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

Phenotypic signatures of urbanization are scale-dependent : a multi-trait study on a classic urban exploiter

Understanding at which spatial scales anthropogenic selection pressures operate most strongly is a prerequisite for efficient conservation and management of urban biodiversity. Heterogeneity in findings on the strength and direction of urbanization effects may result from a lack of consensus on which spatial scales are most adequate when studying biotic effects of urbanization. Therefore, here, using the house sparrow (Passer domesticus) as model, we test the hypothesis that more than one spatial scale will explain variation among phenotypic stress markers. By applying a unique hierarchical sampling design enabling us to differentiate between local and regional effects of urbanization, we here show that the strength and direction of relationships with the percentage of built-up area - a simple structural measure of urbanization - vary among phenotypic stress markers and across the spatial range over which urbanization is measured. While inverse relationships with scaled body mass and bill height of adult house sparrows (Passer domesticus) were strongest when the degree of urbanization was quantified at city-level, similar relationships with corticosterone concentrations in feathers were only detected at the scale of individual home ranges. In contrast, tarsus length, wing length, and two measures of feather development were not significantly related to urbanization at any spatial scale. As the suite of phenotypic stress markers applied in this study revealed signatures of urbanization over a broad spatial range, we conclude that measures aimed at mitigating impacts of urbanization on free-ranging populations should best be implemented at multiple spatial scales too

An Introduction to Non-diffusive Transport Models

The process of diffusion is the most elementary stochastic transport process. Brownian motion, the representative model of diffusion, played a important role in the advancement of scientific fields such as physics, chemistry, biology and finance. However, in recent decades, non-diffusive transport processes with non-Brownian statistics were observed experimentally in a multitude of scientific fields. Examples include human travel, in-cell dynamics, the motion of bright points on the solar surface, the transport of charge carriers in amorphous semiconductors, the propagation of contaminants in groundwater, the search patterns of foraging animals and the transport of energetic particles in turbulent plasmas. These examples showed that the assumptions of the classical diffusion paradigm, assuming an underlying uncorrelated (Markovian), Gaussian stochastic process, need to be relaxed to describe transport processes exhibiting a non-local character and exhibiting long-range correlations. This article does not aim at presenting a complete review of non-diffusive transport, but rather an introduction for readers not familiar with the topic. For more in depth reviews, we recommend some references in the following. First, we recall the basics of the classical diffusion model and then we present two approaches of possible generalizations of this model: the Continuous-Time-Random-Walk (CTRW) and the fractional L\'evy motion (fLm)

Lattice Boltzmann Methods for thermal flows: continuum limit and applications to compressible Rayleigh-Taylor systems

We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible Fourier- Navier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-B\'enard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx \times Lz = 1664 \times 4400 and with Rayleigh numbers up to Ra ~ 2 \times 10^10.Comment: 26 pages, 13 figure

Heat and work distributions for mixed Gauss-Cauchy process

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional external noise, with both sources of perturbations considered as additive and statistically independent forcings. We define thermodynamic quantities for trajectories of the process and analyze contributions to mechanical work and heat. As a working example we consider a particle subjected to a drag force and two independent Levy white noises with stability indices $\alpha=2$ and $\alpha=1$. The fluctuations of dissipated energy (heat) and distribution of work performed by the force acting on the system are addressed by examining contributions of Cauchy fluctuations to either bath or external force acting on the system