Figure 1

(Color online) Averaged agent density and pathline results with $P=1$ and ${\rho }_y=0$. Results are given for different amounts of motility bias in the $x$ direction with ${\rho }_x=0$ (left column), ${\rho }_x=0.1$ (middle column), and ${\rho }_x=0.5$ (right column). Snapshots of a single realization at $t=0$ and 200 are given in rows (a) and (b), respectively, showing the evolution of a population of agents and the position of a tagged agent initially at (114,10) is shown with an enlarged green bullet. Row (c) shows the averaged density profiles $⟨C⟩$ (solid blue) extracted from the simulation data compared with the continuum solution of Eq. (1) $C$ (dotted red). Rows (d)–(e) compare the evolution of the mean position and variance for the tagged agent. Continuum results (dotted red) are compared with simulation data (solid blue). All simulation results are averaged over 100 Monte Carlo realizations with $\Delta =\tau =1$. All continuum models are solved numerically with a spatial discretization $\delta x=0.1$ and temporal discretization $h=0.25$.Reuse & Permissions

Figure 2

(Color online) Unbiased pathline simulation data corresponding to the results in the left column of Fig. 1 show the convergence behavior with respect to $M$, the number of Monte Carlo realizations. The evolution of (a) the agent position and (b) the variance are given for averages over $M=10$ (blue), $M=100$ (green), and $M=500$ (red) simulations. All results correspond to $\Delta =\tau =P=1$, ${\rho }_y={\rho }_x=0$, and $\left[p_x\left(0\right),p_y\left(0\right)\right]=\left(114,10\right)$.Reuse & Permissions