Numerical simulation of chemotactic bacteria aggregation via mixed finite elements

Americo Marrocco

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 4, page 617-630
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Marrocco, Americo. "Numerical simulation of chemotactic bacteria aggregation via mixed finite elements." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.4 (2003): 617-630. <http://eudml.org/doc/245871>.

@article{Marrocco2003,
abstract = {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.},
author = {Marrocco, Americo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {biophysics; chemotaxis; numerical simulation; mixed finite element; Biophysics},
language = {eng},
number = {4},
pages = {617-630},
publisher = {EDP-Sciences},
title = {Numerical simulation of chemotactic bacteria aggregation via mixed finite elements},
url = {http://eudml.org/doc/245871},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Marrocco, Americo
TI - Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 4
SP - 617
EP - 630
AB - 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.
LA - eng
KW - biophysics; chemotaxis; numerical simulation; mixed finite element; Biophysics
UR - http://eudml.org/doc/245871
ER -

References

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  2. [2] M.P. Brenner, L.S. Levitov and E.O. Budrene, Physical mechanisms for chemotactic pattern formation bybacteria. Biophys. J. 74 (1998) 1677–1693. 
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  8. [8] M.A. Herrero and J.J.L. Velázquez, Chemotactic collapse for the keller-segel model. J. Math. Biol. 35 (1996) 177–194. Zbl0866.92009
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  10. [10] F. Hecht and A. Marrocco, Numerical simulation of heterojunction structures using mixed finite elements and operator splitting, in 10th International Conference on Computing Methods in Applied Sciences and Engineering, R. Glowinski Ed., Nova Science Publishers, Le Vésinet (February 1992) 271–286. 
  11. [11] F. Hecht and A. Marrocco, Mixed finite element simulation of heterojunction structures including a boundary layer model for the quasi-fermi levels. COMPEL 13 (1994) 757–770. Zbl0824.65136
  12. [12] W. Jäger and S. Luckhaus, On explosion of solution to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. 239 (1992) 819–824. Zbl0746.35002
  13. [13] E.F. Keller and L.A. Segel, Model for chemotaxis. J. Theor. Biol. 30 (1971) 225–234. Zbl1170.92307
  14. [14] A. Marrocco and Ph. Montarnal, Simulation des modèles energy-transport à l’aide des éléments finis mixtes. C.R. Acad. Sci. Paris I 323 (1996) 535–541. Zbl0858.65111
  15. [15] Ph. Montarnal, Modèles de transport d’énergie des semi-conducteurs, études asymptotiques et résolution par des éléments finis mixtes. Ph.D. thesis, Université Paris VI (octobre 1997). 
  16. [16] A. Marrocco, 2d simulation of chemotactic bacteria aggregation. Rapport de recherche 4667, INRIA (décembre 2002). 

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