Density stratified environments: The double-tank method

We present an alternative method of producing density stratifications in the laboratory based on the 'double-tank' method proposed by Oster (Sci Am 213:70-76, 1965). We refer to Oster's method as the 'forced-drain' approach, as the volume flow rates between connecting tanks are controlled by mechanical pumps. We first determine the range of density profiles that may be established with the forced-drain approach other than the linear stratification predicted by Oster. The dimensionless density stratification is expressed analytically as a function of three ratios: the volume flow rate ratio n, the ratio of the initial liquid volumes λ and the ratio of the initial densities ψ. We then propose a method which does not require pumps to control the volume flow rates but instead allows the connecting tanks to drain freely under gravity. This is referred to as the 'free-drain' approach. We derive an expression for the density stratification produced and compare our predictions with saline stratifications established in the laboratory using the 'free-drain' extension of Oster's method. To assist in the practical application of our results we plot the region of parameter space that yield concave/convex or linear density profiles for both forced-drain and free-drain approaches. The free-drain approach allows the experimentalist to produce a broad range of density profiles by varying the initial liquid depths, cross-sectional and drain opening areas of the tanks. One advantage over the original Oster approach is that density profiles with an inflexion point can now be established. © 2008 Springer-Verlag.

Collective motion: Bistability and trajectory tracking

This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to Instability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking.