Factorised Steady States in Mass Transport Models on an Arbitrary Graph

We study a general mass transport model on an arbitrary graph consisting of $L$ nodes each carrying a continuous mass. The graph also has a set of directed links between pairs of nodes through which a stochastic portion of mass, chosen from a site-dependent distribution, is transported between the nodes at each time step. The dynamics conserves the total mass and the system eventually reaches a steady state. This general model includes as special cases various previously studied models such as the Zero-range process and the Asymmetric random average process. We derive a general condition on the stochastic mass transport rules, valid for arbitrary graph and for both parallel and random sequential dynamics, that is sufficient to guarantee that the steady state is factorisable. We demonstrate how this condition can be achieved in several examples. We show that our generalized result contains as a special case the recent results derived by Greenblatt and Lebowitz for $d$-dimensional hypercubic lattices with random sequential dynamics.Comment: 17 pages 1 figur

Condensation phase transitions of symmetric conserved-mass aggregation model on complex networks

We investigate condensation phase transitions of symmetric conserved-mass aggregation (SCA) model on random networks (RNs) and scale-free networks (SFNs) with degree distribution $P(k) \sim k^{-\gamma}$. In SCA model, masses diffuse with unite rate, and unit mass chips off from mass with rate $\omega$. The dynamics conserves total mass density $\rho$. In the steady state, on RNs and SFNs with $\gamma>3$ for $\omega \neq \infty$, we numerically show that SCA model undergoes the same type condensation transitions as those on regular lattices. However the critical line $\rho_c (\omega)$ depends on network structures. On SFNs with $\gamma \leq 3$, the fluid phase of exponential mass distribution completely disappears and no phase transitions occurs. Instead, the condensation with exponentially decaying background mass distribution always takes place for any non-zero density. For the existence of the condensed phase for $\gamma \leq 3$ at the zero density limit, we investigate one lamb-lion problem on RNs and SFNs. We numerically show that a lamb survives indefinitely with finite survival probability on RNs and SFNs with $\gamma >3$, and dies out exponentially on SFNs with $\gamma \leq 3$. The finite life time of a lamb on SFNs with $\gamma \leq 3$ ensures the existence of the condensation at the zero density limit on SFNs with $\gamma \leq 3$ at which direct numerical simulations are practically impossible. At $\omega = \infty$, we numerically confirm that complete condensation takes place for any $\rho > 0$ on RNs. Together with the recent study on SFNs, the complete condensation always occurs on both RNs and SFNs in zero range process with constant hopping rate.Comment: 6 pages, 6 figure

Observations of Intercastes in Solenopsis Invicta Buren

The red imported fire ant, Solenopsis invicta Buren, exhibits classical polymorphism, which is defined as the coexistence of 2 or more functionally different castes of the same sex (Wilson 1971). The 2 basic castes are the worker and the female sexuals

Stability transitions for axisymmetric relative equilibria of Euclidean symmetric Hamiltonian systems

In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of Hamiltonian systems with Euclidean symmetry, we investigate different mechanisms of stability: stability by energy-momentum confinement, KAM, and Nekhoroshev stability, and we explain the transitions between these. We apply our results to the Kirchhoff model for the motion of an axisymmetric underwater vehicle, and we numerically study dissipation induced instability of KAM stable relative equilibria for this system.Comment: Minor revisions. Typographical errors correcte

OBDD-Based Representation of Interval Graphs

A graph $G = (V,E)$ can be described by the characteristic function of the edge set $\chi_E$ which maps a pair of binary encoded nodes to 1 iff the nodes are adjacent. Using \emph{Ordered Binary Decision Diagrams} (OBDDs) to store $\chi_E$ can lead to a (hopefully) compact representation. Given the OBDD as an input, symbolic/implicit OBDD-based graph algorithms can solve optimization problems by mainly using functional operations, e.g. quantification or binary synthesis. While the OBDD representation size can not be small in general, it can be provable small for special graph classes and then also lead to fast algorithms. In this paper, we show that the OBDD size of unit interval graphs is $O(\ | V \ | /\log \ | V \ |)$ and the OBDD size of interval graphs is $O(\ | V \ | \log \ | V \ |)$which both improve a known result from Nunkesser and Woelfel (2009). Furthermore, we can show that using our variable order and node labeling for interval graphs the worst-case OBDD size is$\Omega(\ | V \ | \log \ | V \ |)$. We use the structure of the adjacency matrices to prove these bounds. This method may be of independent interest and can be applied to other graph classes. We also develop a maximum matching algorithm on unit interval graphs using$O(\log \ | V \ |)$operations and a coloring algorithm for unit and general intervals graphs using$O(\log^2 \ | V \ |)$ operations and evaluate the algorithms empirically.Comment: 29 pages, accepted for 39th International Workshop on Graph-Theoretic Concepts 201

