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Active Brownian particles and run-and-tumble particles separate inside a maze

View Article: PubMed Central - PubMed

ABSTRACT

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

No MeSH data available.


(a) Theory for MFPT for large Pr: Parameters used in deriving Eq. (6) are indicated. (b) Linear rate theory: The circular maze is mapped on a one-dimensional lattice. Each zone of the maze is equivalent to a site on this lattice. kmn denotes the transition rate to jump from zone/site m to zone/site n.
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f3: (a) Theory for MFPT for large Pr: Parameters used in deriving Eq. (6) are indicated. (b) Linear rate theory: The circular maze is mapped on a one-dimensional lattice. Each zone of the maze is equivalent to a site on this lattice. kmn denotes the transition rate to jump from zone/site m to zone/site n.

Mentions: In case of an ABP, a simple random-walk model describes the asymptotic behavior of the MFPT in the limit of large persistence number Pr. In this case the particle orientation is mostly aligned with the local boundary normal and the orientation angle θ also describes the location of the ABP in the annulus [see Fig. 3(a)]. We can now calculate the MFPT to go from one wall opening to the next one and thereby to pass to the next zone in the maze. The total MFPT is then the sum over all openings reached. The orientation angle just changes by rotational diffusion. So, in order to escape through an opening, the orientation angle has to diffuse from θ0 (the position of the previous opening) either to θ1 or θ2 [see Fig. 3(a)]. This is equivalent to the first-passage problem of a particle diffusing in one dimension with two absorbing boundaries at θ1 and θ2. Using the standard formalism6162, which we summarize in the supplementary material, the MFPT for a particle initially at θ0 for reaching one of the absorbing boundaries can be calculated:


Active Brownian particles and run-and-tumble particles separate inside a maze
(a) Theory for MFPT for large Pr: Parameters used in deriving Eq. (6) are indicated. (b) Linear rate theory: The circular maze is mapped on a one-dimensional lattice. Each zone of the maze is equivalent to a site on this lattice. kmn denotes the transition rate to jump from zone/site m to zone/site n.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5120314&req=5

f3: (a) Theory for MFPT for large Pr: Parameters used in deriving Eq. (6) are indicated. (b) Linear rate theory: The circular maze is mapped on a one-dimensional lattice. Each zone of the maze is equivalent to a site on this lattice. kmn denotes the transition rate to jump from zone/site m to zone/site n.
Mentions: In case of an ABP, a simple random-walk model describes the asymptotic behavior of the MFPT in the limit of large persistence number Pr. In this case the particle orientation is mostly aligned with the local boundary normal and the orientation angle θ also describes the location of the ABP in the annulus [see Fig. 3(a)]. We can now calculate the MFPT to go from one wall opening to the next one and thereby to pass to the next zone in the maze. The total MFPT is then the sum over all openings reached. The orientation angle just changes by rotational diffusion. So, in order to escape through an opening, the orientation angle has to diffuse from θ0 (the position of the previous opening) either to θ1 or θ2 [see Fig. 3(a)]. This is equivalent to the first-passage problem of a particle diffusing in one dimension with two absorbing boundaries at θ1 and θ2. Using the standard formalism6162, which we summarize in the supplementary material, the MFPT for a particle initially at θ0 for reaching one of the absorbing boundaries can be calculated:

View Article: PubMed Central - PubMed

ABSTRACT

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily. According to our simulations and a rate theory, which we developed, ABPs in steady state accumulate in the outermost region of the Matryoshka-like mazes, while RTPs occupy all locations within the maze with nearly equal probability. These results suggest a novel technique for separating different types of self-propelled particles by designing appropriate confining geometries without using chemical or biological agents.

No MeSH data available.