Communication: Green-Kubo approach to the average swim speed in active Brownian systems

Sharma, Abhinav; Brader, Joseph M.

doi:10.1063/1.4966153

Cited by 35 publications

(65 citation statements)

References 22 publications

(57 reference statements)

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“…In Ref. [74,78], a similar linear dependence of v(ρ) on ρ was found for a system of ABPs in three spatial dimensions. Reference [79] considers a system of reproducing bacteria and uses the function v(ρ) = v 0 e −cρρ for the densitydependent swimming speed.…”

Section: A Density-dependent Swimming Speedsupporting

confidence: 67%

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Bickmann¹,

Wittkowski²

2020

J. Phys.: Condens. Matter

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We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For maximal accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B + as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Anderson potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature. arXiv:1909.03369v1 [cond-mat.soft] 8 Sep 2019 2 The actual particle number density or number concentration of the ABPs is given by 2πρ( r, t).

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Section: A Density-dependent Swimming Speedsupporting

confidence: 67%

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Bickmann¹,

Wittkowski²

2020

J. Phys.: Condens. Matter

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“…We have demonstrated that the average swim speed, which describes how the motion of each particle is obstructed by its neighbors, can be obtained from a history integral over the equilibrium autocorrelation of tagged-particle force fluctuations [3]. The theory was tested using active Brownian dynamics simulations and provides a solid basis for the development of first-principles theoretical approaches.…”

Section: Introductionmentioning

confidence: 99%

Brownian systems with spatially inhomogeneous activity

Sharma

Brader

2017

Phys. Rev. E

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We generalize the Green-Kubo approach, previously applied to bulk systems of spherically symmetric active particles [J. Chem. Phys. 145, 161101 (2016)], to include spatially inhomogeneous activity. The method is applied to predict the spatial dependence of the average orientation per particle and the density. The average orientation is given by an integral over the self part of the Van Hove function and a simple Gaussian approximation to this quantity yields an accurate analytical expression. Taking this analytical result as input to a dynamic density functional theory approximates the spatial dependence of the density in good agreement with simulation data. All theoretical predictions are validated using Brownian dynamics simulations.

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“…ABP has been characterized in terms of thermodynamic quantities such as pressure and chemical potential [28][29][30][31][32][33] and its phase behaviour analysed in great detail [34][35][36][37][38][39]. Several recent works have studied its linear response (and of similar active particles modelled in terms of an Ornstein-Uhlenbeck process) from different viewpoints: (i) introducing an effective temperature characterizing FDT violations [40][41][42][43] ; (ii) taking equilibrium as the reference state and considering activity as a perturbation of it [24,25,44]; (iii) deriving expressions of linear response functions in terms of weighted averages over the unperturbed dynamics [43,45,46], in the same spirit as the Malliavin weights sampling [47]. In the present letter, we first characterize the violations of the FDT in ABP, showing how the non-equilibrium character of activity comes into play in an extended FDT that we establish, and then derive Green-Kubo expressions for its transport coefficients in terms of its non-equilibrium fluctuations.…”

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confidence: 99%

Linear Response Theory and Green-Kubo Relations for Active Matter

2019

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We address the question of how interacting active systems in a non-equilibrium steady-state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for Active Brownian Particles (ABP) which highlights the role played by the local violation of detailed balance due to activity. By making use of a Markovian approximation we derive closed Green-Kubo expressions for the diffusivity and mobility of ABP and quantify the deviations from the Stokes-Einstein relation. We compute the linear response function to an external force using unperturbed simulations of ABP and compare the results with the analytical predictions of the transport coefficients. Our results show the importance of the interplay between activity and interactions in the departure from equilibrium linear response.

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Communication: Green-Kubo approach to the average swim speed in active Brownian systems

Cited by 35 publications

References 22 publications

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Brownian systems with spatially inhomogeneous activity

Linear Response Theory and Green-Kubo Relations for Active Matter

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