160 research outputs found
The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is
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 A key identity
used in that proof was later generalised by Smirnov so as to apply to a general
O(n) loop model with (the case corresponding to SAWs).
We modify this model by restricting to a half-plane and introducing a surface
fugacity 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 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 , 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 , taken at its critical point , tends to 0 as
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 . 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 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
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
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