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.

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under large claim assumptions

We present a mesoscopic model, based on the Boltzmann equation, for the interaction between a solid wall and a nonideal fluid. We present an analytic derivation of the contact angle in terms of the surface tension between the liquid-gas, the liquid-solid, and the gas-solid phases. We study the dependency of the contact angle on the two free parameters of the model, which determine the interaction between the fluid and the boundaries, i.e. the equivalent of the wall density and of the wall-fluid potential in molecular dynamics studies. We compare the analytical results obtained in the hydrodynamical limit for the density profile and for the surface tension expression with the numerical simulations. We compare also our two-phase approach with some exact results obtained by E. Lauga and H. Stone ?J. Fluid. Mech. 489, 55 ?2003?? and J. Philip ?Z. Angew. Math. Phys. 23, 960 ?1972?? for a pure hydrodynamical incompressible fluid based on Navier-Stokes equations with boundary conditions made up of alternating slip and no-slip strips. Finally, we show how to overcome some theoretical limitations connected with the discretized Boltzmann scheme proposed by X. Shan and H. Chen ?Phys. Rev. E 49, 2941 ?1994?? and we discuss the equivalence between the surface tension defined in terms of the mechanical equilibrium and in terms of the Maxwell construction.

The regularized linear wavelet estimator has been recently proposed as an alternative to the spline smoothing estimator, one of the most used linear estimator for the standard nonparametric regression problem. It has been demonstrated that the regularized linear wavelet estimator attains the optimal rate of convergence in the mean integrated squared error sense and compares favorably with the smoothing spline estimator in finite-sample situations, especially for less smooth response functions. We investigate further this estimator, extending Bayesian aspects of smoothing splines considered earlier in the literature. We first consider a Bayesian formalism in the wavelet domain that gives rise to the regularized linear wavelet estimator obtained in the standard nonparametric regression setting. We then use the posterior distribution to construct pointwise Bayesian credible intervals for the resulting regularized linear wavelet function estimate. Simulation results show that the wavelet-based pointwise Bayesian credible intervals have good empirical coverage rates for standard nominal coverage probabilities and compare favorably with the corresponding intervals obtained by smoothing splines, especially for less smooth response functions. Moreover, their construction algorithm is of order O(n) and it is easily implemented.

We consider a Bayesian approach to multiple hypothesis testing. A hierarchical prior model is based on imposing a prior distribution $\pi(k)$ on the number of hypotheses arising from alternatives (false nulls). We then apply the maximum a posteriori (MAP) rule to find the most likely configuration of null and alternative hypotheses. The resulting MAP procedure and its closely related step-up and step-down versions compare ordered Bayes factors of individual hypotheses with a sequence of critical values depending on the prior. We discuss the relations between the proposed MAP procedure and the existing frequentist and Bayesian counterparts. A more detailed analysis is given for the normal data, where we show, in particular, that choosing a specific $\pi(k)$, the MAP procedure can mimic several known familywise error (FWE) and false discovery rate (FDR) controlling procedures. The performance of MAP procedures is illustrated on a simulated example.

We consider the testing problem in the mixed-effects functional analysis of variance models. We develop asymptotically optimal (minimax) testing procedures for testing the significance of functional global trend and the functional fixed effects based on the empirical wavelet coefficients of the data. Wavelet decompositions allow one to characterize various types of assumed smoothness conditions on the response function under the nonparametric alternatives. The distribution of the functional random-effects component is defined in the wavelet domain and captures the sparseness of wavelet representation for a wide variety of functions. The simulation study presented in the paper demonstrates the finite sample properties of the proposed testing procedures. We also applied them to the real data from the physiological experiments.