Sergio Chibbaro

Reductionism, Emergence and Levels of Reality

Newton’s third law does not apply to the interaction between philosophers (‘them’) and physicists (‘us’). It has usually been asymmetrical, with ‘us’ influencing ‘them’, without ‘them’ acting on ‘us’. In a way this is natural, because the raw material that philosophers study are the discoveries and theories of science and the interactions between scientists, while the primary preoccupation of physicists is not the study of philosophy or philosophers. I do not deny that there have been eminent scientists (Einstein, Poincare, Bohr...) who have pondered on the philosophical significance of the scientific picture of the world, and much of what they said has been immediately appreciated by practicing scientists. But their wise intellectual interventions have usually been outside the philosophical mainstream.

Weak first- and second-order numerical schemes for stochastic differential equations appearing in Lagrangian two-phase flow modeling

Weak first- and second-order numerical schemes are developed to integrate the stochastic differential equations that arise in mean-field - pdf methods (Lagrangian stochastic approach) for modeling polydispersed turbulent two-phase flows. These equations present several challenges, the foremost being that the problem is characterized by the presence of different time scales that can lead to stiff equations, when the smallest time-scale is significantly less than the time-step of the simulation. The numerical issues have been detailed by Minier [Monte Carlo Meth. and Appl. 7 295-310, (2000)] and the present paper proposes numerical schemes that satisfy these constraints. This point is really crucial for physical and engineering applications, where various limit cases can be present at the same time in different parts of the domain or at different times. In order to build up the algorithm, the analytical solutions to the equations are first carried out when the coefficients are constant. By freezing the coefficients in the analytical solutions, first and second order unconditionally stable weak schemes are developed. A prediction/ correction method, which is shown to be consistent for the present stochastic model, is used to devise the second-order scheme. A complete numerical investigation is carried out to validate the schemes, having included also a comprehensive study of the different error sources. The final method is demonstrated to have the required stability, accuracy and efficiency.

Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows

In this paper, we establish a set of criteria which are applied to discuss various formulations under which Lagrangian stochastic models can be found. These models are used for the simulation of fluid particles in single-phase turbulence as well as for the fluid seen by discrete particles in dispersed turbulent two-phase flows. The purpose of the present work is to provide guidelines, useful for experts and non-experts alike, which are shown to be helpful to clarify issues related to the form of Lagrangian stochastic models. A central issue is to put forward reliable requirements which must be met by Lagrangian stochastic models and a new element brought by the present analysis is to address the single- and two-phase flow situations from a unified point of view. For that purpose, we consider first the single-phase flow case and check whether models are fully consistent with the structure of the Reynolds-stress models. In the two-phase flow situation, coming up with clear-cut criteria is more difficult and...

On the foundations of statistical mechanics: ergodicity, many degrees of freedom and inference

We review the main aspects of the foundations of statistical mechanics. In particular we explain why many degrees of freedom are necessary, while chaos (in the sense of positive Lyapunov exponents) is only marginally relevant, for the emergence of statistical laws in macroscopic systems.

Reaction spreading on graphs

We study reaction-diffusion processes on graphs through an extension of the standard reaction-diffusion equation starting from first principles. We focus on reaction spreading, i.e., on the time evolution of the reaction product M(t). At variance with pure diffusive processes, characterized by the spectral dimension d{s}, the important quantity for reaction spreading is found to be the connectivity dimension d{l}. Numerical data, in agreement with analytical estimates based on the features of n independent random walkers on the graph, show that M(t)∼t{d{l}}. In the case of Erdös-Renyi random graphs, the reaction product is characterized by an exponential growth M(t)e{αt} with α proportional to ln(k), where (k) is the average degree of the graph.

Lagrangian filtered density function for LES-based stochastic modelling of turbulent particle-laden flows

The Eulerian-Lagrangian approach based on Large-Eddy Simulation (LES) is one of the most promising and viable numerical tools to study particle-laden turbulent flows, when the computational cost of Direct Numerical Simulation (DNS) becomes too expensive. The applicability of this approach is however limited if the effects of the Sub-Grid Scales (SGSs) of the flow on particle dynamics are neglected. In this paper, we propose to take these effects into account by means of a Lagrangian stochastic SGS model for the equations of particle motion. The model extends to particle-laden flows the velocity-filtered density function method originally developed for reactive flows. The underlying filtered density function is simulated through a Lagrangian Monte Carlo procedure that solves a set of Stochastic Differential Equations (SDEs) along individual particle trajectories. The resulting model is tested for the reference case of turbulent channel flow, using a hybrid algorithm in which the fluid velocity field is pro...

A Finite Volume Scheme For Hybrid Turbulent Two-Phase Flow Models

In this paper, we present a new hybrid method for the computation of dispersed twophase flows. As with the classical hybrid method, an Eulerian (or mean-field) and a Lagrangian (or PDF) points of view are coupled but, in the present approach, the hybrid Euler/Lagrange description is extended to the simulation of the particle phase. In particular, the particle volumetric fraction and the particle mean velocity are obtained as solutions of partial differential equations on a mesh where a part of the information is provided by the Lagrangian description as a source term in the evolution equations. The second objective of the paper is to propose a novel numerical technique which relies on the hyperbolic nature of the underlying equations and makes use of relaxation techniques. The numerical ideas are explained and first computational results illustrate the feasability of the new hybrid method.

Elastic wave turbulence and intermittency.

We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by d cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only.

Simultaneous temperature and velocity Lagrangian measurements in turbulent thermal convection

We report joint Lagrangian velocity and temperature measurements in turbulent thermal convection. Measurements are performed using an improved version (extended autonomy) of the neutrally-buoyant instrumented particle that was used by to performed experiments in a parallelepipedic Rayleigh-Benard cell. The temperature signal is obtained from a RFtransmitter. Simultaneously, we determine particles position and velocity with one camera, which grants access to the Lagrangian heat flux. Due to the extended autonomy of the present particle, we obtain well converged temperature and velocity statistics, as well as pseudo-eulerian maps of velocity and heat flux. Present experimental results have also been compared with the results obtained by a corresponding campaign of Direct Numerical Simulations and Lagrangian Tracking of massless tracers. The comparison between experimental and numerical results show the accuracy and reliability of our experimental measurements. Finally, the analysis of lagrangian velocity and temperature frequency spectra is shown and discussed. In particular, we observe that temperature spectra exhibit an anomalous f^2.5 frequency scaling, likely representing the ubiquitous passive and active scalar behavior of temperature

From Microscopic Reversibility to Macroscopic Irreversibility

The idea that natural phenomena proceed in a well-defined temporal direction, and therefore that the past is clearly distinguishable from the future, is based on indisputable empirical evidence.