565 research outputs found
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
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