Geodesic
Proliferating Lévy Walkers and Front Propagation
H. Stage1 ; S. Fedotov1 ; V. Méndez2
1 School of Mathematics, The University of Manchester, M13 9PL Manchester, UK
2 Universitat Autónoma de Barcelona, Departament de Física, Facultat de Ciències. Edifici Cc 08193-Cerdanyola del Vallès (Barcelona) Spain
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 157-178

Voir la notice de l'article provenant de la source EDP Sciences

We develop non-linear integro-differential kinetic equations for proliferating Lévy walkers with birth and death processes. A hyperbolic scaling is applied directly to the general equations to get the Hamilton-Jacobi equations that will allow to determine the rate of front propagation. We found the conditions for switching, birth and death rates under which the propagation velocity reaches the maximum value, i.e. the walker’s speed. In the strong anomalous case the death rate was found to influence the velocity of propagation to fall below the walker’s maximum speed.
DOI : 10.1051/mmnp/201611310

H. Stage 1 ; S. Fedotov 1 ; V. Méndez 2

1 School of Mathematics, The University of Manchester, M13 9PL Manchester, UK
2 Universitat Autónoma de Barcelona, Departament de Física, Facultat de Ciències. Edifici Cc 08193-Cerdanyola del Vallès (Barcelona) Spain 
@article{10_1051_mmnp_201611310,
     author = {H. Stage and S. Fedotov and V. M\'endez},
     title = {Proliferating {L\'evy} {Walkers} and {Front} {Propagation}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {157--178},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2016},
     doi = {10.1051/mmnp/201611310},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611310/}
}
TY  - JOUR
AU  - H. Stage
AU  - S. Fedotov
AU  - V. Méndez
TI  - Proliferating Lévy Walkers and Front Propagation
JO  - Mathematical modelling of natural phenomena
PY  - 2016
SP  - 157
EP  - 178
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611310/
DO  - 10.1051/mmnp/201611310
LA  - en
ID  - 10_1051_mmnp_201611310
ER  - 
%0 Journal Article
%A H. Stage
%A S. Fedotov
%A V. Méndez
%T Proliferating Lévy Walkers and Front Propagation
%J Mathematical modelling of natural phenomena
%D 2016
%P 157-178
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/201611310/
%R 10.1051/mmnp/201611310
%G en
%F 10_1051_mmnp_201611310
H. Stage; S. Fedotov; V. Méndez. Proliferating Lévy Walkers and Front Propagation. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 157-178. doi: 10.1051/mmnp/201611310

[1] W. Alt Journal of Mathematical Biology 1980 147 177

[2] G. Ariel, A. Rabani, S. Benisty Nature Communications 2015 1 6

[3] E. Bouin, V. Calvez, G. Nadin Mathematical Models and Methods in Applied Sciences 2014 1165 1195

[4] E. Bouin, V. Calvez, G. Nadin Archive for Rational Mechanics and Analysis 2015 571 617

[5] S. Fedotov Physical Review Letters 2001 926 929

[6] S. Fedotov Physical Review E 2010 1 7

[7] S. Fedotov Physical Review E 020101 2016

[8] S. Fedotov, N. Korabel Physical Review E 2015 1 7

[9] S. Fedotov, A. Tan, A. Zubarev Physical Review E 2015 1 10

[10] J. Fort, V. Méndez Physical Review E 1999 5894 5901

[11] J. Fort, V. Méndez Physical Review Letters 1999

[12] S. Goldstein Quarterly Journal of Mechanics and Applied Mathematics 1951 129 156

[13] T. Hillen, H. G. Othmer SIAM Journal of Applied Mathematics 2000 751 775

[14] N. E. Humphries, N. Queiroz, J. R. M. Dyer Nature Letter 2010 1066 1069

[15] Y. Jung, E. Barkai, R. J. Silbey Chemical Physics 2002 181 194

[16] M. Kac Rocky Mountain Journal of Mathematics 1974 497 510

[17] V. Méndez, D. Campos, S. Fedotov Physical Review E 2004 1 7

[18] V. Méndez, D. Campos, I. Gómez-Portillo Physical Review E 2010 1 9

[19] V. Méndez, S. Fedotov, W. Horsthemke. Reaction-Transport Systems. Springer, 2010.

[20] C. T Mierke, The integrin αv β3 increases cellular stiffness and cytoskeletal remodeling dynamics to facilitate cancer cell invasion. New Journal of Physics (2013).

[21] C. T. Mierke, B. Frey, M. Fellner Journal of Cell Biology 2011 1 23

[22] J. D. Murray. Mathematical Biology I: An Introduction. Springer, 2002.

[23] A. Nepomnyashchy Mathematical Modelling of Natural Phenomena 2016 26 36

[24] H. G. Othmer, T. Hillen SIAM Journal of Applied Mathematics 2002 1222 1250

[25] D. A. Raichlen, B. M. Wood, A. D. Gordon PNAS 2013 728 733

[26] A. M. Reynolds, A. D. Smith, D. R. Reynolds Journal of Experimental Biology 2007 1955 61

[27] I. M. Sokolov, R. Metzler Physical Review E 010101 2003

[28] P. Straka, S. Fedotov Journal of Theoretical Biology 2015 71 83

[29] P.F. Tilles, S. V. Petrovskii Ecological Complexity 2015 86 92

[30] A. Yadav, S. Fedotov, V. Méndez Physics Letters A 2007 374 378

[31] V. Zaburdaev, S. Denisov, J. Klafter Reviews of Modern Physics 2015 483 530

Cité par Sources :