Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

We compute the generating functions of a O(n) model (loop gas model) on a random lattice of any topology. On the disc and the cylinder, they were already known, and here we compute all the other topologies. We find that the generating functions (and the correlation functions of the lattice) obey the topological recursion, as usual in matrix models, i.e they are given by the symplectic invariants of their spectral curve.Comment: pdflatex, 89 pages, 12 labelled figures (15 figures at all), minor correction

Dielectrophoresis-Driven Spreading of Immersed Liquid Droplets

In recent years electrowetting-on-dielectric (EWOD) has become an effective tool to control partial wetting. EWOD uses the liquid−solid interface as part of a capacitive structure that allows capacitive and interfacial energies to adjust by changes in wetting when the liquid−solid interface is charged due to an applied voltage. An important aspect of EWOD has been its applications in micro fluidics in chemistry and biology and in optical devices and displays in physics and engineering. Many of these rely on the use of a liquid droplet immersed in a second liquid due to the need either for neutral buoyancy to overcome gravity and shield against impact shocks or to encapsulate the droplet for other reasons, such as in microfluidic-based DNA analyses. Recently, it has been shown that nonwetting oleophobic surfaces can be forcibly wetted by nonconducting oils using nonuniform electric fields and an interface-localized form of liquid dielectrophoresis (dielectrowetting). Here we show that this effect can be used to create films of oil immersed in a second immiscible fluid of lower permittivity. We predict that the square of the thickness of the film should obey a simple law dependent on the square of the applied voltage and with strength dependent on the ratio of difference in permittivity to the liquid-fluid interfacial tension, Δε/γLF. This relationship is experimentally confirmed for 11 liquid−air and liquid−liquid combinations with Δε/γLF having a span of more than two orders of magnitude. We therefore provide fundamental understanding of dielectrowetting for liquid-in-liquid systems and also open up a new method to determine liquid−liquid interfacial tensions

Kinetic Inductance of Josephson Junction Arrays: Dynamic and Equilibrium Calculations

We show analytically that the inverse kinetic inductance $L^{-1}$ of an overdamped junction array at low frequencies is proportional to the admittance of an inhomogeneous equivalent impedance network. The $ij^{th}$ bond in this equivalent network has an inverse inductance $J_{ij}\cos(\theta_i^0-\theta_j^0-A_{ij})$, where $J_{ij}$ is the Josephson coupling energy of the $ij^{th}$ bond, $\theta_i^0$ is the ground-state phase of the grain $i$, and $A_{ij}$ is the usual magnetic phase factor. We use this theorem to calculate $L^{-1}$ for square arrays as large as $180\times 180$. The calculated $L^{-1}$ is in very good agreement with the low-temperature limit of the helicity modulus $\gamma$ calculated by conventional equilibrium Monte Carlo techniques. However, the finite temperature structure of $\gamma$, as a function of magnetic field, is \underline{sharper} than the zero-temperature $L^{-1}$, which shows surprisingly weak structure. In triangular arrays, the equilibrium calculation of $\gamma$ yields a series of peaks at frustrations $f = \frac{1}{2}(1-1/N)$, where $N$ is an integer $\geq 2$, consistent with experiment.Comment: 14 pages + 6 postscript figures, 3.0 REVTe

Roughening Transition in a One-Dimensional Growth Process

A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is non-conserving. Some aspects of models in this class are related to directed percolation in 1+1 dimensions, although unlike directed percolation the models have no absorbing states. Scaling relations are derived and compared with Monte Carlo simulations.Comment: 4 pages, 3 Postscript figures, 1 Postscript formula, uses RevTe

Belief-propagation algorithm and the Ising model on networks with arbitrary distributions of motifs

We generalize the belief-propagation algorithm to sparse random networks with arbitrary distributions of motifs (triangles, loops, etc.). Each vertex in these networks belongs to a given set of motifs (generalization of the configuration model). These networks can be treated as sparse uncorrelated hypergraphs in which hyperedges represent motifs. Here a hypergraph is a generalization of a graph, where a hyperedge can connect any number of vertices. These uncorrelated hypergraphs are tree-like (hypertrees), which crucially simplify the problem and allow us to apply the belief-propagation algorithm to these loopy networks with arbitrary motifs. As natural examples, we consider motifs in the form of finite loops and cliques. We apply the belief-propagation algorithm to the ferromagnetic Ising model on the resulting random networks. We obtain an exact solution of this model on networks with finite loops or cliques as motifs. We find an exact critical temperature of the ferromagnetic phase transition and demonstrate that with increasing the clustering coefficient and the loop size, the critical temperature increases compared to ordinary tree-like complex networks. Our solution also gives the birth point of the giant connected component in these loopy networks.Comment: 9 pages, 4 figure

Orientations, lattice polytopes, and group arrangements II: Modular and integral flow Polynomials of graphs

