Universal and Non-Universal First-Passage Properties of Planar Multipole Flows

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability, $p(t)$, exhibits power-law decay with a velocity-dependent exponent in radial flow and an order-dependent exponent in multipolar flows. For the latter, there also occur diffusive ``echo'' shoulders and exponential decays associated with stagnation points in the flow. For spatially extended dipole sinks, the spatial distribution of the collected tracer is independent of the overall magnitude of the flow field.Comment: 7 pages, LaTe

Lattice-Boltzmann Method for Non-Newtonian Fluid Flows

We study an ad hoc extension of the Lattice-Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear-rate is no-longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution

Hybrid method for simulating front propagation in reaction-diffusion systems

We study the propagation of pulled fronts in the $A \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we concentrate on the corrections to the deterministic behavior due to the number of particles per site $\Omega$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\Omega$ which allows us to show the importance in the dynamics of microscopic pulled fronts of the interplay of microscopic fluctuations and their macroscopic relaxation.Comment: 5 pages, 4 figure

Velocity of vortices in inhomogeneous Bose-Einstein condensates

We derive, from the Gross-Pitaevskii equation, an exact expression for the velocity of any vortex in a Bose-Einstein condensate, in equilibrium or not, in terms of the condensate wave function at the center of the vortex. In general, the vortex velocity is a sum of the local superfluid velocity, plus a correction related to the density gradient near the vortex. A consequence is that in rapidly rotating harmonically trapped Bose-Einstein condensates, unlike in the usual situation in slowly rotating condensates and in hydrodynamics, vortices do not move with the local fluid velocity. We indicate how Kelvin's conservation of circulation theorem is compatible with the velocity of the vortex center being different from the local fluid velocity. Finally we derive an exact wave function for a single vortex near the rotation axis in a weakly interacting system, from which we derive the vortex precession rate.Comment: 5 pages, one .eps figure. Published versio

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

Nanoscale fluid flows in the vicinity of patterned surfaces

Molecular dynamics simulations of dense and rarefied fluids comprising small chain molecules in chemically patterned nano-channels predict a novel switching from Poiseuille to plug flow along the channel. We also demonstrate behavior akin to the lotus effect for a nanodrop on a chemically patterned substrate. Our results show that one can control and exploit the behavior of fluids at the nanoscale using chemical patterning.Comment: Phys. Rev. Lett. in pres

Molecular scale contact line hydrodynamics of immiscible flows

From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard interfacial free energy. Our hydrodynamic model yields interfacial and velocity profiles matching those from the molecular dynamics simulations at the molecular-scale vicinity of the contact line. In particular, the behavior at high capillary numbers, leading to the breakup of the fluid-fluid interface, is accurately predicted.Comment: 33 pages for text in preprint format, 10 pages for 10 figures with captions, content changed in this resubmissio

Boundary conditions at a fluid - solid interface

We study the boundary conditions at a fluid-solid interface using molecular dynamics simulations covering a broad range of fluid-solid interactions and fluid densities, and both simple and chain-molecule fluids. The slip length is shown to be independent of the type of flow, but rather is related to the fluid organization near the solid, as governed by the fluid-solid molecular interactions.Comment: REVtex, to appear in Physical Review Letter

Two dimensional fermions in three dimensional YM

Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table