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Register a new userSwimmer suspensions on substrates: anomalous stability and long-range order
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We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations at zero wavenumber. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature ${bf 503}$, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability
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We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.
We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a Maxwell-Boltzmann distribution. The PDFs are symmetric around zero velocity and show a Gaussian core and exponential tails over more than six orders of magnitude of probability. Following the excellent agreement of our theory and simulation data, we demonstrate that the distribution functions scale with the shear rate, the particle volume concentration, as well as the fluid viscosity.
We introduce and study in two dimensions a new class of dry, aligning, active matter that exhibits a direct transition to orientational order, without the phase-separation phenomenology usually observed in this context. Characterized by self-propelled particles with velocity reversals and ferromagnetic alignment of polarities, systems in this class display quasi-long-range polar order with continuously-varying scaling exponents and yet a numerical study of the transition leads to conclude that it does not belong to the Berezinskii-Kosterlitz-Thouless universality class, but is best described as a standard critical point with algebraic divergence of correlations. We rationalize these findings by showing that the interplay between order and density changes the role of defects.
Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as ``pushers and ``pullers, display qualitatively different collective behaviours: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher--puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction $chi$ of pullers is increased and disappears for $chi geq 0.5$. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1:1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer--swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1:1 pusher--puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.
In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is non-perturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its non-trivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.
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