were subjected to phylogenetic analysis using the neighbor-joining, maximum parsimony, maximum likelihood, and Bayesian methods. Results The mitochondrial gene tree largely supports the existence of three major clades. The western populations (clade I) may be considered as Alburnoides eichwaldii , whereas the Talar river populations (clade II) are represented as Alburnoides sp. 1 and the eastern populations (clade III) may be distinct taxa of Alburnoides sp.2. Conclusion This molecular evidence supports the hypothesis that A. bipunctatus does not exist in the south Caspian Sea basin of Iran, and that the western and eastern populations are distinct taxa

On the stability of Dirac sheet configurations

Using cooling for SU(2) lattice configurations, purely Abelian constant magnetic field configurations were left over after the annihilation of constituents that formed metastable Q=0 configurations. These so-called Dirac sheet configurations were found to be stable if emerging from the confined phase, close to the deconfinement phase transition, provided their Polyakov loop was sufficiently non-trivial. Here we show how this is related to the notion of marginal stability of the appropriate constant magnetic field configurations. We find a perfect agreement between the analytic prediction for the dependence of stability on the value of the Polyakov loop (the holonomy) in a finite volume and the numerical results studied on a finite lattice in the context of the Dirac sheet configurations