Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The solution algorithm is then described and finally we give some preliminary numerical results. Especially our method is well adapted to compute the concentration of bacteria.

[1]  A. E. Boukili.  Arclength continuation methods and applications to 2D drift‐diffusion semiconductor equations , 1996 .

[2]  L. Segel,et al.  Model for chemotaxis. , 1971, Journal of theoretical biology.

[3]  H. Bhadeshia.  Diffusion , 1995, Theory of Transformations in Steels.

[4]  MIXED FINITE ELEMENT SIMULATION OF HETEROJUNCTION STRUCTURES INCLUDING A BOUNDARY LAYER MODEL FOR THE QUASI‐FERMI LEVELS , 1994 .

[5]  R. Glowinski,et al.  Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics , 1987 .

[6]  M. A. Herrero,et al.  Chemotactic collapse for the Keller-Segel model , 1996, Journal of mathematical biology.

[7]  M. Brenner,et al.  Physical mechanisms for chemotactic pattern formation by bacteria. , 1998, Biophysical journal.

[8]  Collapsing bacterial cylinders. , 1999, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Leo P. Kadanoff,et al.  Diffusion, attraction and collapse , 1999 .

[10]  A. Marrocco,et al.  Simulation de modèles energy transport à l'aide des éléments finis mixtes , 1996 .

[11]  Benoît Perthame,et al.  A chemotaxis model motivated by angiogenesis , 2003 .

[12]  Miguel A. Herrero,et al.  Finite-time aggregation into a single point in a reaction - diffusion system , 1997 .

[13]  A. Marrocco.  2D simulation of chemotactic bacteria aggregation , 2002 .

[14]  W. Jäger,et al.  On explosions of solutions to a system of partial differential equations modelling chemotaxis , 1992 .