IIMAS - FENOMEC
UNAM
Two mixing problems: minitornados and the most irrational rotation
Resumen:
Rotation by an irrational angle defines an ergodic dynamical system on a circle. The golden angle may be considered to be the most irrational angle, and we will find, through direct examination of the circle map, and through PDE models for pattern formation at plant apices (where the golden number appears naturally in nature) that this angle allows for the quickest mixing and thereby maximal packing efficiency on plants. We will then turn to PDE models for another problem of mixing involving the nucleation and growth reaction between ammonia and hydrochloric acid to produce periodic precipitation patterns (Liesegang rings) and minitornados.
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