Fluctuations of Energy Flux in Wave Turbulence

Falcon, Éric; Aumaître, Sébastien; Falcón, Claudio; Laroche, C.; Fauve, S.

doi:10.1103/physrevlett.100.064503

Cited by 68 publications

(116 citation statements)

References 36 publications

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“…For all values of D and γ, the PDFs exhibit two asymmetric exponential tails and a cusp near I ≃ 0. Note that this typical PDF shape has been also observed in various more complex systems (granular gases [10], wave turbulence [22] and convection [12,28]). As shown in Fig.…”

Section: Statistical Properties Of the Injected Powersupporting

confidence: 62%

“…The asymmetry is driven by the damping rate: The more the mean dissipation increases, the less the negative events of injected power occur. This electronic circuit is one of the simplest system to understand the properties of the energy flux fluctuations shared by other dissipative out-ofequilibrium systems (such as in granular gases [10], wave turbulence [22] and convection [12,28]). …”

Section: Introductionmentioning

confidence: 99%

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Fluctuations of energy flux in a simple dissipative out-of-equilibrium system

Falcón¹,

Falcon

2009

Phys. Rev. E

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We report the statistical properties of the fluctuations of the energy flux in an electronic RC circuit driven with a stochastic voltage. The fluctuations of the power injected in the circuit are measured as a function of the damping rate and the forcing parameters. We show that its distribution exhibits a cusp close to zero and two asymmetric exponential tails, the asymmetry being driven by the mean dissipation. This simple experiment allows to capture the qualitative features of the energy flux distribution observed in more complex dissipative systems. We also show that the large fluctuations of injected power averaged on a time lag do not verify the Fluctuation Theorem even for long averaging time. This is in contrast with the findings of previous experiments due to their small range of explored fluctuation amplitude. The injected power in a system of N components either correlated or not is also studied to mimic systems with large number of particles, such as in a dilute granular gas.

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Section: Statistical Properties Of the Injected Powersupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Fluctuations of energy flux in a simple dissipative out-of-equilibrium system

Falcón¹,

Falcon

2009

Phys. Rev. E

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“…We can then compute the integral over ω by using Cauchy's residue theorem, which requires to locate the poles of χ(ω) in the complex frequency plane (they are not restricted to be in the lower half plane, in contrast with the poles of the causal response function χ(ω)). Fortunately, this nontrivial task has already been accomplished in I in order to calculate the quantitẏ S J ≡ lim t→∞ (1/t) ln J t / J t involved in the second-lawlike inequality (26) obtained from time reversal (we recall that the Jacobian J [X] becomes a path-independent quantity J t when the dynamics is linear [6]). Specifically, it was shown in I [Eq.…”

Section: Calculation Of the (Boundary-independent) Scgfmentioning

confidence: 99%

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

2017

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This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like inequalities that provide bounds to the average extracted work. Here we study stochastic fluctuations of time-integrated observables such as the heat exchanged with the environment, the extracted work, or the (apparent) entropy production. We use a path-integral formalism and focus on the long-time behavior in the stationary cooling regime, stressing the role of rare events. This is illustrated by a detailed analytical and numerical study of a Langevin harmonic oscillator driven by a linear feedback.

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“…Interestingly, many experimental and theoretical results have shown that deviations from wave-turbulence predictions can be found for rare events, e.g. intermittency [8,[25][26][27][28][29]. This seems to be the case when a more general theoretical framework [30][31][32][33][34] is required, because the nonlinearities are not small [35,36].…”

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confidence: 99%

Wave-turbulence theory of four-wave nonlinear interactions

et al. 2017

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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 Schrödinger 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.Introduction Dispersive waves are ubiquitous in nature, and their nonlinear interactions make them intriguing and challenging [1,2]. Wave Turbulence is the theory that describes the statistical properties of large numbers of incoherent interacting waves, with tools such as the wave kinetic equation analytically derived in the late sixties. This equation describes the evolution of the wave spectrum in time, when homogeneity and weak nonlinearity are assumed [3][4][5]. It has been applied to numerous phenomena, including ocean waves [6][7][8], capillary waves [9, 10] Alfvén waves [11], optical waves [12] and solid oscillations [13][14][15][16][17][18]. It is the analogue of the Boltzmann equation for classical particles and it allows the RayleighJeans equilibrium state as well as non-equilibrium solutions, in terms of Kolmogorov-Zakharov (KZ) spectra [19].To characterise the invariant measure of the dynamics, that is to find the complete statistical description concerning all quantities of interest, an important step has been taken by Sagdeev and Zaslavski [20], who obtained the Brout-Prigogine equation for the probability density function (pdf) of wave turbulence [21]. More recently, this statistical framework has been nicely revisited using the diagrammatic technique [4] and performing analytical calculations, in the 3-wave case [22][23][24]. Interestingly, many experimental and theoretical results have shown that deviations from wave-turbulence predictions can be found for rare events, e.g. intermittency [8,[25][26][27][28][29]. This seems to be the case when a more general theoretical framework [30][31][32][33][34] is required, because the nonlinearities are not small [35,36].In this communication, the complete wave-turbulence theory is developed for a fully general 4-wave system, whose hamiltonian is expressed by the following canoni-

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Fluctuations of Energy Flux in Wave Turbulence

Cited by 68 publications

References 36 publications

Fluctuations of energy flux in a simple dissipative out-of-equilibrium system

Fluctuations of energy flux in a simple dissipative out-of-equilibrium system

Stochastic thermodynamics of Langevin systems under time-delayed feedback control. II. Nonequilibrium steady-state fluctuations

Wave-turbulence theory of four-wave nonlinear interactions

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