Response of active Brownian particles to shear flow

Abstract

We study the linear response of interacting active Brownian particles in an external potential to simple shear flow. Using a path integral approach, we derive the linear response of any state observable to initiating shear in terms of correlation functions evaluated in the unperturbed system. For systems and observables which are symmetric under exchange of the x and y coordinates, the response formula can be drastically simplified to a form containing only state variables in the corresponding correlation functions (compared to the generic formula containing also time derivatives). In general, the shear couples to the particles by translational as well as rotational advection, but in the aforementioned case of xy symmetry only translational advection is relevant in the linear regime. We apply the response formulas analytically in solvable cases and numerically in a specific setup. In particular, we investigate the effect of a shear flow on the morphology and the stress of N confined active particles in interaction, where we find that the activity as well as additional alignment interactions generally increase the response.

Chemical Langevin equation: A path-integral view of Gillespie's derivation

“…Although path integrals [47] are most well-known in the context of quantum mechanics and quantum field theory [19,[48][49][50][51][52], they have also proven useful for understanding classical stochastic phenomena like Brownian motion [53][54][55], conformational transitions [56][57][58], quantitative finance [50,59,60], population dynamics [61][62][63][64][65], neuron firing [66][67][68][69][70][71][72], gene regulation [36,[73][74][75][76][77], and chemical kinetics [78][79][80][81][82].…”

Brownian systems perturbed by mild shear: Comparing response relations

“…Based on the approaches of Refs. [29,32,35], we demonstrate in detail how the response to shear can be equivalently replaced by the response to a potential, thanks to certain symmetries (Sec. III).…”

“…Yet linear response theory for equilibrium Brownian systems is still far from being understood comprehensively. Although it is known that one can use different response formulas to compute a certain response for a particular scenario [2,14,23,29,32,35], the comparison of the formulas (e.g., in terms of their statistical efficiency) was only very recently performed [29,32,35]. Such a comparison can help choosing the best formula for a particular case, in order to minimize computational resources or experimental measurement time.…”

“…Another important aspect, which has not been studied in detail, concerns the role of system properties in response computations. For example, certain symmetries of the considered system allow to compute the response via alternative ways [29,32,35]. One more fact is that underdamped Brownian particles have been investigated much less frequently than overdamped ones, because the latter model is more simple yet widely applicable in many practical cases.…”

Migration of active filaments under Poiseuille flow in a microcapillary tube

“…Few more recent studies have analysed trajectories of motion for the spherical and elongated colloids [40,41], which revealed a helical path near the surfaces, a tumbling motion and swinging like dynamics near the centreline for the elongated colloids in the cylindrical channel. Most of the simulation studies so far have focused in two dimensions or in the absence of hydrodynamic effects [8][9][10][11][13][14][15][16][17][17][18][19][20][21][22]22,38,39,[67][68][69][70][71][72]. It is important to get the understanding of elongated microswimmers' dynamics in the presence of hydrodynamics and steric interactions in a cylindrical geometry, since most of the natural microswimmers are elongated in shape and live near the surfaces and in-counter external perturbations in the form of fluid flow [2,[73][74][75].…”