Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology—pruning in the foraging state—causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.

Figure 1

Bright-field image of a P. polycephalum individual cut from a larger network (left) and the same individual 100 contraction periods later (right).

Figure 2

(a) Change in the area of a cloud of dispersing particles, according to the numerical solution of the full Taylor dispersion and the dispersion cloud method, for the starting point circled in blue; see network inset. (b) Particles spread in a random walk defined by transition probabilities and times, allowing the definition of local dispersion coefficients. (c) Particles effectively spread as a Gaussian cloud of radius $r_i$ from site $i$, with a rate averaged over the local dispersions. This method yields the effective dispersion at long time scales in (d).

Figure 3

(a) Maps of the root mean square flow velocity, and (b) effective dispersion, for the initial network (left) and the same individual 100 contraction periods later (right).

Figure 4

Average effective dispersion as a function of distance to the center for unpruned (a) and pruned (b) states (shaded areas mark standard deviations). The base dashed line represents the molecular diffusivity $\kappa ={10}^{-10}{\mathrm{m}}^2/\mathrm{s}$. Note the difference in scales. Blue and black curves represent data from hierarchical (ii) and nonhierarchical cases (i), respectively. Insets are colored to show effective dispersion.