Driven active matter: Fluctuations and a hydrodynamic instability

Kirkpatrick, T. R.; Bhattacherjee, J. K.

doi:10.1103/physrevfluids.4.024306

Cited by 10 publications

(8 citation statements)

References 57 publications

(71 reference statements)

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“…The case σ = 10 reported in Ref. [20] is consistent with a backward Hopf bifurcation. There, a limit cycle was observed for r < r H provided the initial conditions were sufficiently close to the center of the limit cycle.…”

Section: Fixed Points and Bifurcationssupporting

confidence: 68%

“…In Ref. [20] the driven form of active matter was studied where a gradient in the density of active particles was considered in one particular direction. To study the effect of non-linearity in this problem a Lorenz-like model was set up.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [20] we studied the properties of the steady-state and showed how they were significantly different from that of the standard Lorenz model.…”

Section: Introductionmentioning

confidence: 99%

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Transition to turbulence in driven active matter

2020

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A Lorenz-like model was set up recently, to study the hydrodynamic instabilities in a driven active matter system. This Lorenz model differs from the standard one in that all three equations contain non-linear terms. The additional non-linear term comes from the active matter contribution to the stress tensor. In this work, we investigate the non-linear properties of this Lorenz model both analytically and numerically. The significant feature of the model is the passage to chaos through a complete set of period-doubling bifurcations above the Hopf point for inverse Schmidt numbers above a critical value. Interestingly enough, at these Schmidt numbers a strange attractor and stable fixed points coexist beyond the homoclinic point. At the Hopf point, the strange attractor disappears leaving a high-period periodic orbit. This periodic state becomes the expected limit cycle through a set of bifurcations and then undergoes a sequence of period-doubling bifurcations leading to the formation of a strange attractor. This is the first situation where a Lorenz-like model has shown a set of consecutive period-doubling bifurcations in a physically relevant transition to turbulence.arXiv:1908.06247v3 [physics.flu-dyn]

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Section: Fixed Points and Bifurcationssupporting

confidence: 68%

Section: Introductionmentioning

confidence: 99%

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Transition to turbulence in driven active matter

2020

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“…Similar long-ranged correlation exist in more complex fluids such as binary mixtures with either a concentration gradient or a thermal gradient, 3,25,26 and in wet active matter. 27 These systems therefore also support the super-diffusive propagation of perturbations.…”

Section: Discussionmentioning

confidence: 77%

Rigidity and Superfast Signal Propagation in Fluids and Solids in Non-Equilibrium Steady States

2021

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In the 1980s it was theoretically predicted that correlations of various observables in a fluid in a non-equilibrium steady state (NESS) are extraordinarily long-ranged, extending, in a well-defined sense, over the size of the system. This is to be contrasted with correlations in an equilibrium fluid, whose range is typically just a few particle diameters. These NESS correlations were later confirmed by numerous experimental studies. Unlike long-ranged correlations at critical points, these correlations are generic in the sense that they exist for any temperature as long as the system is in a NESS. In equilibrium systems, generic long-ranged correlations are caused by spontaneously broken continuous symmetries and are associated with a generalized rigidity, which in turn leads to a new propagating excitation or mode. For example, in a solid, spatial rigidity leads to transverse sound waves, while in a superfluid, phase rigidity leads to temperature waves known as second sound at finite temperatures, and phonons at zero temperature. More generally, long-ranged spatial correlations imply rigidity irrespective of their physical origin. This implies that a fluid in a NESS should also display a type of rigidity and related anomalous transport behavior. Here we show that this is indeed the case. For the particular case of a simple fluid in a constant temperature gradient, the anomalous transport behavior takes the form of a super-diffusive spread of a constant-pressure temperature perturbation. We also discuss the case of an elastic solid, where we predict a spread that is faster than ballistic.

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“…This effective body force originates from projecting the advection nonlinearity in the Boussinesq model onto the 2D order parameter model. This force has a functional analog in models of active matter in which an active stress breaks equilibrium symmetry relations [22][23][24] and hence directly allows non-variational flows.…”

Section: A the Generalized Swift-hohenberg Modelmentioning

confidence: 99%

Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals

Vitral¹,

Mukherjee²,

Leo³

et al. 2020

Preprint

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Rotating spiral patterns in Rayleigh-Bénard convection are known to induce azimuthal flows, which raises the question of how different neighboring spirals interact with each other in spiral chaos, and the role of hydrodynamics in this regime. Far from the core, we show that spiral rotations lead to an azimuthal body force that is irrotational and of magnitude proportional to the topological index of the spiral and its angular frequency. The force, although irrotational, cannot be included in the pressure field as it would lead to a nonphysical, multivalued pressure. We calculate the asymptotic dependence of the resulting flow, and show that it leads to a logarithmic dependence of the azimuthal velocity on distance r away from the spiral core in the limit of negligible damping coefficient. This solution dampens to approximately 1/r when accounting for no-slip boundary conditions for the convection cell's plate. This flow component can provide additional hydrodynamic interactions among spirals including those observed in spiral defect chaos. We show that the analytic prediction for the azimuthal velocity agrees with numerical results obtained from both two-dimensional generalized Swift-Hohenberg and three-dimensional Boussinesq models, and find that the velocity field is affected by the size and charges of neighboring spirals. Numerically, we identify a correlation between the appearance of spiral defect chaos and the balancing between the mean-flow advection and the diffusive dynamics related to roll unwinding.

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Driven active matter: Fluctuations and a hydrodynamic instability

Cited by 10 publications

References 57 publications

Transition to turbulence in driven active matter

Transition to turbulence in driven active matter

Rigidity and Superfast Signal Propagation in Fluids and Solids in Non-Equilibrium Steady States

Spiral defect chaos in Rayleigh-Bénard convection: Asymptotic and numerical studies of azimuthal flows induced by rotating spirals

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