On the Heat Transfer in Rayleigh-Benard systems

In this paper we discuss some theoretical aspects concerning the scaling laws of the Nusselt number versus the Rayleigh number in a Rayleigh-Benard cell. We present a new set of numerical simulations and compare our findings against the predictions of existing models. We then propose a new theory which relies on the hypothesis of Bolgiano scaling. Our approach generalizes the one proposed by Kadanoff, Libchaber and coworkers and solves some of the inconsistencies raised in the recent literature.Comment: 10 pages, 5 figure

Rayleigh and Prandtl number scaling in the bulk of Rayleigh-Benard turbulence

The Rayleigh (Ra) and Prandtl (Pr) number scaling of the Nusselt number Nu, the Reynolds number Re, the temperature fluctuations, and the kinetic and thermal dissipation rates is studied for (numerical) homogeneous Rayleigh-Benard turbulence, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient. This system serves as model system for the bulk of Rayleigh-Benard flow and therefore as model for the so called ``ultimate regime of thermal convection''. With respect to the Ra dependence of Nu and Re we confirm our earlier results \cite{loh03} which are consistent with the Kraichnan theory \cite{kra62} and the Grossmann-Lohse (GL) theory \cite{gro00,gro01,gro02,gro04}, which both predict $Nu \sim Ra^{1/2}$ and $Re \sim Ra^{1/2}$. However the Pr dependence within these two theories is different. Here we show that the numerical data are consistent with the GL theory $Nu \sim Pr^{1/2}$, $Re \sim Pr^{-1/2}$. For the thermal and kinetic dissipation rates we find \eps_\theta/(\kappa \Delta^{2}L^{-2}) \sim (Re Pr)^{0.87} and \eps_u/(\nu^3 L^{-4}) \sim Re^{2.77}, also both consistent with the GL theory, whereas the temperature fluctuations do not depend on Ra and Pr. Finally, the dynamics of the heat transport is studied and put into the context of a recent theoretical finding by Doering et al. \cite{doe05}.Comment: 8 pages, 9 figure

Matched filters for coalescing binaries detection on massively parallel computers

We discuss some computational problems associated to matched filtering of experimental signals from gravitational wave interferometric detectors in a parallel-processing environment. We then specialize our discussion to the use of the APEmille and apeNEXT processors for this task. Finally, we accurately estimate the performance of an APEmille system on a computational load appropriate for the LIGO and VIRGO experiments, and extrapolate our results to apeNEXT.Comment: 19 pages, 6 figure

The Hypothesis of Superluminal Neutrinos: comparing OPERA with other Data

The OPERA Collaboration reported evidence for muonic neutrinos traveling slightly faster than light in vacuum. While waiting further checks from the experimental community, here we aim at exploring some theoretical consequences of the hypothesis that muonic neutrinos are superluminal, considering in particular the tachyonic and the Coleman-Glashow cases. We show that a tachyonic interpretation is not only hardly reconciled with OPERA data on energy dependence, but that it clashes with neutrino production from pion and with neutrino oscillations. A Coleman-Glashow superluminal neutrino beam would also have problems with pion decay kinematics for the OPERA setup; it could be easily reconciled with SN1987a data, but then it would be very problematic to account for neutrino oscillations.Comment: v1: 10 pages, 2 figures; v2: 12 pages, 2 figures, improved discussion of CG case as for pion decay and neutrino oscillations, added reference

Towards a unified lattice kinetic scheme for relativistic hydrodynamics

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultra-relativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Juettner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard benchmark tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering (BAMPS) and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes

Universality of anisotropic fluctuations from numerical simulations of turbulent flows

We present new results from a direct numerical simulation of a three dimensional homogeneous Rayleigh-Benard system (HRB), i.e. a convective cell with an imposed linear mean temperature profile along the vertical direction. We measure the SO(3)-decomposition of both velocity structure functions and buoyancy terms. We give a dimensional prediction for the values of the anisotropic scaling exponents in this Rayleigh-Benard systems. Measured scaling does not follow dimensional estimate, while a better agreement can be found with the anisotropic scaling of a different system, the random-Kolmogorov-flow (RKF). Our findings support the conclusion that scaling properties of anisotropic fluctuations are universal, i.e. independent of the forcing mechanism sustaining the turbulent flow.Comment: 4 pages, 3 figure

Kinetic approach to relativistic dissipation

Despite a long record of intense efforts, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude a complete understanding. In particular, no unique pathway from kinetic theory to hydrodynamics has been identified as yet, with different approaches leading to different values of the transport coefficients. In this Letter, we approach the problem by matching data from lattice kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favour of the Chapman-Enskog procedure, as suggested by recently theoretical analyses, along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method to capture the emergence of dissipative effects in relativistic fluids

Evolution of a double-front Rayleigh-Taylor system using a GPU-based high resolution thermal Lattice-Boltzmann model

We study the turbulent evolution originated from a system subjected to a Rayleigh-Taylor instability with a double density at high resolution in a 2 dimensional geometry using a highly optimized thermal Lattice Boltzmann code for GPUs. The novelty of our investigation stems from the initial condition, given by the superposition of three layers with three different densities, leading to the development of two Rayleigh-Taylor fronts that expand upward and downward and collide in the middle of the cell. By using high resolution numerical data we highlight the effects induced by the collision of the two turbulent fronts in the long time asymptotic regime. We also provide details on the optimized Lattice-Boltzmann code that we have run on a cluster of GPU

Energy-efficiency evaluation of Intel KNL for HPC workloads

Energy consumption is increasingly becoming a limiting factor to the design of faster large-scale parallel systems, and development of energy-efficient and energy-aware applications is today a relevant issue for HPC code-developer communities. In this work we focus on energy performance of the Knights Landing (KNL) Xeon Phi, the latest many-core architecture processor introduced by Intel into the HPC market. We take into account the 64-core Xeon Phi 7230, and analyze its energy performance using both the on-chip MCDRAM and the regular DDR4 system memory as main storage for the application data-domain. As a benchmark application we use a Lattice Boltzmann code heavily optimized for this architecture and implemented using different memory data layouts to store its lattice. We assessthen the energy consumption using different memory data-layouts, kind of memory (DDR4 or MCDRAM) and number of threads per core