Separation of heavy particles in turbulence

We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time scales of the flow. Because of inertia, particles drift relative to the fluid. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast. This allows us to introduce Langevin description for separation dynamics. We describe the behavior of the Lyapunov exponent and give the analogue of Richardson's law for separation above viscous scale

Enantiomeric discrimination of chiral crown ether ionophores containing phenazine subcyclic unit by ion-selective potentiometry

In this paper the enatiomeric selectivity of two chiral phenazino-18-crown-6 ether hosts ((R,R)-\textbf1 and (R,R)-\textbf2) is quantified. These hosts were incorporated into plasticized PVC membranes and used as recognition elements of ion-selective electrodes. The potentiometric response towards the two enantiomers of 1-phenylethylammonium ions (PEA+) was measured. Potentiometric selectivity coefficients were calculated which reflect the ratio of the stability constants of the diastereomeric complexes. Ligand (R,R)-\textbf1 does not show enantiomeric recognition, while ligand (R,R)-\textbf2 has a slight preference for the (S)-(-) enantiomer over the (R)-(+) enantiomer manifested by a selectivity coefficient of 0.77. The results were compared to enantioselectivity patterns of the ligands towards α -(1-naphthyl)ethyl ammonium perchlorate (NEA+ClO4-) enantiomers measured by circular dichroism and by 1H NMR titrations

Multifractal Clustering in Compressible Flows

International audienceA quantitative relationship is found between the multifractal properties of the asymptotic mass distribution in a random dissipative system and the long-time fluctuations of the local stretching rates of the dynamics. It captures analytically the fine aspects of the strongly intermittent clustering of dynamical trajectories. Applied to a simple compressible hydrodynamical model with known stretching-rate statistics, the relation produces a nontrivial spectrum of multifractal dimensions that is confirmed numerically

Fluctuation relation and pairing rule for Lyapunov exponents of inertial particles in turbulence

We study the motion of small particles in a random turbulent. flow assuming a linear law of friction. We derive a symmetry relation obeyed by the large deviations of the. finite- time Lyapunov exponents in the phase space. The relation applies when either the statistics of the strain matrix is invariant under the transposition or when it is time reversible. We show that, as a result, the Lyapunov exponents come in pairs whose sum is equal to minus the inverse relaxation time of the particles. We use the pairing to consider the Kaplan - Yorke dimension of the particles' attractor in the phase space. In particular, the results apply to case of the. flow which is white noise in time