no. 6
Asymmetric Potentials and Motor Effect : a Homogenization Approach
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2055-2071. 
@article{AIHPC_2009__26_6_2055_0,
     author = {Perthame, Beno{\^\i}T and Souganidis, Panagiotis E.},
     title = {Asymmetric {Potentials} and {Motor} {Effect} : a {Homogenization} {Approach}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2055--2071},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.10.003},
     mrnumber = {2569885},
     zbl = {1180.35081},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.003/}
}
TY  - JOUR
AU  - Perthame, BenoîT
AU  - Souganidis, Panagiotis E.
TI  - Asymmetric Potentials and Motor Effect : a Homogenization Approach
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
SP  - 2055
EP  - 2071
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.003/
DO  - 10.1016/j.anihpc.2008.10.003
LA  - en
ID  - AIHPC_2009__26_6_2055_0
ER  - 
%0 Journal Article
%A Perthame, BenoîT
%A Souganidis, Panagiotis E.
%T Asymmetric Potentials and Motor Effect : a Homogenization Approach
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2055-2071
%V 26
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.003/
%R 10.1016/j.anihpc.2008.10.003
%G en
%F AIHPC_2009__26_6_2055_0
Perthame, BenoîT; Souganidis, Panagiotis E. Asymmetric Potentials and Motor Effect : a Homogenization Approach. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2055-2071. doi : 10.1016/j.anihpc.2008.10.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.003/

[1] Allaire G., Capdeboscq Y., Homogenization of a Spectral Problem in Neutronic Multigroup Diffusion, Comput. Methods Appl. Mech. Engrg. 187 (1-2) (2000) 91-117. | MR | Zbl

[2] Allaire G., Orive R., Homogenization of Periodic Non Self-Adjoint Problems With Large Drift and Potential, COCV 13 (2007) 735-749. | Numdam | MR | Zbl

[3] Allaire G., Raphael A.-L., Homogenization of a Convection-Diffusion Model With Reaction in a Porous Medium, C. R. Acad. Sci. Paris, Ser. I 334 (2007) 523-528. | MR | Zbl

[4] Astumian R. D., Hänggi P., Brownian Motors, Phys. Today 55 (11) (2002) 33-39.

[5] Barles G., Evans L. C., Souganidis P. E., Wavefront Propagation for Reaction Diffusion Systems of PDE, Duke Math. J. 61 (1990) 835-858. | MR | Zbl

[6] Barles G., Perthame B., Concentrations and Constrained Hamilton-Jacobi Equations Arising in Adaptive Dynamics, in: Danielli D. (Ed.), Recent Developments in Nonlinear Partial Differential Equations, Contemp. Math., vol. 439, Amer. Math. Soc., 2007, pp. 57-68. | MR | Zbl

[7] A. Blanchet, J. Dolbeault, M. Kowalczyk, Stochastic Stokes' drift, homogenized functional inequalities, and large time behaviour of Brownian ratchets, preprint, 2008. | MR

[8] Budhiraja A., Fricks J., Molecular Motors, Brownian Ratchets, and Reflected Diffusions, Discrete Contin. Dynam. Systems B 6 (4) (2006) 711-734. | MR | Zbl

[9] Capdeboscq Y., Homogenization of a Neutronic Critical Diffusion Problem With Drift, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 567-594. | MR | Zbl

[10] Chipot M., Hastings S., Kinderlehrer D., Transport in a Molecular Motor System, M2AN Math. Model. Numer. Anal. 38 (6) (2004) 1011-1034. | EuDML | Numdam | MR | Zbl

[11] Chipot M., Kinderlehrer D., Kowalczyk M., A Variational Principle for Molecular Motors, dedicated to Piero Villaggio on the occasion of his 70th birthday, Meccanica 38 (5) (2003) 505-518. | MR | Zbl

[12] Collet P., Martinez S., Asymptotic Velocity of One Dimensional Diffusions With Periodic Drift, J. Math. Biol. 56 (2008) 765-792. | MR | Zbl

[13] Crandall M. G., Ishii H., Lions P.-L., User's Guide to Viscosity Solutions of Second Order Partial Differential Equations, Bull. Amer. Math. Soc. 27 (1992) 1-67. | MR | Zbl

[14] Diekmann O., Jabin P.-E., Mischler S., Perthame B., The Dynamics of Adaptation: an Illuminating Example and a Hamilton-Jacobi Approach, Th. Pop. Biol. 67 (4) (2005) 257-271. | Zbl

[15] Doering C., Ermentrout B., Oster G., Rotary DNA Motors, Biophys. J. 69 (6) (1995) 2256-2267.

[16] Dolbeault J., Kinderlehrer D., Kowalczyk M., Remarks About the Flashing Rachet, in: Partial Differential Equations and Inverse Problems, Contemp. Math., vol. 362, Amer. Math. Soc., Providence, RI, 2004, pp. 167-175. | MR | Zbl

[17] Donato P., Piatniski A., Averaging of Nonstationary Parabolic Operators With Large Lower Order Terms, in: Multiscale Problems and Asymptotic Analysis, Gakuto Internat. Ser. Math. Sci. Appl., vol. 24, Gakkotosho, Tokyo, 2006, pp. 153-165. | MR | Zbl

[18] Evans L. C., The Perturbed Test Function Method for Viscosity Solutions of Nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 359-375. | MR | Zbl

[19] Evans L. C., Souganidis P. E., A PDE Approach to Geometric Optics for Certain Reaction-Diffusion Equations, Indiana Univ. Math. J. 38 (1989) 141-172. | MR | Zbl

[20] Jülicher F., Ajdari A., Prost J., Modeling Molecular Motors, Rev. Modern Phys. 69 (4) (1997) 1269-1281.

[21] S. Hastings, D. Kinderlehrer, J.B. McLeod, Diffusion mediated transport with a look at motor proteins, preprint, 2007. | MR

[22] Howard J., Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associates, Inc., 2001.

[23] Huxley A. F., Muscle Structure and Theories of Contraction, Prog. Biophys. Chem. 7 (1957) 255-318.

[24] Kinderlehrer D., Kowalczyk M., Diffusion-Mediated Transport and the Flashing Ratchet, Arch. Ration. Mech. Anal. 161 (2) (2002) 149-179. | MR | Zbl

[25] Perthame B., The General Relative Entropy Principle - Applications in Perron-Frobenius and Floquet Theories and a Parabolic System for Biomotors, Rend. Accad. Nazi. Sci. XL Mem. Mat. Appl. XXIX (1) (2005) 307-326. | MR

[26] Perthame B., Transport Equations in Biology, Frontiers in Mathematics, Birkhäuser, 2007. | MR | Zbl

[27] B. Perthame, P.E. Souganidis, Asymmetric potentials and motor effect: a large deviation approach, Arch. Rat. Mech. Anal., in press. | MR | Zbl

[28] Peskin C. S., Ermentrout B., Oster G., The Correlation Ratchet: a Novel Mechanism for Generating Directed Motion by ATP Hydrolysis, in: Mow V. C., (Eds.), Cell Mechanics and Cellular Engineering, Springer, New York, 1995.

Cité par Sources :