Vortex crystals

Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.published or submitted for publicationis peer reviewe

A pulsed source-sink fluid mixing device,

Abstract-Efficient fluid mixing can be achieved in a high-aspect-ratio volume by periodically pulsing an arrangement of source-sink pairs. In order to conserve fluid and promote mixing, the fluid extracted through a sink is subsequently injected through a source. We present an implementation of this approach that consists of a disposable chip with embedded microchannels and external fluidic control. When both the mixing chamber geometry and the source-sink arrangement are fixed, mixing is controlled by choosing , the fraction of the mixing chamber volume that is exchanged with each pulse. Experimental results in a rectangular chamber show that the value of has a significant effect on mixing efficiency. This device shows promise for enhancing the performance of massively parallel sensing systems such as DNA microarrays. [1592

Topological fluid mechanics of point vortex motions

Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. Restricting to three vortices with zero net circulation, the symmetries are used to reduce each system to a one-degree-of-freedom Hamiltonian. The phase portrait of the reduced system is subdivided into regimes using the separatrix motions, and a braid representing the topology of all vortex motions in each regime is computed. This braid also describes the isotopy class of the advection homeomorphism induced by the vortex motion. The Thurston???Nielsen theory is then used to analyze these isotopy classes, and in certain cases strong implications about the chaotic dynamics of the advection can be drawn. This points to an important mechanism by which the topological kinematics of large-scale, two-dimensional fluid motions generate chaotic advection.published or submitted for publicationis peer reviewe