Team:IPN-UNAM-Mexico/Modeling/FirstAp

[[Image:Month-icon.png | 50px]]First approach: Classical model with estimated diffusion constants
To do this we considered the molecular weight of the AHL molecules and we estimated the diameter of the molecules taking into account the linear structure of them. From the articles of A. Einstein: “On the Motion—Required by the Molecular Kinetic Theory of Heat—of Small Particles Suspended in a Stationary Liquid” and “A new determination of molecular dimensions” we used the method to estimate the diffusion coefficients from the diameter of the molecule using the modified friction coefficient of the water in presence of glucose to improve the accuracy as described.

The equations are:



Obtaining the following values:



Using Comsol Multipysics Comsol Multipysics we made a simulation with values previously used by Murray [14] and the previously estimated diffusion coefficients of PAI and AI molecules with the reaction-diffusion equations of the Gierer and Meinhardt model. The simulation was made in a circular area with zero flux boundary conditions and all the parameters values found in the literature.



As expected we obtained a spots pattern in a specific diameter value and a stripes pattern using a smaller diameter, both starting with a sinusoidal distribution of the activator and the inhibitor.