98 research outputs found
Stability analysis of a class of two-dimensional multipolar vortex equilibria
Published versio
Three-dimensional stability of Burgers vortices
Burgers vortices are explicit stationary solutions of the Navier-Stokes
equations which are often used to describe the vortex tubes observed in
numerical simulations of three-dimensional turbulence. In this model, the
velocity field is a two-dimensional perturbation of a linear straining flow
with axial symmetry. The only free parameter is the Reynolds number , where is the total circulation of the vortex and is
the kinematic viscosity. The purpose of this paper is to show that Burgers
vortex is asymptotically stable with respect to general three-dimensional
perturbations, for all values of the Reynolds number. This definitive result
subsumes earlier studies by various authors, which were either restricted to
small Reynolds numbers or to two-dimensional perturbations. Our proof relies on
the crucial observation that the linearized operator at Burgers vortex has a
simple and very specific dependence upon the axial variable. This allows to
reduce the full linearized equations to a vectorial two-dimensional problem,
which can be treated using an extension of the techniques developped in earlier
works. Although Burgers vortices are found to be stable for all Reynolds
numbers, the proof indicates that perturbations may undergo an important
transient amplification if is large, a phenomenon that was indeed observed
in numerical simulations.Comment: 31 pages, no figur
Scaling Limits for Internal Aggregation Models with Multiple Sources
We study the scaling limits of three different aggregation models on Z^d:
internal DLA, in which particles perform random walks until reaching an
unoccupied site; the rotor-router model, in which particles perform
deterministic analogues of random walks; and the divisible sandpile, in which
each site distributes its excess mass equally among its neighbors. As the
lattice spacing tends to zero, all three models are found to have the same
scaling limit, which we describe as the solution to a certain PDE free boundary
problem in R^d. In particular, internal DLA has a deterministic scaling limit.
We find that the scaling limits are quadrature domains, which have arisen
independently in many fields such as potential theory and fluid dynamics. Our
results apply both to the case of multiple point sources and to the
Diaconis-Fulton smash sum of domains.Comment: 74 pages, 4 figures, to appear in J. d'Analyse Math. Main changes in
v2: added "least action principle" (Lemma 3.2); small corrections in section
4, and corrected the proof of Lemma 5.3 (Lemma 5.4 in the new version);
expanded section 6.
Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering
Bacterial processes ranging from gene expression to motility and biofilm
formation are constantly challenged by internal and external noise. While the
importance of stochastic fluctuations has been appreciated for chemotaxis, it
is currently believed that deterministic long-range fluid dynamical effects
govern cell-cell and cell-surface scattering - the elementary events that lead
to swarming and collective swimming in active suspensions and to the formation
of biofilms. Here, we report the first direct measurements of the bacterial
flow field generated by individual swimming Escherichia coli both far from and
near to a solid surface. These experiments allowed us to examine the relative
importance of fluid dynamics and rotational diffusion for bacteria. For
cell-cell interactions it is shown that thermal and intrinsic stochasticity
drown the effects of long-range fluid dynamics, implying that physical
interactions between bacteria are determined by steric collisions and
near-field lubrication forces. This dominance of short-range forces closely
links collective motion in bacterial suspensions to self-organization in driven
granular systems, assemblages of biofilaments, and animal flocks. For the
scattering of bacteria with surfaces, long-range fluid dynamical interactions
are also shown to be negligible before collisions; however, once the bacterium
swims along the surface within a few microns after an aligning collision,
hydrodynamic effects can contribute to the experimentally observed, long
residence times. As these results are based on purely mechanical properties,
they apply to a wide range of microorganisms.Comment: 9 pages, 2 figures, http://www.pnas.org/content/108/27/1094
Boundaries can steer active Janus spheres
The advent of autonomous self-propulsion has instigated research towards making colloidal machines that can deliver mechanical work in the form of transport, and other functions such as sensing and cleaning. While much progress has been made in the last 10 years on various mechanisms to generate self-propulsion, the ability to steer self-propelled colloidal devices has so far been much more limited. A critical barrier in increasing the impact of such motors is in directing their motion against the Brownian rotation, which randomizes particle orientations. In this context, here we report directed motion of a specific class of catalytic motors when moving in close proximity to solid surfaces. This is achieved through active quenching of their Brownian rotation by constraining it in a rotational well, caused not by equilibrium, but by hydrodynamic effects. We demonstrate how combining these geometric constraints can be utilized to steer these active colloids along arbitrary trajectories
Disparate SAR Data of Griseofulvin Analogues for the Dermatophytes Trichophyton mentagrophytes, T. rubrum, and MDA-MB-231 Cancer Cells
Generalized Contour Dynamics: A Review
Contour dynamics is a computational technique to solve for the motion of vortices in incompressible inviscid flow. It is a Lagrangian technique in which the motion of contours is followed, and the velocity field moving the contours can be computed as integrals along the contours. Its best-known examples are in two dimensions, for which the vorticity between contours is taken to be constant and the vortices are vortex patches, and in axisymmetric flow for which the vorticity varies linearly with distance from the axis of symmetry. This review discusses generalizations that incorporate additional physics, in particular, buoyancy effects and magnetic fields, that take specific forms inside the vortices and preserve the contour dynamics structure. The extra physics can lead to time-dependent vortex sheets on the boundaries, whose evolution must be computed as part of the problem. The non-Boussinesq case, in which density differences can be important, leads to a coupled system for the evolution of both mean interfacial velocity and vortex sheet strength. Helical geometry is also discussed, in which two quantities are materially conserved and whose evolution governs the flow
- …