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Register a new userPower law tails of time correlations in a mesoscopic fluid model
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In a quenched mesoscopic fluid, modelling transport processes at high densities, we perform computer simulations of the single particle energy autocorrelation function C_e(t), which is essentially a return probability. This is done to test the predictions for power law tails, obtained from mode coupling theory. We study both off and on-lattice systems in one- and two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent agreement with the results of computer simulations. We also account for finite size effects, such that smaller systems are fully covered by the present theory as well.
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We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L{e}vy distribution. For both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {it beyond the truncation cutoff}, which leads to a crossover between a L{e}vy stable power law and the present ``dynamically-generated power law. We show that the process can explain the crossover behavior recently observed in the $S&P500$ stock index.
Newton viscosity law for the momentum flux and Fouriers law for the heat flux define Navier-Stokes hydrodynamics for a simple, one component fluid. There is ample evidence that a hydrodynamic description applies as well to a mesoscopic granular fluid with the same form for Newtons viscosity law. However, theory predicts a qualitative difference for Fouriers law with an additional contribution from density gradients even at uniform temperature. The reasons for the absence of such terms for normal fluids are indicated, and a related microscopic explanation for their existence in granular fluids is presented.
We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.
We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and the order size. We find that the order imbalance distributions of individual stocks have power-law tails. However, the tail index fluctuates remarkably from stock to stock. We also investigate the distributions of aggregated order imbalance of all stocks at different timescales $Delta{t}$. We find no clear trend in the tail index with respect $Delta{t}$. All the analyses suggest that the distributions of order imbalance are asymmetric.
We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the systems equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.
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