We prove the existence of a traveling wave solution u of the harmonic heat flow in an infinitely long cylinder of radius R, which connects two locally stable and axially symmetric steady states at + and - infinity infinity. Here u is a director field, with values in the unit sphere. The traveling wave has a singular point on the cylinder axis. As R goes to infinity we obtain a traveling wave defined in all space.

In this paper we deal with the numerical approximation of integro-differential equations arising in financial applications in which jump processes act as the underlying stochastic processes. Our aim is to find finite differences schemes which are high-order accurate for large time simulations. Therefore, we study the asymptotic time behavior of such equations and we define as {\it asymptotic high-order schemes} those schemes that are consistent with this behavior. Numerical tests are presented to investigate the efficiency and the accuracy of such approximations.

We consider a mathematical model for fluid-dynamic flows on networks which is based on conservation laws. Road networks are considered as graphs composed by arcs that meet at some junctions. The crucial point is represented by junctions, where interactions occurr and the problem is underdetermined. The approximation of scalar conservation laws along arcs is carried out by using conservative methods, such as the classical Godunov scheme and the more recent discrete velocities kinetic schemes with the use of suitable boundary conditions at junctions. Riemann problems are solved by means of a simulation algorithm which proceeds processing each junction. We present the algorithm and its application to some simple test cases and to portions of urban network.

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.