On the discrete kinetic theory for active particles. Mathematical tools

Mathematical and Computer Modelling

Volumn 43, Issue 7-8, 2006, Pages 933-944

  Chauviere, A ^a   Brazzoli, I ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Active particles; Discrete microscopic variable; Kinetic theory

Indexed keywords

MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS;

ACTIVE PARTICLES; DISCRETE MICROSCOPIC VARIABLE; MATHEMATICAL TOOLS;

KINETIC THEORY;

EID: 33645034895     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.10.001     Document Type: Article

References (25)

1. D. Helbing Traffic and related self-driven many-particle systems Rev. Modern Phys. 73 2001 1067 1141
2. N. Bellomo, V. Coscia, and M. Delitala On the mathematical theory of vehicular traffic flow: I. Fluid dynamic and kinetic modelling Math. Models Methods Appl. Sci. 12 2002 1801 1843
3. M. Lo Schiavo Kinetic population models for social dynamics: Dependence on structural parameters Comput. Mathods Appl. 44 2002 1129 1146
4. M. Lo Schiavo Modelling political dynamics by generalized kinetic (Boltzmann) models Math. Comput. Modelling 37 2003 261 281
5. L. Bertotti, and M. Delitala From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences Math. Models Methods Appl. Sci. 14 2004 1061 1084
6. B. Carbonaro, and N. Serra Towards mathematical models in psychology: a stochastic description of human feelings Math. Models Methods Appl. Sci. 12 2002 1463 1498
7. B. Carbonaro, and C. Giordano A second step towards mathematical models in psychology: a stochastic description of human feelings Math. Comput. Modelling 41 2005 587 614
8. N. Bellomo, and E. De Angelis Strategies of applied mathematics towards an immuno mathematical theory on tumors and immune system interactions Math. Models Methods Appl. Sci. 8 1998 1403 1429
9. M. Kolev Mathematical modeling of the competition between tumors and immune system considering the role of antibodies Math. Comput. Modelling 37 2003 1143 1152
10. L. Derbel Analysis of a new model for tumor-immune system competition including long time scale effects Math. Models Methods Appl. Sci. 14 2004 1657 1682
11. A. Bellouquid, and M. Delitala Kinetic (cellular) models of cell progression and competition with the immune system Z. Agnew. Math. Phys. 55 2004 1 24
12. L. Arlotti, N. Bellomo, and E. De Angelis Generalized kinetic (Boltzmann) models: Mathematical structures and applications Math. Models Methods Appl. Sci. 12 2002 579 604
13. A. Bellouquid, and M. Delitala Mathematical methods and tools of kinetic theory towards modelling complex biological system Math. Models Methods Appl. Sci. 15 2005 1639 1666
14. N. Bellomo, A. Bellouquid, and M. Delitala Mathematical topics on the modelling of complex multicellular systems and tumor immune system competition Math. Models Methods Appl. Sci. 14 2004 1683 1733
15. M. Willander, E. Mamontov, and Z. Chiragwandi Modelling living fluids with the subdivision into the components in terms of probability distributions Math. Models Methods Appl. Sci. 14 2004 1495 1521
16. I. Prigogine, and R. Herman Kinetic Theory of Vehicular Traffic 1971 Elsevier New York
17. E. Jager, and L. Segel On the distribution of dominance in a population of interacting anonymous organisms SIAM J. Appl. Math. 52 1992 1442 1468
18. N. Bellomo, and G. Forni Dynamics of tumor interaction with the host immune system Math. Comput. Modelling 20 1994 107 122
19. L. Greller, F. Tobin, and G. Poste Tumor heterogeneity and progression: conceptual foundation for modeling Invas. Metast. 16 1996 177 208
20. N. Bellomo, and P. Maini Preface and special issue on "multiscale cancer modelling - a new frontier in applied mathematics" Math. Models Methods Appl. Sci. 15 2005 ii vii
21. R.M. May Uses and abuses of mathematics in biology Science 303 2004 790 793
22. R. Reed Why is mathematical biology so hard? Notices Amer. Math. Soc. 51 2004 338 342
23. R.A. Gatenby, and P.K. Maini Mathematical oncology: cancer summed up Nature 421 2003 321 323
24. R.A. Gatenby, T.L. Vincent, and R.J. Gillies Evolutionary dynamics in carcinogenesis Math. Models Methods Appl. Sci. 15 2005 1619 1638
25. M.A. Novak, and K. Sigmund Evolutionary dynamics of biological games Science 303 2004 793 799