A steady system begins to oscillate, as seen in the Belousov-Zhabotinsky reaction. 4. Mathematical Modeling and Dynamics
Morphogenesis (how embryos develop shape) and the synchronization of fireflies. pattern formation and dynamics in nonequilibrium systems pdf
Proposed by Alan Turing, these involve chemical species reacting and diffusing at different rates. This mechanism explains biological markings like tiger stripes or seashell patterns. 3. The Role of Symmetry Breaking A steady system begins to oscillate, as seen
A classic example where a fluid layer is heated from below. Once the temperature gradient is steep enough, the fluid organizes into hexagonal cells or rolls to transport heat more efficiently than simple conduction. Proposed by Alan Turing, these involve chemical species
As nonequilibrium systems are driven further from equilibrium, the steady patterns often break down into . This state is characterized by "defects"—dislocations in the pattern where the order is lost. The movement and interaction of these defects drive the long-term dynamics of the system, creating a state that is disordered in both space and time but still governed by deterministic laws. 6. Applications Across Disciplines
A uniform fluid (translationally invariant) develops a specific periodic structure (like stripes), "choosing" a specific orientation and position.