Spatially correlated random walks and turbulence

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The wide applicability of the random walks (RW) to natural phenomena relies just on the possibility to introduce appropriate generalizations on the probabilistic nature of displacements. A straightforward generalization is realized by assuming correlations in displacements to obtain the so called correlated random walks (CRW).

This possibility extends also to a set of particles distributed in space leading to the definition of spatially correlated random walks.… Read the rest

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Role of microscopic chaos to macroscopic transport

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The discovery that simple deterministic nonlinear systems could display dynamical evolution characterized by a randomness similar to stochastic processes changed very much researchers’ attitude toward determinism and predictability of natural phenomena. Determinstic chaos has been successfully invoked to interpret several irregular behaviors, however its role to the fundaments of statistical physics still remains debated in modern statistical mechanics. In other terms, one is tempted to think that a macroscopic system with chaotic microscopic interactions is more robust with respect to statistical mechanical principles thant the same system with non-chaotic interactions.… Read the rest

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Transport in binary mixtures

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When a binary fluid mixture at the critical concentration is cooled from a high temperature to a sufficiently low temperature (below a critical one), the original homogeneous phase becomes unstable and spontaneously evolves into two phases separated by an interface. As time advances, an out-of-equilibrium process of phase ordering takes place through the formation of domains of a single phase that grows algebraically in time as L(t)~t1/3.… Read the rest

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Lagrangian Turbulence

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Recently, part of the research activity on turbulence has focused on temporal properties of turbulent statistics which are much less known than the equivalent spatial properties, and are expected to bring information on some of the mechanisms responsible for intermittency in turbulence, for example lagrangian motion is strongly affected by the presence of vortical motion around vortex filaments (see Figure 1).… Read the rest

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Scalar Turbulence

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The ability of efficiently mixing transported substances is one of the most distinctive properties of turbulence. For instance, it is turbulence (induced by the spoon) that allows cream to rapidly invade a cup of coffee, indeed if only molecular diffusion would be at play in the coffee at rest the same process would require many hours! Given the statistical complexity of a turbulent velocity field, it is natural to wonder about the resulting complexity in the statistical features of the transported concentration field of a substance (e.g.… Read the rest

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Inertial Particles in Turbulent Flows

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We already mentioned that enhanced mixing is probably one of the most distinguishing feature of turbulence. When a turbulent flow is seeded with particulate matter having a finite size and/or density different from that of the carrier fluid, new features appear. The figure on the left show the instantaneous position particles which are heavier (e.g. water drops in air) resp. lighter (e.g.… Read the rest

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