The Local Time Distribution of a Particle Diffusing on a Graph

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included

Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

Intercultural communication - integration potential in teaching foreign students

Detailed investigation of the morphology of the pore space in clay is a key factor in understanding the sealing capacity, coupled flows, capillary processes and associated deformation present in mudstones. Actually, the combination of ion milling tools (FIB and BIB), cryogenic techniques and SEM imaging offers a new alternative to study in-situ elusive microstructures in wet geomaterials and has the high potential to make a step change in our understanding of how fluids occur in pore space. By using this range of techniques, it is possible to quantify porosity, stabilize in-situ fluids in pore space, preserve the natural structures at nm-scale, produce high quality polished cross-sections for high resolution SEM imaging and reconstruct accurately microstructure networks in 3D by serial cross sectioning

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.Comment: 21 pages, 4 color figure

Scars on quantum networks ignore the Lyapunov exponent

We show that enhanced wavefunction localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical Lyapunov exponent. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation ratios.Comment: 5 pages, 2 figure

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps 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

Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each link. We establish the boundary conditions to be used at the vertices and we derive general expressions for the average time spent on a part of the graph before absorption and, also, for the Laplace transform of the joint law of the occupation times. Exit times distributions and splitting probabilities are also studied and several examples are discussed.Comment: Accepted for publication in J. Phys.

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

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