Active Particles with Polarized Effective Attraction







  • Velocity correlation function quantifies the particle velocity correlation on the two-body (pair) level. Perfectly correlated pair dynamics is associated with C(r) = 1. This is the case when the velocities of all particles are perfectly aligned, e.g., indicating the cells are following one another during collective migration. On the other hand, C(r) = −1 is associated with anti-parallel velocities, i.e., when the cells are moving towards one another. C(r) = 0 indicates no correlations among the particles (migrating cells).

    Enter the step, click "Calculate" button, see velocity correlation funtion for the step. Pay attention that calculating velocity correlation function must be after running simulation.

    Step:

  • Because of computation time, we restrict the parameters whthin these ranges. Density ∈ (0,0.5]. Radius ∈ [0.001,0.5]. Dr and Angle Tolerance ∈ [0,360] in degree. Run Step ∈ [10,20000]. It may take a couple of minutes for large number of particles. Click "Run Simulation" button to see results!

    Density:

    Radius:

    Dr:

    Angle Tolerance:

    Run Step:

  • About APPA Model
    Active-particle model with polarized effective attractions (APPA) is a model for emergent multi-cellular migration dynamics resulted from ECM-mediated mechanical communications. Research regarding this model has been published on PRE. The following picture is a schematic illustration of the effective polarized attraction between two migrating cells, which depends on both the positions and velocities of the cells. Specifically, the effective attraction is non-zero only when the two cells are moving towards one another (i.e., with the velocities anti-parallel aligned within a prescribed tolerance).


    About Simulation
    Particle simulation of the cells is carried out in a periodic box of size 1. In the simulation, boundary distance condition is used between any pair of particles. There are 4 adjustable parameters. Density is the number density of particles. Radius is the radius of particles. The number of particles is caculated based on the density and the radius. Dr is strength of diffusive noise affecting particles. The mean of the gassuian distribution is 0, and standard deviation is Dr. Angle tolerance is the value within which two velocity directions are considered under anti-parallel (marked as red shade in the illustration).

    Details of the parameters and model can be found in the paper Modeling multicellular dynamics regulated by extracellular-matrix-mediated mechanical communication via active particles with polarized effective attraction.