110
6 Ratchet Dimer Brownian Motor with Hydrodynamic Interactions
6. von Gehlen, S., Evstigneev, M., Reimann, P.: Dynamics of a dimer in a symmetric potential:
Ratchet effect generated by an internal degree of freedom. Phys. Rev. E 77, 031136 (2008)
7. Lipowsky, R., Chai, Y., Klumpp, S., Liepelt, S., Müller, M.J.I.: Molecular motor traffic: from
biological nanomachines to macroscopic transport. Phys. A 372, 34–51 (2006)
8. Tao, Y.G., Kapralb, R.: Design of chemically propelled nanodimer motors. J. Chem. Phys. 128,
164518 (2008)
9. Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (2001)
10. Block, S.M.: Nanometres and piconewtons: the macromolecular mechanics of kinesinTrends.
Cell Biol. 5, 169–175 (1995)
11. Visscher, K., Schnitzer, M.J., Block, S.M.: Single kinesin molecules studied with a molecular
force clamp. Nature 400, 184–189 (1999)
12. Schnitzer, M.J., Visscher, K., Block, S.M.: Force production by single kinesin motors. Nat.
Cell Biol. 2, 718–723 (2000)
13. Speer, D., Eichhorn, R., Evstigneev, M., Reimann, P.: Dimer motion on a periodic substrate:
spontaneous symmetry breaking and absolute negative mobility. Phys. Rev. E 85, 061132
(2012)
14. Zimmermann, E., Seifert, U.: Efficiencies of a molecular motor: a generic hybrid model applied
to the F1-ATPase. New J. Phys. 14, 103023 (2012)
15. Pinkoviezky, I., Gov, N.S.: Modelling interacting molecular motors with an internal degree of
freedom. New J. Phys. 15, 025009 (2013)
16. Ermak, D.L., McCammon, J.A.: Brownian dynamics with hydrodynamic interactions. J. Chem.
Phys. 69(4), 1352–1360 (1978)
17. Kemps, J.A.L., Bhattacharjee, S.: Particle tracking model for colloid transport near planar
surfaces covered with spherical asperities. Langmuir 25(12), 6887–6897 (2009)
18. Günther, S., Kruse, K.: A simple self-organized swimmer driven by molecular motors. Eur.
Phys. Lett. 84, 68002 (2008)
19. Ramia, M., Tullock, D.L., Phan-Thien, N.: The role of hydrodynamic interaction in the
locomotion of microorganisms. Biophys. J. 65, 755–778 (1993)
20. MunJu, K., Powers, T.R.: Hydrodynamic interactions between rotating helices. Phys. Rev. E
69, 061910 (2004)
21. Fornés, J.A.: Hydrodynamic interactions induce movement against an external load in a ratchet
dimer Brownian motor. J. Colloid Interface Sci. 341, 376–379 (2010)
22. Grimm, A., Stark, H.: Hydrodynamic interactions enhance the performance of Brownian
ratchets. SoftMatter 7, 3219 (2011)
23. Polson, J.M., Bylhouwer, B., Zuckermann, M.J., Horton, A.J., Scott, W.M.: Dynamics of a
polymer in a Brownian ratchet. Phys. Rev. E 82, 051931 (2010)
24. Dickinson, E.: Brownian dynamic with hydrodynamic interactions: the application to protein
diffusional problems. Chem. Soc. Rev. 14, 421–455 (1985)
25. Oseen, C.W.: Hydrodynamik, Akademische Verlag Leipzig (1927)
26. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Claredon Press, Oxford (1986)
27. https://ocw.mit.edu/courses/nuclear-engineering/22-103-microscopic-theory-of-transportfall-2003/lecture-notes/lec3.pdf
28. Freund, J.A., Schimansky-Geier, L.: Diffusion in discrete ratchets. Phys. Rev. E 60(2), 1304
(1999)
29. Cubero, D., Rensoni, J.: Brownian Ratchets. Cambridge University Press, Cambridge (2016)
30. Houtman, D., Pagonabarraga, I., Lowe, C.P., Esseling-Ozdoba, A., Emons, A.M.C., Eiser, E.:
Hydrodynamic flow caused by active transport along cytoskeletal elements. Europhys. Lett.
78, 18001 (2007)
6 Ratchet Dimer Brownian Motor with Hydrodynamic Interactions
6. von Gehlen, S., Evstigneev, M., Reimann, P.: Dynamics of a dimer in a symmetric potential:
Ratchet effect generated by an internal degree of freedom. Phys. Rev. E 77, 031136 (2008)
7. Lipowsky, R., Chai, Y., Klumpp, S., Liepelt, S., Müller, M.J.I.: Molecular motor traffic: from
biological nanomachines to macroscopic transport. Phys. A 372, 34–51 (2006)
8. Tao, Y.G., Kapralb, R.: Design of chemically propelled nanodimer motors. J. Chem. Phys. 128,
164518 (2008)
9. Howard, J.: Mechanics of Motor Proteins and the Cytoskeleton. Sinauer Associates, Sunderland (2001)
10. Block, S.M.: Nanometres and piconewtons: the macromolecular mechanics of kinesinTrends.
Cell Biol. 5, 169–175 (1995)
11. Visscher, K., Schnitzer, M.J., Block, S.M.: Single kinesin molecules studied with a molecular
force clamp. Nature 400, 184–189 (1999)
12. Schnitzer, M.J., Visscher, K., Block, S.M.: Force production by single kinesin motors. Nat.
Cell Biol. 2, 718–723 (2000)
13. Speer, D., Eichhorn, R., Evstigneev, M., Reimann, P.: Dimer motion on a periodic substrate:
spontaneous symmetry breaking and absolute negative mobility. Phys. Rev. E 85, 061132
(2012)
14. Zimmermann, E., Seifert, U.: Efficiencies of a molecular motor: a generic hybrid model applied
to the F1-ATPase. New J. Phys. 14, 103023 (2012)
15. Pinkoviezky, I., Gov, N.S.: Modelling interacting molecular motors with an internal degree of
freedom. New J. Phys. 15, 025009 (2013)
16. Ermak, D.L., McCammon, J.A.: Brownian dynamics with hydrodynamic interactions. J. Chem.
Phys. 69(4), 1352–1360 (1978)
17. Kemps, J.A.L., Bhattacharjee, S.: Particle tracking model for colloid transport near planar
surfaces covered with spherical asperities. Langmuir 25(12), 6887–6897 (2009)
18. Günther, S., Kruse, K.: A simple self-organized swimmer driven by molecular motors. Eur.
Phys. Lett. 84, 68002 (2008)
19. Ramia, M., Tullock, D.L., Phan-Thien, N.: The role of hydrodynamic interaction in the
locomotion of microorganisms. Biophys. J. 65, 755–778 (1993)
20. MunJu, K., Powers, T.R.: Hydrodynamic interactions between rotating helices. Phys. Rev. E
69, 061910 (2004)
21. Fornés, J.A.: Hydrodynamic interactions induce movement against an external load in a ratchet
dimer Brownian motor. J. Colloid Interface Sci. 341, 376–379 (2010)
22. Grimm, A., Stark, H.: Hydrodynamic interactions enhance the performance of Brownian
ratchets. SoftMatter 7, 3219 (2011)
23. Polson, J.M., Bylhouwer, B., Zuckermann, M.J., Horton, A.J., Scott, W.M.: Dynamics of a
polymer in a Brownian ratchet. Phys. Rev. E 82, 051931 (2010)
24. Dickinson, E.: Brownian dynamic with hydrodynamic interactions: the application to protein
diffusional problems. Chem. Soc. Rev. 14, 421–455 (1985)
25. Oseen, C.W.: Hydrodynamik, Akademische Verlag Leipzig (1927)
26. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Claredon Press, Oxford (1986)
27. https://ocw.mit.edu/courses/nuclear-engineering/22-103-microscopic-theory-of-transportfall-2003/lecture-notes/lec3.pdf
28. Freund, J.A., Schimansky-Geier, L.: Diffusion in discrete ratchets. Phys. Rev. E 60(2), 1304
(1999)
29. Cubero, D., Rensoni, J.: Brownian Ratchets. Cambridge University Press, Cambridge (2016)
30. Houtman, D., Pagonabarraga, I., Lowe, C.P., Esseling-Ozdoba, A., Emons, A.M.C., Eiser, E.:
Hydrodynamic flow caused by active transport along cytoskeletal elements. Europhys. Lett.
78, 18001 (2007)