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Due to their morphology, the dynamics of bacteria suspended in media can exhibit complex behaviors. In the presence of a shear, swimming bacteria experience a drift perpendicular to the shear plane. This drift, termed rheotaxis, is studied here semi-analytically, numerically and experimentally. We find the dependency of bacterial orientation and bacterial speed on the shear rate, in the presence of rotational diffusion. This enables us to show that the drift speed of bacteria perpendicular to the shear is predominantly due to bacterial propulsion, and not rheotactic forces. Comparing the drift speed of bacteria and diffusion leads to the definition of a P\'{e}clet number. The rheotactic effect increases with the shear, reaching a plateau at very large P\'{e}clet numbers, in good agreement with experiments of rheotaxis performed in microfluidic droplets., Comment: 15 pages, 9 figures

We investigate both experimentally and numerically the impact of liquid drops on deep pools of aqueous glycerol solutions with variable pool viscosity and air pressure. With this approach we are able to address drop impacts on substrates that continuously transition from low-viscosity liquids to almost solids. We show that the generic corolla spreading out from the impact point consists of two distinct sheets, namely an ejecta sheet fed by the drop liquid and a second sheet fed by the substrate liquid, which evolve on separated timescales. These two sheets contribute to a varying extent to the corolla overall dynamics and splashing, depending in particular on the viscosity ratio between the two liquids., Comment: 5 pages, 3 figures

In fluid turbulence, energy is transferred from a scale to another by an energy cascade that depends only on the energy dissipation rate. It leads by dimensional arguments to the Kolmogorov 1941 (K41) spectrum. Remarkably the normal modes of vibrations in elastic plates manifests an energy cascade with the same K41 spectrum in the fully non-linear regime. Moreover, the elastic deformations present large "eddies" together with a myriad of small "crumpling eddies", such that folds, developable cones, and more complex stretching structures, in close analogy with spots, swirls, vortices and other structures in hydrodynamic turbulence. We characterize the energy cascade, the validity of the constant energy dissipation rate over the scales and the role of intermittency via the correlation functions.

We present a study of viscous fingering using the Volume Of Fluid method and a central injection geometry, assuming a Laplacian field and a simple surface tension law. As in experiments we see branched structures resulting from the Saffman-Taylor instability. We find that the area $A$ of a viscous-fingering cluster varies as a simple power law $A \sim L^{\alpha}$ of its interface length $L$. Our results are compared to previously published simulations in which the viscosity of the invading fluid is vanishing. We find differences in exponent $\alpha$ and in the appearance of detached droplets and bubbles.

The splashing of a drop impacting onto a liquid pool produces a range of different sized micro-droplets. At high impact velocities, the most significant source of these droplets is a thin liquid jet emerging at the start of the impact from the neck that connects the drop to the pool. We use ultra-high-speed video imaging in combination with high-resolution numerical simulations to show how the ejecta gives way to irregular splashing. At higher Reynolds number, its base becomes unstable, shedding vortex rings into the liquid from the free surface in an axisymmetric von K��rm��n vortex street, thus breaking the ejecta sheet as it forms., 5 pages, 4 figure, 2 supplemental videos

We review the main properties of a supersolid. We describe first the macroscopic equation that satisfies a supersolid based on general arguments and symmetries and show that such solids might exhibit simultaneously or independently both elastic behavior and superfluidity. We then explain why a supersolid state should exist for solids at very low temperature but with a very small superfluid fraction. Finally, we propose a mean-field model, based on the Gross-Pitaevski\u{\i} equation, which presents the general properties expected for a supersolid and should therefore provide a consistent framework to study its dynamical properties., Comment: Lecture notes of the 4th Warsaw School on Statistical Ohysics

We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence a nonlinear wave system evolves in long-time creating a slow transfer of energy from one mode to another. We derive this kinetic equation for the spectral transfer in terms of the second order moment. We show explicitly that such a non-equilibrium theory describes the approach to an equilibrium wave spectrum, and describes also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations confirming this scenario.