Michaelis-Menten equation is a basic equation of enzyme kinetics and gives an acceptable approximation of real chemical reaction processes. Analyzing the derivation of this equation yields the fact that its good performance of approximating real reaction processes is due to MichaelisMenten curve (15). This curve is derived from Quasi-Steady-State Assumption(QSSA), which has been proved always t...

We perform a thorough study of the blow up profiles associated to following second order reaction-diffusion equation with non-homogeneous reaction:?tu=?xx(um)+|x|?up, in range exponents 10. classify solutions self-similar form, that are likely represent typical patterns for general solutions. thus show coefficient |x|? has strong influence on qualitative aspects related finite time u...

It may often be tempting to take a fractional diffusion equation and simply create a fractional reactiondiffusion equation by including an additional reaction term of the same form as one would include for a standard Fickian system. However, in real systems, fractional diffusion equations typically arise due to complexity and heterogeneity at some unresolved scales. Thus, while transport of a c...

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain ...

sions can be obtained by using the generating function in solving the master equation. In addition, our approach allows for the computation of the probabilities for the number of S1 molecules at a certain time t when the reaction parameters, i.e., the initial number of molecules X1(0) and X2(0) of S1 and S2 , respectively, and the reaction rates c1 and c2 , are given. The master equation is a d...