Fluctuations of entropy production in turbulent thermal convection

We report on a numerical experiment performed to analyze fluctuations of the entropy production in turbulent thermal convection, a physical configuration that represents here a prototypical case of an out-of-equilibrium dissipative system. We estimate the entropy production from instantaneous measurements of the local temperature and velocity fields sampled along the trajectory of a large number of point-wise Lagrangian tracers. The entropy production is characterized by large fluctuations and becomes often negative. This represents a sort of "finite-time" violation of the second principle of thermodynamics, since the direction of the energy flux is opposite to that prescribed by the external gradient. We clearly show that the fluctuations of entropy production observed in the present system verify the fluctuation relation (FR), even though the system is time-irreversible

Compressibility, laws of nature, initial conditions and complexity

We critically analyse the point of view for which laws of nature are just a mean to compress data. Discussing some basic notions of dynamical systems and information theory, we show that the idea that the analysis of large amount of data by means of an algorithm of compression is equivalent to the knowledge one can have from scientific laws, is rather naive. In particular we discuss the subtle conceptual topic of the initial conditions of phenomena which are generally incompressible. Starting from this point, we argue that laws of nature represent more than a pure compression of data, and that the availability of large amount of data, in general, is not particularly useful to understand the behaviour of complex phenomena.Comment: 19 Pages, No figures, published on Foundation of Physic

Low-dimensional modelling of flame dynamics in heated microchannels

This paper presents simulations of stoichiometric methane/air premixed flames into a microchannel at atmospheric pressure. These simulations result from numerical resolutions of reduced-order models. Indeed, combustion control into microchannels would be allowed by fast simulations that in turn enable real-time adjustments of the device's parameters. Former experimental studies reported the occurrence of a Flame Repetitive Extinction/Ignition (FREI) phenomenon provided that a temperature gradient is sustained at the channel's walls. Conducting unsteady one-dimensional simulations including complex chemistry, a late numerical study tried to explain the occurrence of this phenomenon. The present study therefore explores low-dimensional models that potentially reproduce the FREI phenomenon. Provided a calibration of some empirical constants, an unsteady two-dimensional model including one-step chemical reaction is shown to decently reproduce the FREI regime all along the range of mixture flow rates investigated by the experimental studies. Complementing the aforementioned numerical study, furthermore, when the channel's diameter is varied, the two-dimensional model unveils an unstable regime that a one-dimensional model cannot capture. As two-dimensional hydrodynamics appears to play a key role into the flame's dynamics, therefore the heat rate released by the microcombustor, one-dimensional models are not believed to deliver an adequate strategy of combustion control into such microchannels.Comment: 37 pages, 12 figure

Wave-Turbulence Theory of four-wave nonlinear interactions

The Sagdeev-Zaslavski (SZ) equation for wave turbulence is analytically derived, both in terms of generating function and of multi-point pdf, for weakly interacting waves with initial random phases. When also initial amplitudes are random, the one-point pdf equation is derived. Such analytical calculations remarkably agree with results obtained in totally different fashions. Numerical investigations of the two-dimensional nonlinear Schroedinger equation (NLSE) and of a vibrating plate prove that: (i) generic Hamiltonian 4-wave systems rapidly attain a random distribution of phases independently of the slower dynamics of the amplitudes, vindicating the hypothesis of initially random phases; (ii) relaxation of the Fourier amplitudes to the predicted stationary distribution (exponential) happens on a faster timescale than relaxation of the spectrum (Rayleigh-Jeans distribution); (iii) the pdf equation correctly describes dynamics under different forcings: the NLSE has an exponential pdf corresponding to a quasi-gaussian solution, like the vibrating plates, that also show some intermittency at very strong forcings

Weak versus strong wave turbulence in the MMT model

Within the spirit of fluid turbulence, we consider the one-dimensional Majda-McLaughlin-Tabak (MMT) model that describes the interactions of nonlinear dispersive waves. We perform a detailed numerical study of the direct energy cascade in the defocusing regime. In particular, we consider a configuration with large-scale forcing and small scale dissipation, and we introduce three non- dimensional parameters: the ratio between nonlinearity and dispersion, {\epsilon}, and the analogues of the Reynolds number, Re, i.e. the ratio between the nonlinear and dissipative time-scales, both at large and small scales. Our numerical experiments show that (i) in the limit of small {\epsilon} the spectral slope observed in the statistical steady regime corresponds to the one predicted by the Weak Wave Turbulence (WWT) theory. (ii) As the nonlinearity is increased, the WWT theory breaks down and deviations from its predictions are observed. (iii) It is shown that such departures from the WWT theoretical predictions are accompanied by the phenomenon of intermittency, typical of three dimensional fluid turbulence. We calculate the structure-function as well as the probability density function of the wave field at each scale and show that the degree of intermittency depends on {\epsilon}.Comment: 7 pages, 6 figure