| Abstract: |
| Our investigation of logarithmic spirals is motivated by
disparate experimental results:
{\bf (i)} the discovery of logarithmic spiral shaped precipitate formation
in chemical garden experiments.
Understanding precipitate formation in chemical gardens
is important since analogous precipitates form in
deep ocean hydrothermal vents,
where conditions may be compatible with the emergence of life.
{\bf (ii)} the discovery that logarithmic spiral shaped waves of spreading depression
can spontaneously form and cause macular degeneration in hypoglycemic
chick retina. The role of reaction-diffusion mechanisms in spiral formation
in these diverse experimental settings is
poorly understood. To gain insight we use topological shooting to prove
existence of 0-bump stationary logarithmic spiral solutions, and rotating logarithmic spiral wave solutions,
of the Kopell-Howard lambda-omega reaction-diffusion model. |
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