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Register a new userLinear response approach to active Brownian particles in time-varying activity fields
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In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of the particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.
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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.
Frictional forces affect the rheology of hard-sphere colloids, at high shear rate. Here we demonstrate, via numerical simulations, that they also affect the dynamics of active Brownian particles, and their motility induced phase separation. Frictional forces increase the angular diffusivity of the particles, in the dilute phase, and prevent colliding particles from resolving their collision by sliding one past to the other. This leads to qualitatively changes of motility-induced phase diagram in the volume-fraction motility plane. While frictionless systems become unstable towards phase separation as the motility increases only if their volume fraction overcomes a threshold, frictional system become unstable regardless of their volume fraction. These results suggest the possibility of controlling the motility induced phase diagram by tuning the roughness of the particles.
Recent experimental studies have demonstrated that cellular motion can be directed by topographical gradients, such as those resulting from spatial variations in the features of a micropatterned substrate. This phenomenon, known as topotaxis, is especially prominent among cells persistently crawling within a spatially varying distribution of cell-sized obstacles. In this article we introduce a toy model of topotaxis based on active Brownian particles constrained to move in a lattice of obstacles, with space-dependent lattice spacing. Using numerical simulations and analytical arguments, we demonstrate that topographical gradients introduce a spatial modulation of the particles persistence, leading to directed motion toward regions of higher persistence. Our results demonstrate that persistent motion alone is sufficient to drive topotaxis and could serve as a starting point for more detailed studies on self-propelled particles and cells.
We study the transport of Brownian particles under a constant driving force and moving in channels that present a varying centerline but have constant aperture width. We investigate two types of channels, {it solid} channels in which the particles are geometrically confined between walls and {em soft} channels in which the particles are confined by a periodic potential. We consider the limit of narrow, slowly-varying channels, i.e., when the aperture and the variation in the position of the centerline are small compared to the length of a unit cell in the channel (wavelength). We use the method of asymptotic expansions to determine both the average velocity (or mobility) and the effective diffusion coefficient of the particles. We show that both solid and soft-channels have the same effects on the transport properties up to $O(epsilon^2)$. We also show that the mobility in a solid-channel at $O(epsilon^4)$ is smaller than that in a soft-channel. Interestingly, in both cases, the corrections to the mobility of the particles are independent of the Peclet number and, as a result, the Einstein-Smoluchowski relation is satisfied. Finally, we show that by increasing the solid-channel width from $w(x)$ to $sqrt{6/pi}w(x)$, the mobility of the particles in the solid-channel can be matched to that in the soft-channel up to $O(epsilon^4)$.
We determine the nonlocal stress autocorrelation tensor in an homogeneous and isotropic system of interacting Brownian particles starting from the Smoluchowski equation of the configurational probability density. In order to relate stresses to particle displacements as appropriate in viscoelastic states, we go beyond the usual hydrodynamic description obtained in the Zwanzig-Mori projection operator formalism by introducing the proper irreducible dynamics following Cichocki and Hess, and Kawasaki. Differently from these authors, we include transverse contributions as well. This recovers the expression for the stress autocorrelation including the elastic terms in solid states as found for Newtonian and Langevin systems, in case that those are evaluated in the overdamped limit. Finally, we argue that the found memory function reduces to the shear and bulk viscosity in the hydrodynamic limit of smooth and slow fluctuations and derive the corresponding hydrodynamic equations.
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