The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

Stochastic processes and conformal invariance

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the $c=0$ conformal field theory of percolation. This implies in a rigorous way a connection between CFT and stochastic processes. The finite-size scaling behavior of the average height, interface width and other observables are obtained. The avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents.Comment: 4 pages, 6 figures, revtex4. v2: change of title and minor correction

Carreau fluid in a wall driven corner flow

Taylor’s classical paint scraping problem provides a framework for analyzing wall-driven corner flow induced by the movement of an oblique plane with a fixed velocity U. A study of the dynamics of the inertialess limit of a Carreau fluid in such a system is presented. New perturbation results are obtained both close to, and far from, the corner. When the distance from the corner r is much larger than UΓ , where Γ is the relaxation time, a loss of uniformity arises in the solution near the region, where the shear rate becomes zero due to the presence of the two walls. We derive a new boundary layer equation and find two regions of widths r−nr−n and r−2,r−2, where r is the distance from the corner and n is the power-law index, where a change in behavior occurs. The shear rate is found to be proportional to the perpendicular distance from the line of zero shear. The point of zero shear moves in the layer of size r−2r−2. We also find that Carreau effects in the far-field are important for corner angles less than 2.2 rad

Oscillatory oblique stagnation-point flow toward a plane wall

Two-dimensional oscillatory oblique stagnation-point flow toward a plane wall is investigated. The problem is a eneralisation of the steady oblique stagnation-point flow examined by previous workers. Far from the wall, the flow is composed of an irrotational orthogonal stagnation-point flow with a time-periodic strength, a simple shear flow of constant vorticity, and a time-periodic uniform stream. An exact solution of the Navier-Stokes equations is sought for which the flow streamfunction depends linearly on the coordinate parallel to the wall. The problem formulation reduces to a coupled pair of partial differential equations in time and one spatial variable. The first equation describes the oscillatory orthogonal stagnation-point flow discussed by previous workers. The second equation, which couples to the first, describes the oblique component of the flow. A description of the flow velocity field, the instantaneous streamlines, and the particle paths is sought through numerical solutions of the governing equations and via asymptotic analysis

Numerical and experimental investigations of three-dimensional container filling with Newtonian viscous fluids

This work employs numerical and experimental approaches to investigate three-dimensional container filling with Newtonian viscous fluids. For this purpose, a computer code developed for simulating three-dimensional free surface flows has been used. The CFD Freeflow3D code was specifically designed to deal with unsteady three-dimensional flows possessing multiple moving free surfaces. An experimental apparatus that allows the visualization of the various phenomena that can occur during the filling of containers has been constructed and employed. Experiments on container filling were carried out by varying the fluid velocity at the injection nozzle. This paper presents a computational study on container filling with Newtonian viscous fluids and employs the experimental results to validate the software. The experimental observations were compared with the predictions from the Freeflow3D code and good agreement between the two sets of results is observed. Moreover, the code predictions showed that it is capable of capturing the most relevant phenomena observed in the experiments.The Brazilian authors would like to acknowledge the financial support given by the funding agencies: CNPq - Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (Grant Nos. 302631/2010-0, 301408/2009-2, 472514/2011-3), FAPESP - Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (Grant No. 2011/13930-0) and CAPES Grant Nos. BEX 2844/10-9 and 226/09 (CAPES-FCT). This work is part of the activities developed within the CEPID-CeMEAI FAPESP project Grant No. 2013/07375 - 0 and also benefits from the early collaboration within the framework of the University of Sao Paulo (Brazil) and University of Porto (Portugal) research agreements. The Portuguese authors gratefully acknowledge funding from Fundacao para a Ciencia e Tecnologia (FCT) under the project PEst-C/CTM/LA0025/2013 (Strategic Project - LA 25-2013-2014), project PTDC/MAT/121185/2010 and FEDER, via FCT

Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the Reynolds number

The streamwise and transverse velocities are measured simultaneously in isotropic grid turbulence at relatively high Reynolds numbers, Re(lambda) = 110-330. Using a conditional averaging technique, we extract typical intermittency patterns, which are consistent with velocity profiles of a model for a vortex tube, i.e., Burgers vortex. The radii of the vortex tubes are several of the Kolmogorov length regardless of the Reynolds number. Using the distribution of an interval between successive enhancements of a small-scale velocity increment, we study the spatial distribution of vortex tubes. The vortex tubes tend to cluster together. This tendency is increasingly significant with the Reynolds number. Using statistics of velocity increments, we also study the energetical importance of vortex tubes as a function of the scale. The vortex tubes are important over the background flow at small scales especially below the Taylor microscale. At a fixed scale, the importance is increasingly significant with the Reynolds number.Comment: 8 pages, 3 PS files for 8 figures, to appear in Physical Review

Stochastic model for the dynamics of interacting Brownian particles

Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance equations. We obtain expressions for the heat flux and the pressure tensor which enable one to describe the kinetic and potential energy interchange of the particles with the heat bath. Through the momentum balance we analyze in particular the diffusion regime to obtain the collective diffusion coefficient in terms of the hydrodynamic and the effective forces acting on the Brownian particles.Comment: latex fil

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts

Random noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections

The empirical origin of random noise is described, its influence on DTI variables is illustrated by a review of numerical and in vivo studies supplemented by new simulations investigating high noise levels. A stochastic model of noise propagation is presented to structure noise impact in DTI. Finally, basics of voxelwise and spatial denoising procedures are presented. Recent denoising procedures are reviewed and consequences of the stochastic model for convenient denoising strategies are discussed