Topological relaxation of entangled flux lattices: Single vs collective line dynamics

A symbolic language allowing to solve statistical problems for the systems with nonabelian braid-like topology in 2+1 dimensions is developed. The approach is based on the similarity between growing braid and "heap of colored pieces". As an application, the problem of a vortex glass transition in high-T_c superconductors is re-examined on microscopic levelComment: 4 pages (revtex), 4 figure

Numerical studies of planar closed random walks

Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension $d_H=4/3$. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension $d_H\approx 1.77$.Comment: 15 pages, 15 figure

Area distribution of two-dimensional random walks on a square lattice

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A particular case generalizes the q-binomial theorem to the case of three addends. The distribution fits the L\'evy probability distribution for Brownian curves with its first-order 1/N correction quite well, even for N rather small.Comment: 8 pages, LaTeX 2e. Reformulated in terms of q-commutator

Release of chromatin extracellular traps by phagocytes of Atlantic salmon, Salmo salar (LINNAEUS, 1758)

Neutrophils release chromatin extracellular traps (ETs) as part of the fish innate immune response to counter the threats posed by microbial pathogens. However, relatively little attention has been paid to this phenomenon in many commercially farmed species, despite the importance of understanding host-pathogen interactions and the potential to influence ET release to reduce disease outbreaks. The aim of this present study was to investigate the release of ETs by Atlantic salmon (Salmo salar L.) immune cells. Extracellular structures resembling ETs of different morphology were observed by fluorescence microscopy in neutrophil suspensions in vitro, as these structures stained positively with Sytox Green and were digestible with DNase I. Immunofluorescence studies confirmed the ET structures to be decorated with histones H1 and H2A and neutrophil elastase, which are characteristic for ETs in mammals and other organisms. Although the ETs were released spontaneously, release in neutrophil suspensions was stimulated most significantly with 5 μg/ml calcium ionophore (CaI) for 1 h, whilst the fish pathogenic bacterium Aeromonas salmonicida (isolates 30411 and Hooke) also exerted a stimulatory effect. Microscopic observations revealed bacteria in association with ETs, and fewer bacterial colonies of A. salmonicida Hooke were recovered at 3 h after co-incubation with neutrophils that had been induced to release ETs. Interestingly, spontaneous release of ETs was inversely associated with fish mass (p  < 0.05), a surrogate for age. Moreover, suspensions enriched for macrophages and stimulated with 5 μg/ml CaI released ET-like structures that occasionally led to the formation of large clumps of cells. A deeper understanding for the roles and functions of ETs within innate immunity of fish hosts, and their interaction with microbial pathogens, may open new avenues towards protecting cultured stocks against infectious diseases

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published in PRB. Replaced to repair figure

Zeta functions of quantum graphs

In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process it is convenient to work with new forms for the secular equation of a quantum graph that extend the well known secular equation of the Neumann star graph. In the second half of the article we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.Comment: 32 pages, typos corrected, references adde

Elementary derivation of Spitzer's asymptotic law for Brownian windings and some of its physical applications

A simple derivation of Spitzer'z asymptotic law for Brownian windings [Trans.Am.Math.Soc.87,187 (1958)]is presented along with its generalizations >.These include the cases of planar Brownian walks interacting with a single puncture and Brownian walks on a single truncated cone with variable conical angle interacting with the truncated conical tip.Such situations are typical in the theories of quantum Hall effect and 2+1 quantum gravity, respectively .They also have some applications in polymer physic

Geometric Exponents, SLE and Logarithmic Minimal Models

In statistical mechanics, observables are usually related to local degrees of freedom such as the Q < 4 distinct states of the Q-state Potts models or the heights of the restricted solid-on-solid models. In the continuum scaling limit, these models are described by rational conformal field theories, namely the minimal models M(p,p') for suitable p, p'. More generally, as in stochastic Loewner evolution (SLE_kappa), one can consider observables related to nonlocal degrees of freedom such as paths or boundaries of clusters. This leads to fractal dimensions or geometric exponents related to values of conformal dimensions not found among the finite sets of values allowed by the rational minimal models. Working in the context of a loop gas with loop fugacity beta = -2 cos(4 pi/kappa), we use Monte Carlo simulations to measure the fractal dimensions of various geometric objects such as paths and the generalizations of cluster mass, cluster hull, external perimeter and red bonds. Specializing to the case where the SLE parameter kappa = 4p'/p is rational with p < p', we argue that the geometric exponents are related to conformal dimensions found in the infinitely extended Kac tables of the logarithmic minimal models LM(p,p'). These theories describe lattice systems with nonlocal degrees of freedom. We present results for critical dense polymers LM(1,2), critical percolation LM(2,3), the logarithmic Ising model LM(3,4), the logarithmic tricritical Ising model LM(4,5) as well as LM(3,5). Our results are compared with rigourous results from SLE_kappa, with predictions from theoretical physics and with other numerical experiments. Throughout, we emphasize the relationships between SLE_kappa, geometric exponents and the conformal dimensions of the underlying CFTs.Comment: Added reference

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde