Asymmetric potentials and motor effect : a homogenization approach

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1. [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. Zbl1126.82346MR1765549
2. [2] Allaire G., Orive R., Homogenization of periodic non self-adjoint problems with large drift and potential, COCV13 (2007) 735-749. Zbl1130.35307MR2351401
3. [3] Allaire G., Raphael A.-L., Homogenization of a convection–diffusion model with reaction in a porous medium, C. R. Acad. Sci. Paris, Ser. I334 (2007) 523-528. Zbl1114.35007MR2324490
4. [4] Astumian R.D., Hänggi P., Brownian motors, Phys. Today55 (11) (2002) 33-39. 
5. [5] Barles G., Evans L.C., Souganidis P.E., Wavefront propagation for reaction diffusion systems of PDE, Duke Math. J.61 (1990) 835-858. Zbl0749.35015MR1084462
6. [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. Zbl1137.49027MR2359020
7. [7] A. Blanchet, J. Dolbeault, M. Kowalczyk, Stochastic Stokes' drift, homogenized functional inequalities, and large time behaviour of Brownian ratchets, preprint, 2008. Zbl1196.26023MR2505853
8. [8] Budhiraja A., Fricks J., Molecular motors, brownian ratchets, and reflected diffusions, Discrete Contin. Dynam. Systems B6 (4) (2006) 711-734. Zbl1132.92005MR2223904
9. [9] Capdeboscq Y., Homogenization of a neutronic critical diffusion problem with drift, Proc. Roy. Soc. Edinburgh Sect. A132 (2002) 567-594. Zbl1066.82530MR1912416
10. [10] Chipot M., Hastings S., Kinderlehrer D., Transport in a molecular motor system, M2AN Math. Model. Numer. Anal.38 (6) (2004) 1011-1034. Zbl1077.35060MR2108942
11. [11] Chipot M., Kinderlehrer D., Kowalczyk M., A variational principle for molecular motors, dedicated to Piero Villaggio on the occasion of his 70th birthday, Meccanica38 (5) (2003) 505-518. Zbl1032.92005MR2006911
12. [12] Collet P., Martinez S., Asymptotic velocity of one dimensional diffusions with periodic drift, J. Math. Biol.56 (2008) 765-792. Zbl1145.60324MR2385683
13. [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. Zbl0755.35015MR1118699
14. [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. Zbl1072.92035
15. [15] Doering C., Ermentrout B., Oster G., Rotary DNA motors, Biophys. J.69 (6) (1995) 2256-2267. 
16. [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. Zbl1064.35065MR2091497
17. [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. MR2233176
18. [18] Evans L.C., The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A111 (1989) 359-375. Zbl0679.35001MR1007533
19. [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. Zbl0692.35014MR982575
20. [20] Jülicher F., Ajdari A., Prost J., Modeling molecular motors, Rev. Modern Phys.69 (4) (1997) 1269-1281. 
21. [21] S. Hastings, D. Kinderlehrer, J.B. McLeod, Diffusion mediated transport with a look at motor proteins, preprint, 2007. Zbl05375303MR2410740
22. [22] Howard J., Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associates, Inc., 2001. 
23. [23] Huxley A.F., Muscle structure and theories of contraction, Prog. Biophys. Chem.7 (1957) 255-318. 
24. [24] Kinderlehrer D., Kowalczyk M., Diffusion-mediated transport and the flashing ratchet, Arch. Ration. Mech. Anal.161 (2) (2002) 149-179. Zbl1065.76183MR1870955
25. [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. MR2305078
26. [26] Perthame B., Transport Equations in Biology, Frontiers in Mathematics, Birkhäuser, 2007. Zbl1185.92006MR2270822
27. [27] B. Perthame, P.E. Souganidis, Asymmetric potentials and motor effect: a large deviation approach, Arch. Rat. Mech. Anal., in press. Zbl1171.82012MR2506073
28. [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.