Biology Reference
In-Depth Information
FIGURE 13.2
(a
e
c) The density dependence of traffic jams. In each of these frames, circles represent objects
with random movement (or biased random movement: it does not matter). (a) Shows these particles at low density:
the red particle, like all the others, is free to move and hardly affected by other particles. (b) The density is higher
and collisions limit path lengths
d
very strongly if neighbouring particles move in opposite directions but less when
neighbours are moving in the same direction. This means that what motion there is tends to show local correlation.
(c) The density is very high and most of the objects are locked solid. (d
e
f) The advantage of deliberate correlation.
(d) Shows a free cell on a collision course with a closely packed raft that has already formed (other rafts are omitted
for simplicity). (e) If the cell does not show deliberate correlation behaviour, its own progress is stopped but its
efforts do not contribute to the movement of the raft whereas, if the cell detects the collision and realigns its motility
(f), contributing its own efforts to group motion rather than wasting it and adding nothing but drag to the raft as it
does in (e).
travelling in the same direction as its neighbours, it will be able to continue in that direction
for longer. Under these conditions, the motion of objects becomes correlated, at least locally;
the system behaves more like a liquid (
Figure 13.2
b). As the density increases, this effect
becomes stronger, with groups of objects moving as highly correlated, slow moving rafts,
and adjacent rafts now also showing correlations between their motions, with motion in
general becoming more and more constrained. All motion becomes sluggish, as in a just-
molten glass. Finally, when density is high enough, there is no free space to allow movement
of any kind, and the system is frozen-solid (
Figure 13.2
c).
In a system like that described above, in which all objects are dumb and pay no active
attention to one another, high correlation is a symptom of the loss of motion. Paradoxically,
if objects actively correlate their motions at lower densities than rawmechanics forces them
to, correlation can become not a symptom of stagnation but rather the means of avoiding it.
Consider the glassy liquid phase, and an object that is still alone but moving at right angles