Bifurcation Diagram for Compartmentalized Granular Gases

The bifurcation diagram for a vibro-fluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N=2, this transition takes place via a pitchfork bifurcation but for all N>2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multi-peaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.Comment: Phys. Rev. E, in press. Figure quality has been reduced in order to decrease file-siz

High Resolution Spectroscopy of the X-ray Photoionized Wind in Cygnus X-3 with the Chandra High Energy Transmission Grating Spectrometer

We present a preliminary analysis of the 1--10 keV spectrum of the massive X-ray binary Cyg X-3, obtained with the High Energy Transmission Grating Spectrometer on the Chandra X-ray Observatory. The source reveals a richly detailed discrete emission spectrum, with clear signatures of photoionization-driven excitation. Among the spectroscopic novelties in the data are the first astrophysical detections of a number of He-like 'triplets' (Si, S, Ar) with emission line ratios characteristic of photoionization equilibrium, fully resolved narrow radiative recombination continua of Mg, Si, and S, the presence of the H-like Fe Balmer series, and a clear detection of a ~ 800 km/s large scale velocity field, as well as a ~1500 km/s FWHM Doppler broadening in the source. We briefly touch on the implications of these findings for the structure of the Wolf-Rayet wind.Comment: 11 pages, 3 figures; Accepted for publication in ApJ Letter

Sociologists, archbishops, and 'making a verb of a noun'

Contemporary discussion about race has a tendency to set off out without first checking the rear view mirror. In Theories of Race and Ethnicity: Contemporary Debates and Perspectives, in contrast, Murji and Solomos identify what has and has not been covered, and so appeal at the outset for a 'more sustained' account of changing research agendas of race and ethnic relations. Taken as a whole, the collection allows the editors to contemplate 'what factors explain the mobilizing power of ideas about race and ethnicity in the contemporary environment?' and whether indeed 'it is the "real" rather than race that should be placed in quotation marks'

Transcriptome and membrane fatty acid analyses reveal different strategies for responding to permeating and non-permeating solutes in the bacterium Sphingomonas wittichii

ABSTRACT: BACKGROUND: Sphingomonas wittichii strain RW1 can completely oxidize dibenzo-p-dioxins and dibenzofurans, which are persistent contaminants of soils and sediments. For successful application in soil bioremediation systems, strain RW1 must cope with fluctuations in water availability, or water potential. Thus far, however, little is known about the adaptive strategies used by Sphingomonas bacteria to respond to changes in water potential. To improve our understanding, strain RW1 was perturbed with either the cell-permeating solute sodium chloride or the non-permeating solute polyethylene glycol with a molecular weight of 8000 (PEG8000). These solutes are assumed to simulate the solute and matric components of the total water potential, respectively. The responses to these perturbations were then assessed and compared using a combination of growth assays, transcriptome profiling, and membrane fatty acid analyses. RESULTS: Under conditions producing a similar decrease in water potential but without effect on growth rate, there was only a limited shared response to perturbation with sodium chloride or PEG8000. This shared response included the increased expression of genes involved with trehalose and exopolysaccharide biosynthesis and the reduced expression of genes involved with flagella biosynthesis. Mostly, the responses to perturbation with sodium chloride or PEG8000 were very different. Only sodium chloride triggered the increased expression of two ECF-type RNA polymerase sigma factors and the differential expression of many genes involved with outer membrane and amino acid metabolism. In contrast, only PEG8000 triggered the increased expression of a heat shock-type RNA polymerase sigma factor along with many genes involved with protein turnover and repair. Membrane fatty acid analyses further corroborated these differences. The degree of saturation of membrane fatty acids increased after perturbation with sodium chloride but had the opposite effect and decreased after perturbation with PEG8000. CONCLUSIONS: A combination of growth assays, transcriptome profiling, and membrane fatty acid analyses revealed that permeating and non-permeating solutes trigger different adaptive responses in strain RW1, suggesting these solutes affect cells in fundamentally different ways. Future work is now needed that connects these responses with the responses observed in more realistic scenarios of soil desiccation