We compare experimental data and numerical simulations for the dynamics of inertial particles with finite density in turbulence. In the experiment, bubbles and solid particles are optically tracked in a turbulent flow of water using an Extended Laser Doppler Velocimetry technique. The probability density functions (PDF) of particle accelerations and their auto-correlation in time are computed. Numerical results are obtained from a direct numerical simulation in which a suspension of passive pointwise particles is tracked, with the same finite density and the same response time as in the experiment. We observe a good agreement for both the variance of acceleration and the autocorrelation time scale of the dynamics; small discrepancies on the shape of the acceleration PDF are observed. We discuss the effects induced by the finite size of the particles, not taken into account in the present numerical simulations.

We consider nonlinear difference equations of unbounded order of the form x i = b i - ? i j = 0 a i , j f i - j ( x j ) , i = 0 , 1 , 2 , ... , where f j ( x ) ( j = 0 , ... , i ) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of x i as i -> + ? . Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations

In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.

Motivation: An unbalanced differentiation of T helper cells from precursor type TH0 to the TH1 or TH2 phenotype in immune responses often leads to a pathological condition. In general, immune reactions biased toward TH1 responses may result in auto-immune diseases, while enhanced TH2 responses may cause allergic reactions. The aim of this work is to integrate a gene network of the TH differentiation in an agent-based model of the hyper-sensitivity reaction. The implementation of such a system introduces a second level of description beyond the mesoscopic level of the inter-cellular interaction of the agent-based model. The intra-cellular level consists in the cell internal dynamics of gene activation and transcription. The gene regulatory network includes genes-related molecules that have been found to be involved in the differentiation process in TH cells. Results: The simulator reproduces the hallmarks of an IgE-mediated hypersensitive reaction and provides an example of how to combine the mesoscopic level description of immune cells with the microscopic gene-level dynamics.

A dynamical description for fluid binary mixtures with variable temperature and concentration gradient contributions to entropy and internal energy is given. By using mass, momentum and energy balance equations together with the standard expression for entropy production, a generalized Gibbs-Duhem relation is obtained which takes into account thermal and concentration gradient contributions. Then an expression for the pressure tensor is derived. As examples of applications, interface behavior and phase separation have been numerically studied in two dimensions neglecting the contributions of the velocity field. In the simplest case with a constant thermal gradient, the growth exponent for the averaged size of domains is found to have the usual value z = 1/3 and the domains appear elongated in the direction of the thermal gradient. When the system is quenched by contact with external walls, the evolution of temperature profiles in the system is shown and the domain morphology is characterized by interfaces perpendicular to the thermal gradient.

The stochastic motion of a two-dimensional vesicle in linear shear flow is studied at finite temperature. In the limit of small deformations from a circle, Langevin-type equations of motion are derived, which are highly nonlinear due to the constraint of constant perimeter length. These equations are solved in the low-temperature limit and using a mean-field approach, in which the length constraint is satisfied only on average. The constraint imposes non-trivial correlations between the lowest deformation modes at low temperature. We also simulate a vesicle in a hydrodynamic solvent by using the multi-particle collision dynamics technique, both in the quasi-circular regime and for larger deformations, and compare the stationary deformation correlation functions and the time autocorrelation functions with theoretical predictions. Good agreement between theory and simulations is obtained.

Background: Microarray experiments enable simultaneous measurement of the expression levels of virtually all transcripts present in cells, thereby providing a 'molecular picture' of the cell state. On the other hand, the genomic responses to a pharmacological or hormonal stimulus are dynamic molecular processes, where time influences gene activity and expression. The potential use of the statistical analysis of microarray data in time series has not been fully exploited so far, due to the fact that only few methods are available which take into proper account temporal relationships between samples. Results: We compared here four different methods to analyze data derived from a time course mRNA expression profiling experiment which consisted in the study of the effects of estrogen on hormone-responsive human breast cancer cells. Gene expression was monitored with the innovative Illumina BeadArray platform, which includes an average of 30-40 replicates for each probe sequence randomly distributed on the chip surface. We present and discuss the results obtained by applying to these datasets different statistical methods for serial gene expression analysis. The influence of the normalization algorithm applied on data and of different parameter or threshold choices for the selection of differentially expressed transcripts has also been evaluated. In most cases, the selection was found fairly robust with respect to changes in parameters and type of normalization. We then identified which genes showed an expression profile significantly affected by the hormonal treatment over time. The final list of differentially expressed genes underwent cluster analysis of functional type, to identify groups of genes with similar regulation dynamics. Conclusions: Several methods for processing time series gene expression data are presented, including evaluation of benefits and drawbacks of the different methods applied. The resulting protocol for data analysis was applied to characterization of the gene expression changes induced by estrogen in human breast cancer ZR-75.1 cells over an entire cell cycle.

A pointwise inequality between the radially decreasing symmetrals of minimizers of (possibly) anisotropic variational problems and the minimizers of suitably symmetrized problems is established. As a consequence, a priori sharp estimates for norms of the relevant minimizers are derived.

Sharp constants are exhibited in exponential inequalities corresponding to the limiting case of the Sobolev inequalities in Lorentz-Sobolev spaces of arbitrary order.

We investigate finite difference schemes which approximate 2 × 2 one-dimensional linear dissipative hyperbolic systems. We show that it is possible to introduce some suitable modifications in standard upwinding schemes, which keep into account the long-time behavior of the solutions, to yield numerical approximations which are increasingly accurate for large times when computing small perturbations of stable asymptotic states, respectively, around stationary solutions and in the diffusion (Chapman-Enskog) limit.