A set oriented approach to global optimal control

We describe an algorithm for computing the value function for 'all source, single destination' discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem on a finite graph. The method is illustrated by two numerical examples, namely a single pendulum on a cart and a parametrically driven inverted double pendulum

Epizoic acoelomorph flatworms compete with their coral host for zooplankton

Satisfying nutrient requirement of corals is still a major constraint for maintaining corals in marine aquariums. Corals are polytrophic in nature. Heterotrophic feeding on zooplankton is one of the corals’ strategies to overcome nutrient deficiency. Artemia salina nauplii are commonly used as biocarriers for many fish larvae in aquaculture and can also serve as a biocarrier for coral in aquariums, provided coral acceptability, optimal feeding rate, and digestibility of the nauplii are well understood. Feeding rate and digestibility of coral fed on A. salina nauplii at 100, 2,000, 4,000, 6,000, and 10,000 ind. l-1 under light and dark conditions was assessed in this study. The maximum feeding rates of Galaxea fascicularis under light and dark conditions was 113.6 ind. polyp-1 h-1 and 76.9 ind. polyp-1 h-1, respectively. The daily feeding rates of G. fascicularis varies and depends on nauplii density. Light plays an important role in coral feeding. Nevertheless, the quantity of A. salina nauplii consumed by the coral under light and dark conditions was not significantly different (P > 0.05). A. salina nauplii are well accepted by G. fascicularis. Complete nauplii digestion was observed after 180 min. Digestibility of A. salina nauplii by G. fascicularis was positively correlated with digestion time

Visualizing the transition to chaos in the Lorenz system

The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of the global stable and unstable manifolds in organising the dynamics. More precisely, for the standard system parameters, the origin has a two-dimensional stable manifold and the other two equilibria each have a two-dimensional unstable manifold. The intersections of these manifolds in the three-dimensional phase space form heteroclinic connections from the nontrivial equilibria to the origin. A parameter-dependent visualization of these manifolds clarifies the transition to chaos in the Lorenz syste

Impulse/response functions of individual components of flow-injection manifolds

The dispersion behaviour of the various individual parts making up a flow-injection manifold is often difficult to establish because it is virtually impossible to obtainthe required very small injection and detection volumes. It is shown that it is possible, under suitable experimental conditions, to find the impulse/response functionof each component by means of a deconvolution process of the response functions have been established, the response function of any arrangement can be predicted by convoluting the impulse/response functions of all the individuaol parts involved. Convolution and deconvolution were done in the Fourier domain, by using a fast FT algorithm