Erratum to: On the Correlation Properties of Thermal Noise in Fluids (original) (raw)
Related papers
Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids
In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset " history force " instead of the Stokes friction , which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force F th driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of F th in incompressible fluids. Our calculations show that the time decay of the correlator F th (t)F th (0) is significantly slower than that found in the literature. It is also shown how the " color " of the thermal noise can be determined from the measured positions of the Brownian particles.
On the Colour of Thermal Noise in Fluids
In the paper by Franosch et al., Nature 478, 85 (2011), the positional fluctuations of Brownian microspheres in fluids were studied by confining the particles in an optical trap. Experimental access to short timescales has revealed a resonance peak in the spectrum of these fluctuations, in contrast to the commonly assumed overdamped motion. This work is also interesting as the first measurement of the "colour" of thermal noise driving the Brownian particles through collisions with the fluid molecules. The obtained results are described by the hydrodynamic theory of the Brownian motion in harmonic potentials. In the present work we show that the correlation properties of the thermal noise significantly differ from those determined in the discussed work.
Fluctuations in a fluid under a stationary heat flux II. Slow part of the correlation matrix
Journal of Statistical Physics, 1985
We present a general theory of the Brillouin lines in a fluid subject to a strong stationary heat flux. The combined effects of sound-absorbing walls and of large spatial inhomogeneities induced by the temperature gradient are computed for the first time. Nonequilibrium sound modes, constructed by WKB techniques, are used. No restrictions have to be made in the theory concerning the scattering geometry and the thermal equations of state.
Autocorrelation of density fluctuations for thermally relativistic fluids
Physical Review D, 2013
The autocorrelation of density fluctuations for thermally relativistic fluids is formulated on the basis of the relativistic Navier-Stokes-Fourier equation under the static equilibrium state. The autocorrelation of density fluctuations for thermally relativistic fluids, obtained theoretically, is compared with the autocorrelation of density fluctuations for thermally relativistic fluids, calculated using the stochastic relativistic Boltzmann equation on the basis of the direct simulation Monte Carlo method. The theoretical result of the autocorrelation of density fluctuations for thermally relativistic fluids on the basis of the relativistic Navier-Stokes-Fourier equation gives good agreement with the numerical result of the autocorrelation of density fluctuations for thermally relativistic fluids in the lowest wave number, because we calculated the autocorrelation of density fluctuations for thermally relativistic fluids under the transition regime between the rarefied and continuum regimes.
Thermal noise in confined fluids
The Journal of chemical physics, 2014
In this work, we discuss a combined memory function equation (MFE) and generalized Langevin equation (GLE) approach (referred to as MFE/GLE formulation) to characterize thermal noise in confined fluids. Our study reveals that for fluids confined inside nanoscale geometries, the correlation time and the time decay of the autocorrelation function of the thermal noise are not significantly different across the confinement. We show that it is the strong cross-correlation of the mean force with the molecular velocity that gives rise to the spatial anisotropy in the velocity-autocorrelation function of the confined fluids. Further, we use the MFE/GLE formulation to extract the thermal force a fluid molecule experiences in a MD simulation. Noise extraction from MD simulation suggests that the frequency distribution of the thermal force is non-Gaussian. Also, the frequency distribution of the thermal force near the confining surface is found to be different in the direction parallel and per...
Fluctuations in fluids out of thermal equilibrium
Journal of Statistical Physics, 1989
After a brief review of dynamic correlations in equilibrium fluids, we consider the long-range correlations between the fluctuations in a fluid subjected to a large stationary temperature gradient. These long-range correlations enhance and modify the Rayleigh spectrum of the fluid. We elucidate that the modifications of the Rayleigh line are determined by the coupling of the entropy fluctuations to the transverse velocity fluctuations. Recent attempts to test the theoretical predictions with the aid of light-scattering experiments are discussed.
Physical Review E, 2015
The velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids, has been the first paradigmatic example of a long-time tail phenomenon, and much work has been devoted to detecting such long-lasting correlations and understanding their nature. There is, however, much more to the VAF than simply the evidence of this long-time dynamics. A unified description of the VAF from very short to long times, and of the way it changes with varying density, is still missing. Here we show that an approach based on very general principles makes such a study possible and opens the way to a detailed quantitative characterization of the dynamical processes involved at all time scales. From the analysis of molecular dynamics simulations for a slightly supercritical Lennard-Jones fluid at various densities, we are able to evidence the presence of distinct fast and slow decay channels for the velocity correlation on the time scale set by the collision rate. The density evolution of these decay processes is also highlighted. The method presented here is very general, and its application to the VAF can be considered as an important example.