Computational Studies of Bacterial Colony Model

Ondřej Pártl^{*}

Show more

References

[1] J. Wakita, H. Shimada, H. Itoh, T. Matsuyama and M. Matsushita, “Periodic Colony Formation by Bacterial Species Bacillus Subtilis,” Journal of the Physical Society of Japan, Vol. 70, No. 3, 2001, pp. 911-919.
doi:10.1143/JPSJ.70.911

[2] M. Mimura, H. Sakaguchi and M. Matsushita, “Reaction-Diffusion Modelling of Bacterial Colony Patterns,” Physica A, Vol. 282, No. 1-2, 2000, pp. 283-303.
doi:10.1016/S0378-4371(00)00085-6

[3] J. D. Murray, “Mathematical Biology,” 3rd Edition, Springer, Berlin, 2002.

[4] T. Vicsek, “Pattern Formation in Diffusion-Limited Aggregation,” Physical Review Letters, Vol. 53, No.24, 1984, pp. 2281-2284. doi:10.1103/PhysRevLett.53.2281

[5] I. Golding, Y. Kozlovsky, I. Cohen and E. Ben-Jacob, “Studies of Bacterial Branching Growth Using Reaction-Diffusion Models for Colonial Development,” Physica A, Vol. 260, No. 3-4, 1998, pp. 510-554.
doi:10.1016/S0378-4371(98)00345-8

[6] Y. Kozlovsky, I. Cohen, I. Golding and E. Ben-Jacob, “Lubricating Bacteria Model for Branching Growth of Bacterial Colonies,” Physical Review E, Vol. 59, No.6, 1999, pp. 7025-7035. doi:10.1103/PhysRevE.59.7025

[7] R. Straka and Z. Culík, “Numerical Aspects of a Bacteria Growth Model,” Proceedings of Algoritmy, Vysoké Tatry-Podbanské, 13-18 March 2005, pp. 175-184.

[8] E. Feireisl, D. Hilhorst, M. Mimura and R. Weidenfeld, “On a Nonlinear Diffusion System with Resource-Consumer Interaction,” Hiroshima Mathematical Journal, Vol. 33, No. 2, 2003, pp. 253-295.

[9] S. Brenner and R. Scott, “The Mathematical Theory of Finite Element Methods,” 3rd Edition, Springer, New York, 2008. doi:10.1007/978-0-387-75934-0

[10] H. Fujita, N. Saito and T. Suzuki, “Operator Theory and Numerical Methods,” Elsevier, Amsterdam, 2001.

[11] V. Thomée, “Galerkin Finite Element Methods for Parabolic Problems,” Springer, Berlin, 1997.
doi:10.1007/978-3-662-03359-3

[12] M. Benes, “Mathematical Analysis of Phase-Field Equations with Numerically Efficient Coupling Terms,” Interfaces and Free Boundaries, Vol. 3, No.2, 2001, pp. 201-221. doi:10.4171/IFB/38

[13] T. Oberhuber, “Finite Difference Scheme for the Willmore Flow of Graphs,” Kybernetika, Vol. 43, No. 6, 2007, pp. 855-867.

[14] J. Sembera and M. Benes, “Nonlinear Galerkin Method for Reaction-Diffusion Systems Admitting Invariant Regions,” Journal of Computational and Applied Mathematics, Vol. 136, No. 1-2, 2001, pp. 163-176.
doi:10.1016/S0377-0427(00)00582-3

[15] W. E. Schiesser, “The Numerical Method of Lines,” Academic, New York, 1991.

[16] G. Dziuk, “Convergence of a Semi-Discrete Scheme for the Curve Shortening Flow,” Mathematical Models and Methods in Applied Sciences, Vol. 4. No. 4, 1994, pp. 589-606. doi:10.1142/S0218202594000339

[17] O. Pártl, “Reaction-Diffusion Systems in Mathematical Biology,” Master Thesis, Czech Technical University in Prague, Prague, 2012.