In Fricke-agarose gels, an accurate determination of the spatial dose distribution is hindered by the diffusion of ferric ions. In this work, a model was developed to describe the diffusion process within gel samples of finite length and, thus, permit the reconstruction of the initial spatial distribution of the ferric ions. The temporal evolution of the ion concentration as a function of the initial concentration is derived by solving Fick's second law of diffusion in two dimensions with boundary reflections. The model was applied to magnetic resonance imaging data acquired at high spatial resolution (0.3 mm) and was found to describe accurately the observed diffusion effects.

Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator acting continuously in for close to and/or taking into as and/or with norms blowing up at speed and/or , . Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if as . The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for . We also touch the problem of comparison of results in various scales of spaces.

The role of information management and retrieval in production processes has been gaining in importance in recent years. In this context, the ability to search for and quickly find the small piece of information needed from the huge amount of information available has crucial importance. One category of tools devoted to such a task is represented by search engines. Satisfying the basic needs of the Web user has led to the research of new tools that aim at helping more sophisticated users (communities, companies, interest groups) with more elaborate methods. An example is the use of clustering and classification algorithms or other specific data mining techniques. In such a context, the proper use of a thematic search engine is a crucial tool in supporting and orienting many activities. Several prac- tical and theoretical problems arise in developing such tools, and we try to face some of these in this paper, extending previous work on Web mining. Here we consider two related problems: how to select an appropriate set of keywords for a thematic engine taking into account the semantic and linguistic extensions of the search context, and how to select and rank a subset of relevant pages given a set of search keywords. Both problems are solved using the same framework, based on a graph representation of the available information and on the search of particular node subsets of such a graph. Such subsets are effectively identified by a maximum-weight clique algorithm customized ad hoc for specific problems. The methods have been developed in the framework of a funded research project for the development of new Web search tools, they have been tested on real data, and are currently being implemented in a prototypal thematic search engine. The Web mining method presented in this paper can be applied to Web-based design and manufacturing.

We present a multiscale approach to the modeling of polymer dynamics in the presence of a fluid solvent. The approach combines Langevin molecular dynamics ( MD) techniques with a mesoscopic lattice Boltzmann (LB) method for the solvent dynamics. A unique feature of the present approach is that hydrodynamic interactions between the solute macromolecule and the aqueous solvent are handled explicitly, and yet in a computationally tractable way due to the dual particle-field nature of the LB solver. The suitability of the present LB-MD multiscale approach is demonstrated for the problem of polymer fast translocation through a nanopore. We also provide an interpretation of our results in the context of DNA translocation through a nanopore, a problem that has attracted much theoretical and experimental attention recently.

We propose a discrete lattice version of the Fokker-Planck kinetic equation in close analogy with the lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension D. A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The linear stability of the algorithm with respect to the finite time step Delta t is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in Delta t is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate nontrivial situations. Interactions between Brownian particles may be accounted for by adding a standard Bhatnagar-Gross-Krook collision operator to the discretized Fokker-Planck kernel.

Lyapunov exponents of heavy particles and tracers advected by homogeneous and isotropic turbulent flows are investigated by means of direct numerical simulations. For large values of the Stokes number, the main effect of inertia is to reduce the chaoticity with respect to fluid tracers. Conversely, for small inertia, a counterintuitive increase of the first Lyapunov exponent is observed. The flow intermittency is found to induce a Reynolds number dependency for the statistics of the finite-time Lyapunov exponents of tracers. Such intermittency effects are found to persist at increasing inertia. (c) 2006 American Institute of Physics.

A lattice version of the Fokker-Planck equation is introduced. The resulting numerical method is illustrated through the calculation of the electric conductivity of a one-dimensional charged fluid at zero and finite-temperature.

The scattering of sound-wave perturbations from vortex excitations in hydrodynamic systems with typical Bose-Einstein-condensate (BEC) parameters is investigated by numerical integration of the associated Klein-Gordon equation. The simulations indicate that at sufficiently high angular speeds, in the perturbative limit where back-reaction effects can be neglected, sound wave packets can extract a sizable fraction of the vortex energy through a mechanism of superradiant scattering. It is conjectured that this superradiant regime may be detectable in BEC experiments.

A lattice version of the Fokker-Planck equation, accounting for dissipative interactions, not resolved on the molecular scale, is applied to the study of electrorheological transport of a one-dimensional charged fluid, and is found to yield quantitative agreement with a recent analytical solution.

The Lagrangian statistics of heavy particles and of fluid tracers transported by a fully developed turbulent flow are investigated by means of high resolution direct numerical simulations. The Lagrangian velocity structure functions are measured in a time range spanning about three decades, from a tenth of the Kolmogorov time scale, tau(eta), up to a few large-scale eddy turnover times. Strong evidence is obtained that fluid tracer statistics are contaminated in the time range tau is an element of[1:10]tau(eta) by a bottleneck effect due to vortex filament. This effect is found to be significantly reduced for heavy particles which are expelled from vortices by inertia. These findings help in clarifying the results of a recent study by H. Xu [Phys. Rev. Lett. 96, 024503 (2006)], where differences between experimental and numerical results on scaling properties of fluid tracers were reported. (c) 2006 American Institute of Physics.

We present the results of direct numerical simulations of heavy particle transport in homogeneous, isotropic, fully developed turbulence, up to resolution 512(3) (R-lambda approximate to 185). Following the trajectories of up to 120 million particles with Stokes numbers, St, in the range from 0.16 to 3.5 we are able to characterize in full detail the statistics of particle acceleration. We show that: (i) the root-mean-squared acceleration arms sharply falls off from the fluid tracer value at quite small Stokes numbers; (ii) at a given St the normalized acceleration a(rms)/(is an element of(3)/nu)(1/4) increases with R-lambda consistently with the trend observed for fluid tracers; (iii) the tails of the probability density function of the normalized acceleration a/a(rms) decrease with St. Two concurrent mechanisms lead to the above results: preferential concentration of particles, very effective at small St. and filtering induced by the particle response time, that takes over at larger St.

We present the results of direct numerical simulations (DNS) of turbulent flows seeded with millions of passive inertial particles. The maximum Reynolds number is Re-lambda similar to 200. We consider particles much heavier than the carrier flow in the limit when the Stokes drag force dominates their dynamical evolution. We discuss both the transient and the stationary regimes. In the transient regime, we study the growth of inhomogeneities in the particle spatial distribution driven by the preferential concentration out of intense vortex filaments. In the stationary regime, we study the acceleration fluctuations as a function of the Stokes number in the range St is an element of [0.16 : 3.3]. We also compare our results with those of pure fluid tracers ( St = 0) and we find a critical behavior of inertia for small Stokes values. Starting from the pure monodisperse statistics we also characterize polydisperse suspensions with a given mean Stokes, (St) over bar.

We introduce and discuss a three-dimensional mesoscopic lattice Boltzmann model for the numerical simulation of strongly-interacting fluids with dynamic inhomogeneities. The model is based on an extension of the standard lattice Boltzmann dynamics in which streaming between neighboring lattice sites is constrained by the value of the nonlocal density of the surrounding fluid. The resulting dynamics exhibits typical features of dynamically heterogeneous fluids, such as long-time relaxation, non-Gaussian density distributions and dynamic heterogeneities. Due to its intrinsically parallel dynamics and absence of statistical noise, the method is expected to compute significantly faster than molecular dynamics, Monte Carlo, and lattice glass models.