Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Discontinuous Phase Transitions in Schloegl Models for Autocatalysis
Chi-Jen Wang (National Chung Cheng University)
Abstract:
We consider Schloegl models where particles on a square grid annihilate at rate
![](https://chart.googleapis.com/chart?cht=tx&chl=%24p%24&chf=bg,s,333333&chco=ffffff)
, and are created at rate
![](https://chart.googleapis.com/chart?cht=tx&chl=%24k_%7Bn%7D%24&chf=bg,s,333333&chco=ffffff)
that related to
![](https://chart.googleapis.com/chart?cht=tx&chl=%24n%24&chf=bg,s,333333&chco=ffffff)
neighboring particles in
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5COmega_%7BN%7D%24&chf=bg,s,333333&chco=ffffff)
. Simulation reveals a discontinuous transition between populated and vacuum states, but equistability determined by stationarity of planar interfaces between states depends on interface orientation at least for smaller
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5COmega_%7BN%7D%24&chf=bg,s,333333&chco=ffffff)
. Behavior for large
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5COmega_%7BN%7D%24&chf=bg,s,333333&chco=ffffff)
follows from continuum equations. These depend on interface orientation and
![](https://chart.googleapis.com/chart?cht=tx&chl=%24%5COmega_%7BN%7D%24&chf=bg,s,333333&chco=ffffff)
-shape, but a unique equistability point emerges
![](https://chart.googleapis.com/chart?cht=tx&chl=%24p_%7Beq%7D%3D0.211376...%24&chf=bg,s,333333&chco=ffffff)
imposing a Gibbs phase rule.