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.

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.

In this paper, multi-disciplinary optimization techniques are applied to sail design. Two different mathematical models, providing the solution of the fluid-dynamic and the structural problems governing the behaviour of a complete sailplan, are coupled in a fluid-structure interaction (FSI) scheme, in order to determine the real flying shape of the sails and the forces acting on them. A numerical optimization algorithm is then applied, optimizing the structural pattern of the sailplan in order to maximize the driving force or other significant quantities.

Application of interpolation/approximation techniques (metamodels, for brevity) is commonly adopted in numerical optimization, typically to reduce the overall execution time of the optimization process. A limited number of trial solution are computed, cov- ering the design variable space: those trial points are then used for the determination of an estimate of the objective function in any desired location of the design space.

We present an algorithm to solve Netwon methods for nonlinear hypersingular integral equation of Prandtl's type with the help of GMRES .

Numerical simulations of vesicle suspensions are performed in two dimensions to study their dynamical and rheological properties. An hybrid method is adopted, which combines a mesoscopic approach for the solvent with a curvature-elasticity model for the membrane. Shear flow is induced by two counter-sliding parallel walls, which generate a linear flow profile. The flow behavior is studied for various vesicle concentrations and viscosity ratios between the internal and the external fluid.

Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 1950s with the Kierstead, Slobodkin, and Skellam (KiSS) model, namely a continuous reaction-diffusion equation for a population growing on a patch of finite size L surrounded by a deadly environment with infinite mortality, i.e., an oasis in a desert. The main outcome of the model is that only patches above a critical size allow for population persistence.

We present results from recent direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, with grid resolution up to 5123 and R? ? 185. By following the trajectories of millions of particles with different Stokes numbers, St ? [0.16 : 3.5], we are able to characterize in full detail the statistics of particle acceleration. We focus on the probability density function of the normalised acceleration a/arms and on the behaviour of their rootmean-squared acceleration arms as a function of both St and R?.

Multidimensional extensions of the Bernoulli and Appell polynomials are defined generalizing the corresponding generating functions, and using the Hermite-Kampe de Feriet (or Gould-Hopper) polynomials. Furthermore the differential equations satisfied by the corresponding 2D polynomials are derived exploiting the factorization method, introduced in [15].