Generalized hydrodynamics of a dilute finite-sized particles suspension: Dynamic viscosity

We present a mesoscopic hydrodynamic description of the dynamics of colloidal suspensions. We consider the system as a gas of Brownian particles suspended in a Newtonian heat bath subjected to stationary non-equilibrium conditions imposed by a velocity field. Using results already obtained in previous studies in the field by means of a generalized Fokker-Planck equation, we obtain a set of coupled differential equations for the local diffusion current and the evolution of the total stress tensor. We find that the dynamic shear viscosity of the system contains contributions arising from the finite size of the particles.Comment: To appear in Physical Review

At a time of insurgent parties, can societies believe in election polls?. The Spanish experience

The main purpose of this paper is to use the Spanish case, through an econometric analysis of 226 electoral polls, to explain why polls are making more mistakes in times of great socioeconomic slumps, political instability and the emergence of new political parties. In this context, it is the very instrument with which society tries to reduce the reigning uncertainty that, paradoxically, can ultimately drive uncertainty up. Our results show that the prediction error for the new emerging parties is significantly higher than for the traditional parties and this error is not sensitive to solutions for increasing the reliability of surveys, such as increasing sample size, transparency constantly conducting periodical surveys, the closeness of the approaching election or the survey mode that is used. It can be observed that pollsters do not want to make predictions that vary greatly from the average of the other polls. Finally, editorial bias appears to play a significant role, especially in the case of traditional parties.El principal objetivo de este artículo es explicar por qué las encuestas electorales cometen más errores en épocas de crisis económica, inestabilidad política y con partidos emergentes como Podemos y Ciudadanos. Para ello utilizamos una base de datos de 226 encuestas previas a las elecciones generales españolas de 2016. En este contexto, paradójicamente vemos como el instrumento que la sociedad utiliza para reducir su incertidumbre puede acabar aumentándola. Nuestros resultados muestran como el error de predicción de los nuevos partidos es significativamente mayor que los tradicionales e insensible a las soluciones clásicas para aumentar la precisión de las encuestas, como el tamaño de la muestra, el método de muestreo, la experiencia del encuestador, o la proximidad de la cita electoral. Además, se observa que las empresas que desarrollan las encuestas realizan de forma sistemática predicciones muy próximas a las que han realizado las encuestas recientes de sus competidores. Finalmente, el sesgo editorial parece ser una variable relevante, especialmente en lo relativo a las predicciones de los partidos tradicionale

Truncation effects in superdiffusive front propagation with L\'evy flights

A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a $\lambda$-truncated fractional derivative of order $\alpha$ where $1/\lambda$ is the characteristic truncation length scale. For $\lambda=0$ there is no truncation and fronts exhibit exponential acceleration and algebraic decaying tails. It is shown that for $\lambda \neq 0$ this phenomenology prevails in the intermediate asymptotic regime $(\chi t)^{1/\alpha} \ll x \ll 1/\lambda$ where $\chi$ is the diffusion constant. Outside the intermediate asymptotic regime, i.e. for $x > 1/\lambda$, the tail of the front exhibits the tempered decay $\phi \sim e^{-\lambda x}/x^{(1+\alpha)}$, the acceleration is transient, and the front velocity, $v_L$, approaches the terminal speed $v_* = (\gamma - \lambda^\alpha \chi)/\lambda$ as $t\to \infty$, where it is assumed that $\gamma > \lambda^\alpha \chi$ with $\gamma$ denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, $v_L \sim v_* - \alpha /(\lambda t)$, which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An over-truncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, $1/\nu$, is also identified. In this extreme regime, fronts exhibit exponential tails, $\phi \sim e^{-\nu x}$, and move at the constant velocity, $v=(\gamma - \lambda^\alpha \chi)/\nu$.Comment: Accepted for publication in Phys. Rev. E (Feb. 2009

Non-diffusive transport in plasma turbulence: a fractional diffusion approach

Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time, that incorporate in a unified way space-time non-locality (non-Fickian transport), non-Gaussianity, and non-diffusive scaling. The fractional diffusion model reproduces the shape, and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed super-diffusive scaling

Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non- Gaussian PDFs of particle displacements, with L\'evy flights in one direction but not the other. For zero Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. However, FLR effects seem to eliminate this transition. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of the Larmor radii. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma