The buffered chemostat with non-monotonic response functions

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.Comment: 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Toulouse : France (2013

A modeling approach of the chemostat

Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit this approach by complementing these classic formalisms by stochastic formalisms and to explain the links between these representations in terms of mathematical analysis but also in terms of modeling and numerical simulations. We illustrate this approach on the model of chemostat.Comment: arXiv admin note: substantial text overlap with arXiv:1308.241

Minimal-time bioremediation of natural water resources

We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate. We first characterize the optimal policies among constant and feedback controls, under the assumption of a uniform concentration in the resource. In a second part, we study the influence of an inhomogeneity in the resource, considering two measurements points. With the help of the Maximum Principle, we show that the optimal control law is non-monotonic and terminates with a constant phase, contrary to the homogeneous case for which the optimal flow rate is decreasing with time. This study allows the decision makers to identify situations for which the benefit of using non-constant flow rates is significant

Why does wurtzite form in nanowires of III-V zinc-blende semiconductors?

We develop a nucleation-based model to explain the formation of the wurtzite (WZ) crystalline phase during the vapor-liquid-solid growth of free-standing nanowires of zinc-blende (ZB) semiconductors. We first show that, in nanowires, nucleation generally occurs at the outer edge of the solid/liquid interface (the triple phase line) rather than elsewhere at the solid/liquid interface. In the present case, this entails major differences between ZB and WZ nuclei. Depending on the pertinent interface energies, WZ nucleation is favored at high liquid supersaturation. This explains our systematic observation of ZB during the early stages of nanowire growth.Comment: 4 pages with 4 figures Submitted to Physical Review Letter