Mode Selection in Compressible Active Flow Networks

Abstract

Coherent, large-scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for compressible active flow networks. In contrast to thermally driven systems, we find that active friction selects discrete states with a limited number of oscillation modes activated at distinct fixed amplitudes. Using perturbation theory, we systematically predict the stationary states of noisy networks and find good agreement with a Bayesian state estimation based on a hidden Markov model applied to simulated time series data. Our results suggest that the macroscopic response of active network structures, from actomyosin force networks to cytoplasmic flows, can be dominated by a significantly reduced number of modes, in contrast to energy equipartition in thermal equilibrium. The model is also well suited to study topological sound modes and spectral band gaps in active matter. DOI: 10.1103/PhysRevLett.119.028102 Active networks constitute an important class of nonequilibrium systems spanning a wide range of scales, from the intracellular cytoskeleton [1] and amoeboid organisms [2-4] to macroscopic transport networks [5]. Identifying generic self-organization principles [6,7] that control the dynamics of these biological or artificial far-fromequilibrium systems remains one of the foremost challenges of modern statistical physics. Despite promising experimental [3,[8][9][10] and theoretical [1,4,[11][12][13] advances over the past decade, it is not well understood how the interactions between local energy input, dissipation, and network topology determine the coordinated global behaviors of cells [8] [19], the theory accounts for network activity through a nonlinear friction [19][20][21]. We work in a fully compressible framework allowing accumulated matter at vertices to affect flow through network pressure gradients, generalizing previous work on incompressible pseudoequilibrium active flow networks [22,23], as suited to the many biological systems exhibiting flexible network geometry [3] or variations in the density of active components [7]. Although inherently nonlinear, the model can be systematically analyzed through perturbation theory. Such an analysis shows how slow global dynamics emerge naturally from the fast local dynamics, enabling the prediction of the typical states in large noisy networks; these states have significantly fewer active modes than for energy equipartition [24] in thermal equilibrium. More broadly, our model provides an accessible framework for investigating generic physical phenomena in active systems, including topologically protected sound modes [7] and the influence of spectral band gaps (Supplemental Material [25]).We consider activity-driven mass flow on an arbitrarily oriented graph G ¼ ðV; EÞ with V ¼ jVj vertices and E ¼ jEj edges. The elements of the V × E gradient (incidence) matrix ∇ are ∇ ve ¼ −1 if edge e is oriented outwards from verte...

Flowing Active Liquids in a Pipe: Hysteretic Response of Polar Flocks to External Fields

“…Finally, we have effectively exploited the bistability of active flows to engineer active-fluid oscillators with frequency and amplitude set by the geometry of the container. Together with the virtually unlimited geometries accessible to microfabrication, the intrinsic nonlinearity of active flows offer an effective framework for the design of emergent microfluidic functions [22][23][24]. Our experiments are based on colloidal rollers, see [4].…”

Autonomous Actuation of Zero Modes in Mechanical Networks Far from Equilibrium

“…First, we show that correlated noise generated by an active matter bath [49] can actuate a complex mechanical IZM while markedly suppressing HMs to a degree dependent on temporal correlations, as well as exemplifying experimentally that fluctuation-based IZM actuation can be mimicked by simple high-frequency shaking. We then broaden to self-propulsive Rayleigh activity [55][56][57], appropriate for a network whose nodes have intrinsic motility [58]. We show that this scheme mobilises a full mechanism comprising a propagating domain boundary in the SSH lattice [11,27], suggesting that Goldstone modes of arbitrary complex systems can be mobilised by nonequilibrium driving [51,59,60].…”

“…We now turn to a stronger form of activity. If the masses themselves are motile, able to convert chemical energy to kinetic energy, an effective model is to introduce what amounts to a negative frictional response at low speeds [56,57]. Appealing to expansion techniques, as in the Toner-Tu model [68], we use simple Rayleigh activity [66] with a velocity-dependent propulsive force…”

Emergence of behavior in a self-organized living matter network

“…It is likely that the contraction states with many significant modes here act as noise that can spontaneously cause the organism to 'decide' and reorient its direction of locomotion. P. polycephalum's body-plan as a fluid-filled living network with emerging behavior finds its theoretical counterpart in theories for active flow networks developed recently (48,49). Strikingly, these theories predict selective activation of thick tubes which we observe in the living network as well, prominently appearing among the top ranking modes, see φ 4 Fig.…”