Potential-flow models for channelled two-dimensional premixed flames around near-circular obstacles.

The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity free. Flames confined in channels with asymptotically straight impenetrable walls are considered. Besides a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle or near two symmetric bumps protruding inward. Combining conformal maps and Green's functions, a regularized generalization of Frankel's integro-differential equation for the instantaneous front shape in each configuration is derived and solved numerically. This produces a variety of real looking phenomena: steady fronts (symmetric or not), noise-induced subwrinkles, flashback events, and breathing fronts in pulsating flows. Perspectives and open mathematical and physical problems are finally evoked.

Diamond patterns in the cellular front of an overdriven detonation.

A nonlinear integral-differential equation describing the cellular front of an overdriven detonation is obtained by an analysis carried out in the neighborhood of the instability threshold. The analysis reveals both an unusual mean streaming motion, resulting from the rotational part of the oscillatory flow, and pressure bursts generated by the crossover of cusps representative of Mach stems propagating on the detonation front. A numerical study of the nonlinear equation exhibits the "diamond" patterns observed in experiments. An overall physical understanding is provided.

Quantitative analysis of concentration gradient and ionic currents associated with hyphal tip growth in fungi.

It has been shown previously that the nutrient gradient generated by a tip growing elongated cell induces an ionic current entering the cell tip and looping back in the extracellular medium [L. Limozin, B. Denet and P. Pelcé, Phys. Rev. Lett. 78, 4881 (1997)]. We apply this mechanism to the case of hyphae of fungi, using realistic cell geometries, symport kinetics, proton pump permeabilities, and buffer concentrations. We show that this mechanism contributes to a noticeable part of the external current intensity, related inner electrical field and pH gradient, in agreement with experimental measurements. This provides a good example in biological cells of interaction between shape and field, a common property of growing nonliving systems, such as crystalline dendrites or electrodeposition.