Distribution and pressure of active Lévy swimmers under confinement
arXiv:2104.07117 · doi:10.1088/1751-8121/ac0509
Abstract
Many active matter systems are known to perform Lévy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been observed for microswimmers such as bacteria in microfluidic experiments, where Gaussian noise assumptions are insufficient to explain the data. We introduce \textit{active Lévy swimmers} to model such behavior. The focus is on ideal swimmers that only interact with the walls but not with each other, which reduces to the classical Lévy walk model but now under confinement. We study the density distribution in the channel and force exerted on the walls by the Lévy swimmers, where the boundaries require proper explicit treatment. We analyze stronger confinement via a set of coupled kinetics equations and the swimmers' stochastic trajectories. Previous literature demonstrated that power-law scaling in a multiscale analysis in free space results in a fractional diffusion equation. We show that in a channel, in the weak confinement limit active Lévy swimmers are governed by a modified Riesz fractional derivative. Leveraging recent results on fractional fluxes, we derive steady state solutions for the bulk density distribution of active Lévy swimmers in a channel, and demonstrate that these solutions agree well with particle simulations. The profiles are non-uniform over the entire domain, in contrast to constant-in-the-bulk profiles of active Brownian and run-and-tumble particles. Our theory provides a mathematical framework for Lévy walks under confinement with sliding no-flux boundary conditions and provides a foundation for studies of interacting active Lévy swimmers.
arXiv comment25 pages, 4 figures
References in corpus (25)
- Understanding individual human mobility patterns
- Active Particles in Complex and Crowded Environments
- The scaling laws of human travel
- Motility-Induced Phase Separation
- Physics of Microswimmers - Single Particle Motion and Collective Behavior
- Active Brownian Particles. From Individual to Collective Stochastic Dynamics
- Intermittent search strategies
- Lévy walks
- How far from equilibrium is active matter?
- When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
- Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study
- The statistical physics of active matter: from self-catalytic colloids to living cells
- Loopy Lévy flights enhance tracer diffusion in active suspensions
- On the distribution and swim pressure of run-and-tumble particles in confinement
- Confined run-and-tumble swimmers in one dimension
- E. coli "super-contaminates" narrow ducts fostered by broad run-time distribution
- Steady-State Lévy Flights in a Confined Domain
- Reflected fractional Brownian motion in one and higher dimensions
- 3D spatial exploration by E. coli echoes motor temporal variability
- Probability density of the fractional Langevin equation with reflecting walls
- Non-Gaussian noise without memory in active matter
- Tuning upstream swimming of micro-robots by shape and cargo size
- Fractional Patlak-Keller-Segel equations for chemotactic superdiffusion
- Interacting particles with Lévy strategies: limits of transport equations for swarm robotic systems
- The fractional diffusion limit of a kinetic model with biochemical pathway