23 research outputs found
Antipolar ordering of topological defects in active liquid crystals
ATP-driven microtubule-kinesin bundles can self-assemble into two-dimensional
active liquid crystals (ALCs) that exhibit a rich creation and annihilation
dynamics of topological defects, reminiscent of particle-pair production
processes in quantum systems. This recent discovery has sparked considerable
interest but a quantitative theoretical description is still lacking. We
present and validate a minimal continuum theory for this new class of active
matter systems by generalizing the classical Landau-de Gennes free-energy to
account for the experimentally observed spontaneous buckling of motor-driven
extensile microtubule bundles. The resulting model agrees with recently
published data and predicts a regime of antipolar order. Our analysis implies
that ALCs are governed by the same generic ordering principles that determine
the non-equilibrium dynamics of dense bacterial suspensions and elastic bilayer
materials. Moreover, the theory manifests an energetic analogy with strongly
interacting quantum gases. Generally, our results suggest that complex
non-equilibrium pattern-formation phenomena might be predictable from a few
fundamental symmetry-breaking and scale-selection principles.Comment: final accepted journal version; SI text and movies available at
article on iop.or
Lattices of hydrodynamically interacting flapping swimmers
Fish schools and bird flocks exhibit complex collective dynamics whose
self-organization principles are largely unknown. The influence of
hydrodynamics on such collectives has been relatively unexplored theoretically,
in part due to the difficulty in modeling the temporally long-lived
hydrodynamic interactions between many dynamic bodies. We address this through
a novel discrete-time dynamical system (iterated map) that describes the
hydrodynamic interactions between flapping swimmers arranged in one- and
two-dimensional lattice formations. Our 1D results exhibit good agreement with
previously published experimental data, in particular predicting the
bistability of schooling states and new instabilities that can be probed in
experimental settings. For 2D lattices, we determine the formations for which
swimmers optimally benefit from hydrodynamic interactions. We thus obtain the
following hierarchy: while a side-by-side single-row "phalanx" formation offers
a small improvement over a solitary swimmer, 1D in-line and 2D rectangular
lattice formations exhibit substantial improvements, with the 2D diamond
lattice offering the largest hydrodynamic benefit. Generally, our
self-consistent modeling framework may be broadly applicable to active systems
in which the collective dynamics is primarily driven by a fluid-mediated
memory
The invariant measure of a walking droplet in hydrodynamic pilot-wave theory
We study the long time statistics of a walker in a hydrodynamic pilot-wave
system, which is a stochastic Langevin dynamics with an external potential and
memory kernel. While prior experiments and numerical simulations have indicated
that the system may reach a statistically steady state, its long-time behavior
has not been studied rigorously. For a broad class of external potentials and
pilot-wave forces, we construct the solutions as a dynamics evolving on
suitable path spaces. Then, under the assumption that the pilot-wave force is
dominated by the potential, we demonstrate that the walker possesses a unique
statistical steady state. We conclude by presenting an example of such an
invariant measure, as obtained from a numerical simulation of a walker in a
harmonic potential
The onset of chaos in orbital pilot-wave dynamics
We present the results of a numerical investigation of the emergence of chaos in the orbital dynamics of droplets walking on a vertically vibrating fluid bath and acted upon by one of the three different external forces, specifically, Coriolis, Coulomb, or linear spring forces. As the vibrational forcing of the bath is increased progressively, circular orbits destabilize into wobbling orbits and eventually chaotic trajectories. We demonstrate that the route to chaos depends on the form of the external force. When acted upon by Coriolis or Coulomb forces, the droplet's orbital motion becomes chaotic through a period-doubling cascade. In the presence of a central harmonic potential, the transition to chaos follows a path reminiscent of the Ruelle-Takens-Newhouse scenario
Orbiting pairs of walking droplets: Dynamics and stability
A decade ago, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)]PRLTAO0031-900710.1103/PhysRevLett.97.154101 discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We here present the results of a combined experimental and theoretical investigation of the interactions of such walking droplets. Specifically, we delimit experimentally the different regimes for an orbiting pair of identical walkers and extend the theoretical model of Oza [J. Fluid Mech. 737, 552 (2013)] JFLSA70022-112010.1017/jfm.2013.581 in order to rationalize our observations. A quantitative comparison between experiment and theory highlights the importance of spatial damping of the wave field. Our results also indicate that walkers adapt their impact phase according to the local wave height, an effect that stabilizes orbiting bound states.National Science Foundation (U.S.) (Grant CMMI-1333242)National Science Foundation (U.S.) (Grant DMS-1614043
Resonant interactions in bouncing droplet chains
International audienceIn a pioneering series of experiments, Yves Couder, Emmanuel Fort and coworkers demonstrated that droplets bouncing on the surface of a vertically vibrating fluid bath exhibit phenomena reminiscent of those observed in the microscopic quantum realm. Inspired by this discovery, we here conduct a theoretical and numerical investigation into the structure and dynamics of one-dimensional chains of bouncing droplets. We demonstrate that such chains undergo an oscillatory instability as the system's wave-induced memory is increased progressively. The predicted oscillation frequency compares well with previously reported experimental data. We then investigate the resonant oscillations excited in the chain when the drop at one end is subjected to periodic forcing in the horizontal direction. At relatively high memory, the drops may oscillate with an amplitude larger than that prescribed, suggesting that the drops effectively extract energy from the collective wave field. We also find that dynamic stabilization of new bouncing states can be achieved by forcing the chain at high frequency. Generally, our work provides insight into the collective behavior of particles interacting through long-range and temporally nonlocal forces