Phase-space Lagrangian dynamics of incompressible thermofluids

Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called {\it ideal tracer particles}. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. \ The goal of this paper is to show that the tracer-particle dynamics can be {\it exactly} established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) (Tessarotto \textit{et al.}, 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered.Comment: submitted to Physica

Modelling of anthropogenic pollutant diffusion in the atmosphere and applications to civil protection monitoring

A basic feature of fluid mechanics concerns the frictionless phase-space dynamics of particles in an incompressible fluid. The issue, besides its theoretical interest in turbulence theory, is important in many applications, such as the pollutant dynamics in the atmosphere, a problem relevant for civil protection monitoring of air quality. Actually, both the numerical simulation of the ABL (atmospheric boundary layer) portion of the atmosphere and that of pollutant dynamics may generally require the correct definition of the Lagrangian dynamics which characterizes arbitrary fluid elements of incompressible thermofluids. We claim that particularly important for applications would be to consider these trajectories as phase-space trajectories. This involves, however, the unfolding of a fundamental theoretical problem up to now substantially unsolved: {\it namely the determination of the exact frictionless dynamics of tracer particles in an incompressible fluid, treated either as a deterministic or a turbulent (i.e., stochastic) continuum.} In this paper we intend to formulate the necessary theoretical framework to construct such a type of description. This is based on a phase-space inverse kinetic theory (IKT) approach recently developed for incompressible fluids (Ellero \textit{et al.}, 2004-2008). {\it Our claim is that the conditional frictionless dynamics of a tracer particles - which corresponds to a prescribed velocity probability density and an arbitrary choice of the relevant fluid fields - can be exactly specified}.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

The computational complexity of traditional Lattice-Boltzmann methods for incompressible fluids

It is well-known that in fluid dynamics an alternative to customary direct solution methods (based on the discretization of the fluid fields) is provided by so-called \emph{particle simulation methods}. Particle simulation methods rely typically on appropriate \emph{kinetic models} for the fluid equations which permit the evaluation of the fluid fields in terms of suitable expectation values (or \emph{momenta}) of the kinetic distribution function $f(\mathbf{r,v},t),$ being respectively $\mathbf{r}$ and\textbf{\}$\mathbf{v}$ the position an velocity of a test particle with probability density $f(\mathbf{r,v},t)$. These kinetic models can be continuous or discrete in phase space, yielding respectively \emph{continuous} or \emph{discrete kinetic models} for the fluids. However, also particle simulation methods may be biased by an undesirable computational complexity. In particular, a fundamental issue is to estimate the algorithmic complexity of numerical simulations based on traditional LBM's (Lattice-Boltzmann methods; for review see Succi, 2001 \cite{Succi}). These methods, based on a discrete kinetic approach, represent currently an interesting alternative to direct solution methods. Here we intend to prove that for incompressible fluids fluids LBM's may present a high complexity. The goal of the investigation is to present a detailed account of the origin of the various complexity sources appearing in customary LBM's. The result is relevant to establish possible strategies for improving the numerical efficiency of existing numerical methods.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Lagrangian dynamics of incompressible thermofluids

A key aspect of fluid dynamics is the correct definition of the \textit{% phase-space} Lagrangian dynamics which characterizes arbitrary fluid elements of an incompressible fluid. Apart being an unsolved theoretical problem of fundamental importance, the issue is relevant to exhibit the connection between fluid dynamics and the classical dynamical systems underlying incompressible and non-isothermal fluid, typically founded either on: a) a \textit{configuration-space} Lagrangian description of the dynamics of fluid elements; b) a kinetic description of the molecular dynamics, based on a discrete representation of the fluid. The goal of this paper is to show that the exact Lagrangian dynamics can be established based on the inverse kinetic theory (IKT) for incompressible fluids recently pointed out (Ellero \textit{et al.}, 2004-2006, \cite{Ellero2004}). The result is reached by adopting an IKT approach based on a \textit{restricted phase-space representation} of the fluid, in which the configuration space coincides with the physical fluid domain. The result appears of potential importance in applied fluid dynamics and CFD.Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008

Characterization of LAPPD timing at CERN PS testbeam

Large Area Picosecond PhotoDetectors (LAPPDs) are photosensors based on microchannel plate technology with about 400 cm$^2$ sensitive area. The external readout plane of a capacitively coupled LAPPD can be segmented into pads providing a spatial resolution down to 1 mm scale. The LAPPD signals have about 0.5 ns risetime followed by a slightly longer falltime and their amplitude reaches a few dozens of mV per single photoelectron. In this article, we report on the measurement of the time resolution of an LAPPD prototype in a test beam exercise at CERN PS. Most of the previous measurements of LAPPD time resolution had been performed with laser sources. In this article we report time resolution measurements obtained through the detection of Cherenkov radiation emitted by high energy hadrons. Our approach has been demonstrated capable of measuring time resolutions as fine as 25-30 ps. The available prototype had performance limitations, which prevented us from applying the optimal high voltage setting. The measured time resolution for single photoelectrons is about 80 ps r.m.s.Comment: 35 pages, 23 figure

The Polarised Valence Quark Distribution from semi-inclusive DIS

The semi-inclusive difference asymmetry A^{h^{+}-h^{-}} for hadrons of opposite charge has been measured by the COMPASS experiment at CERN. The data were collected in the years 2002-2004 using a 160 GeV polarised muon beam scattered off a large polarised ^6LiD target and cover the range 0.006 < x < 0.7 and 1 < Q^2 < 100 (GeV/c)^2. In leading order QCD (LO) the asymmetry A_d^{h^{+}-h^{-}} measures the valence quark polarisation and provides an evaluation of the first moment of Delta u_v + Delta d_v which is found to be equal to 0.40 +- 0.07 (stat.) +- 0.05 (syst.) over the measured range of x at Q^2 = 10 (GeV/c)^2. When combined with the first moment of g_1^d previously measured on the same data, this result favours a non-symmetric polarisation of light quarks Delta u-bar = - Delta d-bar at a confidence level of two standard deviations, in contrast to the often assumed symmetric scenario Delta u-bar = Delta d-bar = Delta s-bar = Delta s.Comment: 7 pages, 3 figures, COMPASS, revised: details added, author list update