752 publications from this institution
Enzyme reactions with inhibition and cooperativity are common in biological systems. A theoretical model for competitive and cooperative enzyme activity is formulated in terms of a pair of coupled nonlinear reaction-diffusion equations so as to derive the corresponding rule-based algorithm and nature-derived updating algorithms. A new stochastic cellular automaton is then constructed to simulate this nonlinear system. Numerical simulations show stable 2-D and 3-D pattern formation, and complex patterns have the interesting feature of self-organized criticality.
In the mathematical modelling of compactional flow in porous media, the constitutive relation is typically modelled in terms of a nonlinear relationship between effective pressure and porosity, and compaction is essentially poroelastic. However, at depths deeper than 1km where the pressure is high, compaction becomes more akin to a viscous one. Two mathematical models of compaction in porous media are formulated and the nonlinear equations are then solved numerically. The essential features of numerical profiles of poroelastic and viscous compaction are thus compared with asymptotic solutions. Two distinguished styles of density-driven compaction in fast and slow compacting sediments are analysed and shown in this paper.