We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory of Ehrhart polynomials to obtain properties of modular and integral flow polynomials. The emphasis is on the geometrical treatment through subgroup arrangements and Ehrhart polynomials. Such viewpoint leads to a reciprocity law on the modular flow polynomial, which gives rise to an interpretation on the values of the modular flow polynomial at negative integers and answers a question by Beck and Zaslavsky.Regal Entertainment Group (Competitive Earmarked Research Grants 600703)Regal Entertainment Group (Competitive Earmarked Research Grants 600506)Regal Entertainment Group (Competitive Earmarked Research Grants 600608

Evaluation of repeated electrowetting on three different fluoropolymer top coatings

Degradation of the electrowetting effect by a repeated actuation is evaluated over an extended period (200 min) on electrowetting-on-dielectric samples for three popular fluoropolymer top coatings: Teflon, FluoroPel and Cytop. A conductive liquid droplet is tested in an air environment at electrowetting number Ew ≅ 0.34. A pulse train (6 s period and 50% duty cycle) of three different voltage types is used for the actuation: positive dc, negative dc and 1 kHz ac. For the dc actuations, electrowetting degrades gradually on Cytop but significantly faster on Teflon and FluoroPel under the tested conditions. For the ac actuation, electrowetting degrades gradually on all three materials in a similar fashion. © 2013 IOP Publishing Ltd

Shadowing, Binding and Off-Shell Effects in Nuclear Deep Inelastic Scattering

We present a unified description of nuclear deep inelastic scattering (DIS) over the whole region $0<x<1$ of the Bjorken variable. Our approach is based on a relativistically covariant formalism which uses analytical properties of quark correlators. In the laboratory frame it naturally incorporates two mechanisms of DIS: (I) scattering from quarks and antiquarks in the target and (II) production of quark-antiquark pairs followed by interactions with the target. We first calculate structure functions of the free nucleon and develop a model for the quark spectral functions. We show that mechanism (II) is responsible for the sea quark content of the nucleon while mechanism (I) governs the valence part of the nucleon structure functions. We find that the coherent interaction of $\bar qq$ pairs with nucleons in the nucleus leads to shadowing at small $x$ and discuss this effect in detail. In the large $x$ region DIS takes place mainly on a single nucleon. There we focus on the derivation of the convolution model. We point out that the off-shell properties of the bound nucleon structure function give rise to sizable nuclear effects.Comment: 29 pages (and 10 figures available as hard copies from Authors), REVTE

Phase diagram of the restricted solid-on-solid model coupled to the Ising model

We study the phase transitions of a restricted solid-on-solid model coupled to an Ising model, which can be derived from the coupled XY-Ising model. There are two kinds of phase transition lines. One is a Ising transition line and the other is surface roughening transition line. The latter is a KT transition line from the viewpoint of the XY model. Using a microcanonical Monte Carlo technique, we obtain a very accurate two dimensional phase diagram. The two transition lines are separate in all the parameter space we study. This result is strong evidence that the fully frustrated XY model orders by two separate transitions and that roughening and reconstruction transitions of crystal surfaces occur separately.Comment: 17 pages, source RevTeX file and 8 PS figures are tarred and compressed via uufile

Periostin:contributor to abnormal airway epithelial function in asthma?

Periostin may serve as a biomarker for type-2-mediated eosinophilic airway inflammation in asthma. We hypothesised that type-2 cytokine IL-13 induces airway epithelial expression of periostin, which in turn contributes to epithelial changes observed in asthma.We studied the effect of IL-13 on periostin expression in BEAS-2B and air-liquid interface (ALI)-differentiated primary bronchial epithelial cells (PBECs). Additionally, effects of recombinant human periostin on epithelial-to-mesenchymal transition (EMT) markers and mucin genes were assessed. In bronchial biopsies and induced sputum from asthma patients and healthy controls, we analysed periostin single cell gene expression and protein levels.IL-13 increased POSTN expression in both cell types, which was accompanied by EMT-related features in BEAS-2B. In ALI-differentiated PBECs, IL-13 increased periostin basolateral and apical release. Apical administration of periostin increased the expression of MMP9, MUC5B and MUC5AC In bronchial biopsies, POSTN expression was mainly confined to basal epithelial cells, ionocytes, endothelial cells and fibroblasts, showing higher expression in basal epithelial cells from asthma patients versus controls. Higher protein levels of periostin, expressed in epithelial and subepithelial layers, was confirmed in bronchial biopsies from asthma patients compared to healthy controls. Although sputum periostin levels were not higher in asthma, levels correlated with eosinophil numbers and coughing up mucus.Periostin expression is increased by IL-13 in bronchial epithelial cells and higher in bronchial biopsies from asthma patients. This may have important consequences, as administration of periostin increased epithelial expression of mucin genes, supporting the relationship of periostin with type-2 mediated asthma and mucus secretion