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.
Mots-clés : biophysics, chemotaxis, numerical simulation, mixed finite element
@article{M2AN_2003__37_4_617_0,
author = {Marrocco, Americo},
title = {Numerical simulation of chemotactic bacteria aggregation via mixed finite elements},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {617--630},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003048},
mrnumber = {2018433},
zbl = {1065.92006},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003048/}
}
TY - JOUR AU - Marrocco, Americo TI - Numerical simulation of chemotactic bacteria aggregation via mixed finite elements JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 617 EP - 630 VL - 37 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003048/ DO - 10.1051/m2an:2003048 LA - en ID - M2AN_2003__37_4_617_0 ER -
%0 Journal Article %A Marrocco, Americo %T Numerical simulation of chemotactic bacteria aggregation via mixed finite elements %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 617-630 %V 37 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003048/ %R 10.1051/m2an:2003048 %G en %F M2AN_2003__37_4_617_0
Marrocco, Americo. Numerical simulation of chemotactic bacteria aggregation via mixed finite elements. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 617-630. doi : 10.1051/m2an:2003048. http://archive.numdam.org/articles/10.1051/m2an:2003048/
[1] and, Collapsing bacterial cylinders. Phys. Rev. E 64 (2001) 061904.
[2] , and, Physical mechanisms for chemotactic pattern formation bybacteria. Biophys. J. 74 (1998) 1677-1693.
[3] ,,, and, Diffusion, attraction and collapse. Nonlinearity 12 (1999) 1071-1098. | Zbl
[4] , and, A model motivated by angiogenesis. C. Rendus Acad. Sc. Paris, to appear.
[5] A El Boukili and A. Marrocco, Arclength continuation methods and applications to 2d drift-diffusion semiconductor equations. Rapport de recherche 2546, INRIA (mai 1995).
[6] , Analyse mathématique et simulation numérique bidimensionnelle des dispositifs semi-conducteurs à hétérojonctions par l'approche éléments finis mixtes. Ph.D. thesis, Univ. Pierre et Marie Curie, Paris (décembre 1995).
[7] and, Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics, Studies in Applied Mathematics. SIAM, Philadelphia (1989). | MR | Zbl
[8] and, Chemotactic collapse for the keller-segel model. J. Math. Biol. 35 (1996) 177-194. | Zbl
[9] , and, Finite time aggregation into a single point in a reaction-diffusion system. Nonlinearity 10 (1997) 1739-1754. | Zbl
[10] and, 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] and, Mixed finite element simulation of heterojunction structures including a boundary layer model for the quasi-fermi levels. COMPEL 13 (1994) 757-770. | Zbl
[12] and, On explosion of solution to a system of partial differential equations modelling chemotaxis. Trans. Amer. Math. Soc. 239 (1992) 819-824. | Zbl
[13] and, Model for chemotaxis. J. Theor. Biol. 30 (1971) 225-234.
[14] and, Simulation des modèles energy-transport à l'aide des éléments finis mixtes. C.R. Acad. Sci. Paris I 323 (1996) 535-541. | Zbl
[15] , 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] , 2d simulation of chemotactic bacteria aggregation. Rapport de recherche 4667, INRIA (décembre 2002).
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