The statistics of Lagrangian particles transported by a three-dimensional fully developed turbulent flow is investigated by means of high-resolution direct numerical simulations. The analysis of single trajectories reveals the existence of strong trapping events vortices at the Kolmogorov scale which contaminates inertial range statistics up to 10 tau(eta). For larger time separations, we find that Lagrangian structure functions display intermittency in agreement with the prediction of the multifractal model of turbulence. The study of two-particle dispersion shows that the probability density function of pair separation is very close to the original prediction of Richardson of 1926. Nevertheless, moments of relative dispersion are strongly affected by finite Reynolds effects, thus limiting the possibility to measure numerical prefactors, such as the Richardson constant g. We show how, by using an exit time statistics, it is possible to have a precise estimation of g which is consistent with recent laboratory measurements.

New computation algorithms for a fluid-dynamic mathematical model of flows on networks are proposed, described and tested. First we improve the classical Godunov scheme (G) for a special flux function, thus obtaining a more efficient method, the Fast Godunov scheme (FG) which reduces the number of evaluations for the numerical flux. Then a new method, namely the Fast Shock Fitting method (FSF), based on good theorical properties of the solution of the problem is introduced. Numerical results and efficience tests are presented in order to show the behaviour of FSF in comparison with G, FG and a conservative scheme of second order.

In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler equations: a standard relaxation approximation, but with a diffusive scaling, and the Euler-Poisson equations in the quasineutral regime.

We provide a model of traffic flow on networks, starting from the second order model proposed by Aw and Rascle. The existence of solutions is proved for perturbation of equilibria.

We construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent. The optimization method works for a general ODE system and can be applied to find the optimal schedule in a variety of medical treatments that have been described by a mathematical model.

A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by molecular dynamics (MD) computer simulation and compared to results of lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed.

Two dimensional reduction regression methods to predict a scalar response from a discretized sample path of a continuous time covariate process are presented. The methods take into account the functional nature of the predictor and are both based on appropriate wavelet decompositions. Using such decompositions, prediction methods are devised that are similar to minimum average variance estimation (MAVE) or functional sliced inverse regression (FSIR). Their practical implementation is described, together with their application both to simulated and on real data analyzing three calibration examples of near infrared spectra.

The paper considers regression problems with univariate design points. The design points are irregular and no assumptions on their distribution are imposed. The regression function is retrieved by a wavelet based reproducing kernel Hilbert space (RKHS) technique with the penalty equal to the sum of blockwise RKHS norms. In order to simplify numerical optimization, the problem is replaced by an equivalent quadratic minimization problem with an additional penalty term. The computational algorithm is described in detail and is implemented with both the sets of simulated and real data. Comparison with existing methods showed that the technique suggested in the paper does not oversmooth the function and is superior in terms of the mean squared error. It is also demonstrated that under additional assumptions on design points the method achieves asymptotic optimality in a wide range of Besov spaces.

In this paper we describe an orthogonal similarity transformation for transforming arbitrary symmetric matrices into a diagonal-plus-semiseparable matrix, where we can freely choose the diagonal. Very recently an algorithm was proposed for transforming arbitrary symmetric matrices into similar semiseparable ones. This reduction is strongly connected to the reduction to tridiagonal form. The class of semiseparable matrices can be considered as a subclass of the diagonalplus- semiseparable matrices. Therefore we can interpret the proposed algorithm here as an extension of the reduction to semiseparable form. A numerical experiment is performed comparing thereby the accuracy of this reduction algorithm with respect to the accuracy of the traditional reduction to tridiagonal form, and the reduction to semiseparable form. The experiment indicates that all three reduction algorithms are equally accurate. Moreover it is shown in the experiments that asymptotically all the three approaches have the same complexity, i.e. that they have the same factor preceding the nxnxn term in the computational complexity. Finally we illustrate that special choices of the diagonal create a specific convergence behavior.

We consider an inverse problem which arises in the framework of identification of doping profiles for semiconductor devices, based on current measures for varying voltage. We set formally the inverse problem, and study and discuss the main properties of the resulting problem.

In this paper we present an algorithm able to provide geometrically optimal algebraic grids by using condition numbers as quality measure. In fact, the solution of partial differential equations (PDEs) to model complex problems needs an efficient algorithm to generate a good quality grid since better geometrical grid quality is gained, faster accuracy of the numerical solution can be kept. Moving from classical approaches, we derive new measures based on the condition numbers of appropriate cell matrices to control grid uniformity and orthogonality. We assume condition numbers in appropriate norms as building blocks of objective functions to be minimized for grid optimization.

We study the behavior of a fluid quenched from the disordered into the lamellar phase under the action of a shear flow. The dynamics of the system is described by Navier-Stokes and convection-diffusion equations with the pressure tensor and the chemical potential derived by the Brazovskii free energy. Our simulations are based on a mixed numerical method with the lattice Boltzmann equation and a finite difference scheme for NavierStokes and order parameter equations, respectively. We focus on cases where banded flows are observed with two different slopes for the component of velocity in the direction of the applied flow. Close to the walls the system reaches a lamellar order with very few defects, and the slope of the horizontal velocity is higher than the imposed shear rate. In the middle of the system the local shear rate is lower than the imposed one, and the system looks like a mixture of tilted lamellae, droplets, and small elongated domains. We refer to this as a region with a shear-induced structures (SIS) configuration. The local behavior of the stress shows that the system with the coexisting lamellar and SIS regions is in mechanical equilibrium. This phenomenon occurs, at fixed viscosity, for shear rates under a certain threshold; when the imposed shear rate is sufficiently large, lamellar order develops in the whole system. Effects of different viscosities have been also considered. The SIS region is observed only at low enough viscosity. We compare the above scenario with the usual one of shear banding. In particular, we do not find evidence for a plateau of the stress at varying imposed shear rates in the region with banded flow. We interpret our results as due to a tendency of the lamellar system to oppose the presence of the applied flow.

A two-dimensional finite-difference lattice Boltzmann model for liquid-vapor systems is introduced and analyzed. Two different numerical schemes are used and compared in recovering equilibrium density and velocity profiles for a planar interface. We show that flux limiter techniques can be conveniently adopted to minimize spurious numerical effects and improve the numerical accuracy of the model.