We develop a statistical theory for the dynamics of non-aligning, non-interacting self-propelled particles confined in a convex box in two dimensions. We find that when the size of the box is small compared to the persistence length of a particle's trajectory (strong confinement), the steady-state density is zero in the bulk and proportional to the local curvature on the boundary. Conversely, the theory may be used to construct the box shape that yields any desired density distribution on the boundary, thus offering a general tool to understand and design such confinements. When the curvature variations are small, we also predict the distribution of orientations at the boundary and the exponential decay of pressure as a function of box size recently observed in simulations in a spherical box.
This research output has an Altmetric Attention Score of 8. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 31 July 2014.
All research outputs
#5,327,171
of 28,840,878 outputs
Outputs from Soft Matter
#652
of 9,395 outputs
Outputs of similar age
#54,344
of 332,579 outputs
Outputs of similar age from Soft Matter
#21
of 307 outputs
Altmetric has tracked 28,840,878 research outputs across all sources so far. Compared to these this one has done well and is in the 81st percentile: it's in the top 25% of all research outputs ever tracked by Altmetric.
So far Altmetric has tracked 9,395 research outputs from this source. They receive a mean Attention Score of 3.6. This one has done particularly well, scoring higher than 92% of its peers.
Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 332,579 tracked outputs that were published within six weeks on either side of this one in any source. This one has done well, scoring higher than 83% of its contemporaries.
We're also able to compare this research output to 307 others from the same source and published within six weeks on either side of this one. This one has done particularly well, scoring higher than 92% of its contemporaries.
