Biology Reference
In-Depth Information
FIGURE 26.2
Viscous fingering as a physical model for branching morphogenesis. When a low-viscosity liquid
penetrates one of higher viscosity, either because it is injected between two horizontal plates (a) or because it is
dense and will naturally sink downwards into a less dense liquid in a vertical cell (b), its leading edge breaks up
into 'fingers' for the reasons described in the text. If the apparatus in (a) is constructed using a large (for example,
30 cm
30 cm) plate with a tiny central hole that allows fluid to be injected into the middle, rather than from the
edge, more 'pure' patterns (less affected by edges) result in this form; the apparatus is called a Hele-Shaw cell.
by computer involves several extra assumptions. The first is that the mathematics of stress and
strain are known precisely. In this case, a safe assumption, verified by millions of buildings,
bridges and vehicles, though it will be less safe for complex physical phenomena, especially
in realms such as flow on non-Newtonian fluids. The second is that the mathematics has
been rendered correctly into bug-free computer code. Neither of these assumptions is neces-
sary when something is modelled by direct physical analogy with no recourse to transforma-
tions to and from mathematical abstraction. The continued construction of wind tunnels and
physical models of river erosion bears testament to the inadequacy of mathematical models of
complex systems. Physical models are also useful educationally; most people are much more
impressed by the behaviour of a physical object that they can play with and touch than they
are with something on a computer screen that could just as easily be displaying the unreal
physics of a game's fantasy world or conveying outright lies on unethical websites.
)
Physical models of mechanisms for epithelial branching that rely on feedback (positive
curvature encourages advance, negative curvature discourages it) can be constructed by
slowly injecting a low-viscosity fluid into a higher-viscosity one with which it will not
mix. In typical models, the fluids are trapped in a small space between two coverslips
(
Figure 26.2
a). If the cell thus formed is horizontal, the low-viscosity fluid must be injected.
)
The headlong rush of so many UKMuseums of Science to replace their old physical exhibits, which illustrated
the deep laws of reality, with flashy computer displays and game-like demonstrations continues to baffle me; it
seems the opposite of what science is about.
