A model problem of the flow under an air-cushion vessel is studied. Two different numerical techniques are used to determine the solution of the free-surface elevation and the wave resistance for a range of Froude number, Reynolds number, value of the pressure applied in the cushion, and depth of the water. The first numerical technique uses a velocity potential that satisfies linearized free-surface boundary conditions, whereas the second employs a finite-volume method to find a solution that satisfies the fully nonlinear free-surface boundary conditions. The results clearly show that for high Froude number and practical values of the cushion pressure, the linear-theory solution is in excellent agreement with the more exact nonlinear prediction. For lower Froude number the solution becomes unsteady, and the disagreement between the two methods is larger.

In this paper we present a functional Bayesian method for detecting genes which are temporally differentially expressed between several conditions. We identify the nature of differential expression (e.g., gene is differentially expressed between the first and the second sample but is not differentially expressed between the second and the third) and subsequently we estimate gene expression temporal profiles. The proposed procedure deals successfully with various technical difficulties which arise in microarray time-course experiments such as a small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows to account for various types of errors, thus, offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence, the entire procedure requires very small computational effort. The performance of the procedure is studied using simulated data.

A kinetic description is proposed of a fluid species moving in a porous medium and chemically interacting with it. The porosity is included in the model by a modification of the standard kinetic equations for two gaseous species diffusing in a background medium of two solid species. The validity of the proposed kinetic model is assessed by comparing the resulting macroscopic model, obtained by Chapman-Enskog expansion, with macroscopic models present in literature.

A fully quantitative shape index relying upon the asymmetry of mass distribution of protein molecules along the three space dimensions is proposed. Multidimensional statistical analysis, based on principal component extraction and subsequent linear discriminant analysis, showed the presence of three major 'attractor forms' roughly correspondent to rod-like, discoidal and spherical shapes. This classification of protein shapes was in turn demonstrated to be strictly connected with topological features of proteins, as emerging from complex network invariants of their contact maps. © Arrigo et al.

The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is a mid-infrared emission spectrometer which is part of the core payload of the Envisat satellite, launched by ESA in March 2002. It provides unique observations of the atmospheric spectral radiances in the 4.15 -14.6 ?m spectral interval with innovative limb scanning capabilities for the three dimensional observation of the atmospheric composition and processes. The species, the processes and events that have been studied with this instrument in its 10 years of operation are briefly reviewed.

We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the population dies at fixed rate. In the former it grows either with the logistic or with an Allee effect type dynamics, where the population has to overcome a threshold to glow. We study the conditions for successful invasions and the speed of the invasion process, which is numerically and analytically investigated in several limits. Generically advection enhances the downstream invasion speed but decreases the population size of the invading species, and can even inhibit the invasion process. Remarkably, however, the rate of population increase, which quantifies the invasion efficiency, is maximized by an optimal advection velocity. In models with Allee effect, differently from the logistic case, above a critical unfavorable patch size the population localizes in a favorable patch, being unable to invade the habitat. However, we show that advection, when intense enough, may activate the invasion process.

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e. on the time evolution of the reaction product, $M(t)$. At variance with pure diffusive processes, characterized by the spectral dimension, $d_s$, for reaction spreading the important quantity is found to be the connectivity dimension, $d_l$. Numerical data, in agreement with analytical estimates based on the features of $n$ independent random walkers on the graph, show that $M(t) \sim t^{d_l}$. In the case of Erd\"{o}s-Renyi random graphs, the reaction-product is characterized by an exponential growth $M(t) \sim e^{\alpha t}$ with $\alpha$ proportional to $\ln \lra{k}$, where $\lra{k}$ is the average degree of the graph.

We consider a tumor growth model involving a nonlinear system of partial differential equations which describes the growth of two types of cell population densities with contact inhibition. In one space dimension, it is known that global solutions exist and that they satisfy the so-called segregation property: if the two populations are initially segregated - in mathematical terms this translates into disjoint supports of their densities - this property remains true at all later times. We apply recent results on transport equations and regular Lagrangian flows to obtain similar results in the case of arbitrary space dimension.

The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: the force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational changes at large shear rates, where less stiff polymers are extended by the flow, whereas rather stiff polymers are contracted. In addition, the polymers are aligned by the flow, thereby the two-dimensional semiflexible polymers behave similarly to flexible polymers in three dimensions. The tumbling times display a power-law dependence at high shear rate rates with an exponent comparable to the one of flexible polymers in three-dimensional systems.