In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts.

Flood area detection from multipass Synthetic Aperture Radar (SAR) data can be performed via amplitude change detection techniques. These methods allow flooded zones to be discriminated only when they are flooded at the time of the second passage, and not at the time of the first one. Coherence derived from multipass SAR interferometry can be used instead, as an indicator of changes in the electromagnetic scattering behaviour of the surface, thus potentially revealing all the areas affected by the flood event at any time between the two passes.

This paper presents an approach to model and simulate industrial plant accidents as well as the related emergency management; interoperable simulation is proposed as approach for applying High Level Architecture in this context. The authors are focusing their attention on the disaster simulation and its interaction with the emergency management.

We consider Volterra integral equations on time scales and present our study about the long time behavior of their solutions. We provide sufficient conditions for the stability and investigate the convergence properties when the kernel of the equations vanishes at infinity.

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum.

Distributions of heavy particles suspended in incompressible turbulent flows are investigated by means of high-resolution direct numerical simulations. It is shown that particles form fractal clusters in the dissipative range, with properties independent of the Reynolds number. Conversely, in the inertial range, the particle distribution is not scale-invariant. It is however shown that deviations from uniformity depends only on a rescaled contraction rate, and not on the local Stokes number given by dimensional analysis.

While drawing a link between the papers contained in this issue and those present in a previous one (Vol. 2, Issue 3), this introductory article aims at putting in evidence some trends and challenges on cancer modelling, especially related to the development of multiphase and multiscale models. © EDP Sciences, 2009.