Lattice models of nonequilibrium bacterial dynamics

Thompson, Andrew; Tailleur, Julien; Cates, Michael E.; Blythe, Richard A.

doi:10.1088/1742-5468/2011/02/p02029

Cited by 141 publications

(204 citation statements)

References 38 publications

(63 reference statements)

Supporting

Mentioning

189

Contrasting

Unclassified

Order By: Relevance

“…In two dimensions this shows an exponent L(t) ∼ t α with 0.25 ≤ α ≤ 0.28 (34,55,56,60). This is somewhat below the value of 1/3 expected for passive coarsening (and which was also reported in (32) for RTPs in 2D and in (56) for ABPs in 3D). However it is not yet clear that the difference is numerically significant; it may instead reflect a slow transient approach to an asymptotic 1/3 power (61) (see Section 7.2 below).…”

Section: Phase Separation In Active Brownian Particlesmentioning

confidence: 65%

“…38 can easily be generalized to higher dimensions and we now turn to the 2D case. For symmetric kernels Kij, in the limit of large ρM , the mean-field free energy analysis predicts quantitatively both the occurrence of complete phase-separation and the values of the coexisting densities (32). When ρM is finite, MIPS still occurs but (as is common for partial exclusion models (53)) the coexisting densities are not those predicted by mean-field theory.…”

Section: Phase Separation In Run-and-tumble Particlesmentioning

confidence: 94%

See 1 more Smart Citation

Motility-Induced Phase Separation

Cates

Tailleur

2015

Annu. Rev. Condens. Matter Phys.

1,366

1,566

View full text Add to dashboard Cite

Self-propelled particles include both self-phoretic synthetic colloids and various micro-organisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: the steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density, for either biochemical or steric reasons. This creates positive feedback which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations, but generally breaks down at higher order in gradients: new effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and simulation but including a brief speculative survey of its experimental implications.

show abstract

Section: Phase Separation In Active Brownian Particlesmentioning

confidence: 65%

Section: Phase Separation In Run-and-tumble Particlesmentioning

confidence: 94%

Motility-Induced Phase Separation

Cates

Tailleur

2015

Annu. Rev. Condens. Matter Phys.

1,366

1,566

View full text Add to dashboard Cite

show abstract

“…4). Coarsening in active system is notoriously difficult to assess [44][45][46] and a more precise characterization of this phenomenon will be addressed in future works.…”

Section: Fig 1c)mentioning

confidence: 99%

Active Particles with Soft and Curved Walls: Equation of State, Ratchets, and Instabilities

et al. 2016

View full text Add to dashboard Cite

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general boundaries in two dimensions. We show that, despite the non-uniform pressure along curved walls, an equation of state is recovered upon a proper spatial averaging. This holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by spontaneous shear stresses on the walls. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semi-flexible filaments. Finally, we relate the force exerted on objects immersed in active baths to the particle flux they generate around them.Active forces have recently attracted much interest in many different contexts [1]. In biology, they play crucial roles on scales ranging from the microscopic, where they control cell shape and motion [2] to the macroscopic, where they play a dominant role in tissue dynamics [3,4]. More generally, active systems offer novel engineering perspectives, beyond those of equilibrium systems. In particular, boundaries have been shown to be efficient tools for manipulating active particles. Examples range from rectification of bacterial densities [5,6] and optimal delivery of passive cargoes [7] to powering of microscopic gears [8,9]. Further progress, however, requires a predictive theoretical framework which is currently lacking for active systems. To this end, simple settings have been at the core of recent active matter research.Understanding the effect of boundaries on active matter starts with the mechanical pressure exerted by an active fluid on its containing vessel. This question has been recently studied extensively for dry systems [10][11][12][13][14][15][16][17], revealing a surprisingly complex physics. For generic active fluids, the mechanical pressure is not a state variable [13]. The lack of equation of state, through a dependence on the wall details, questions the role of the mechanical pressure in any possible thermodynamic description of active systems [18,19]; it also leads to a richer phenomenology than in passive systems by allowing more general mechanical interplays between fluids and their containers.Interestingly, for the canonical model of self-propelled spheres of constant propelling forces, on which neither walls nor other particles exert torques, the pressure acting on a solid flat wall has been shown to admit an equation of state [11,12,19]. While the physics of this model does not clearly differ from other active systems, showing for instance wall accumulation [20] and motility-induced phase separation [21][22][23], the mechanical pressure exerted on a flat wall satisfies an equation of state, even in the presence of pairwise interactions [11,12,19]. One might thus hope that the intuition built on the rheology of equilibrium fluids extends to this case. Derived in a particular setting, the robustness of this equation of state however remains an open question. For...

show abstract

“…We explore an approximation scheme for torque-free SPPs with collisional interactions whereby the conservative forces responsible for collisional slow-down of the particles are replaced at mean-field level by a "programmed" slow-down, that is, an effective reduction in the propulsive force at high density. This path was first sketched out in [45] and pursued further in [17,19,46,47,48]. In a more general context it is both legitimate and interesting to consider, in its own right, the case with no conservative force field between particles, and ask about the effects of programmed slow-down among such "ghost" particles.…”

Section: Introductionmentioning

confidence: 99%

Active brownian particles and run-and-tumble particles: A comparative study

Solon

Cates

Tailleur

2015

Eur. Phys. J. Spec. Top.

257

330

View full text Add to dashboard Cite

Abstract. Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed v along a body-axis u that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along u becomes v(ρ) < v. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed v that is an explicit function or functional of the density ρ. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.

show abstract

Lattice models of nonequilibrium bacterial dynamics

Cited by 141 publications

References 38 publications

Motility-Induced Phase Separation

Motility-Induced Phase Separation

Active Particles with Soft and Curved Walls: Equation of State, Ratchets, and Instabilities

Active brownian particles and run-and-tumble particles: A comparative study

Contact Info

Product

Resources

About