Bibliography
47
x(i+1,j)=xij - Vo*dV(i,j)*dt+ eta(i,j)*D*FDN*dt + . . .
D*Fload*dt + dw(i,j);
end
end
MEANeta=(sum(eta,2))/NR;
MEANXR=(sum(x,2))/NR;
t=(1:N)*dt;
figure(1); plot(t,MEANXR); grid;
%figure(2); plot(t,MEANeta); grid;
save MEANXR.DAT MEANXR -ascii;
Bibliography
1. Derényi, I., Astumian, R.D.: Brownian ratchets and their application to biological transport
processes and macromolecular separation. In: Kasianowicz, J.J., Kellermayer, M.S.Z., Deamer,
D.W. (eds.) Structure and Dynamics of Confined Polymers. NATO Science Series. Series 3:
High Technology, vol. 87. Springer, Dordrecht (2002). https://doi.org/10.1007/978-94-0100401-5-17
2. Cubero, D., Renzoni, F.: Brownian Ratchets: From Statistical Physics to Bio and Nano-motors.
Cambridge University Press. ISBN 978-1-107-06352-5 (2016)
3. Bug, A.L.R., Berne, B.J.: Shaking-induced transition to a nonequilibrium state. Phys. Rev. Lett.
59, 948 (1987)
4. Ajdari, A.J., Prost, J.: Mouvement induit par un potentiel periodique de basse symetrie: Dielectrophorese pulsee. J. Comptes Rendus de l’Académie des Sciences, Paris 315, 1635–1639
(1992)
5. Magnasco, M.O.: Forced thermal ratchets. Phys. Rev. Lett. 71(10), 1477–1481. https://doi.org/
10.1103/PhysRevLett.71.1477 (1993)
6. Astumian, R.D., Bier, M.: Fluctuation driven ratchets: molecular motors. Phys. Rev. Lett.
72(11), 1766–1769 (1994)
7. Astumian, R.D.: Thermodynamics and kinetics of a Brownian motor. Science 276, 917–922
(1997)
8. Astumian, R.D., Derényi, I.: Fluctuation driven transport and models of molecular motors and
pumps. Eur. Biophys. J. 27, 474–489 (1998)
9. Barik, D., Ghosh, P.K., Ray, D.S.: Langevin dynamics with dichotomous noise; direct simulation and applications. J. Stat. Mech. (2006). Online at stacks.iop.org/JSTAT/2006/P03010
10. Bena, I.: Dichotomous Markov noise: exact results for out-of-equilibrium system. Int. J. Mod.
Phys. B 20, 2825 (2006)
11. Bader, J.S., Hammond, R.W., Henck, S.A., Deem, M.W., McDermott, G.A., Bustillo, J.M.,
Simpson, J.W., Mulhern, G.T., Rothberg, J.M.: DNA transport by a micromachined Brownian
ratchet device. Proc. Natl. Acad. Sci. U. S. A. 96, 13165 (1999)
12. Doering, C.R.: Randomly rattled ratchets. IL Nuovo Cimento D. 17(7–8), 685–697 (1995)
13. Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361(2–4),
57–265 (2002)
14. Mogilner, A., Elston, T., Wang, H., Oster, G.: Molecular motors: examples. In: Fall, C.,
Marland, E., Tyson, J., Wagner, J. (eds.) Joel Keizer’s Computational Cell Biology, Chapter 13.
A motor driven by a “flashing potential”, vol. 13.2, p. 361 (2002). https://doi.org/10.1016/
S0370-1573(01)00081-3
47
x(i+1,j)=xij - Vo*dV(i,j)*dt+ eta(i,j)*D*FDN*dt + . . .
D*Fload*dt + dw(i,j);
end
end
MEANeta=(sum(eta,2))/NR;
MEANXR=(sum(x,2))/NR;
t=(1:N)*dt;
figure(1); plot(t,MEANXR); grid;
%figure(2); plot(t,MEANeta); grid;
save MEANXR.DAT MEANXR -ascii;
Bibliography
1. Derényi, I., Astumian, R.D.: Brownian ratchets and their application to biological transport
processes and macromolecular separation. In: Kasianowicz, J.J., Kellermayer, M.S.Z., Deamer,
D.W. (eds.) Structure and Dynamics of Confined Polymers. NATO Science Series. Series 3:
High Technology, vol. 87. Springer, Dordrecht (2002). https://doi.org/10.1007/978-94-0100401-5-17
2. Cubero, D., Renzoni, F.: Brownian Ratchets: From Statistical Physics to Bio and Nano-motors.
Cambridge University Press. ISBN 978-1-107-06352-5 (2016)
3. Bug, A.L.R., Berne, B.J.: Shaking-induced transition to a nonequilibrium state. Phys. Rev. Lett.
59, 948 (1987)
4. Ajdari, A.J., Prost, J.: Mouvement induit par un potentiel periodique de basse symetrie: Dielectrophorese pulsee. J. Comptes Rendus de l’Académie des Sciences, Paris 315, 1635–1639
(1992)
5. Magnasco, M.O.: Forced thermal ratchets. Phys. Rev. Lett. 71(10), 1477–1481. https://doi.org/
10.1103/PhysRevLett.71.1477 (1993)
6. Astumian, R.D., Bier, M.: Fluctuation driven ratchets: molecular motors. Phys. Rev. Lett.
72(11), 1766–1769 (1994)
7. Astumian, R.D.: Thermodynamics and kinetics of a Brownian motor. Science 276, 917–922
(1997)
8. Astumian, R.D., Derényi, I.: Fluctuation driven transport and models of molecular motors and
pumps. Eur. Biophys. J. 27, 474–489 (1998)
9. Barik, D., Ghosh, P.K., Ray, D.S.: Langevin dynamics with dichotomous noise; direct simulation and applications. J. Stat. Mech. (2006). Online at stacks.iop.org/JSTAT/2006/P03010
10. Bena, I.: Dichotomous Markov noise: exact results for out-of-equilibrium system. Int. J. Mod.
Phys. B 20, 2825 (2006)
11. Bader, J.S., Hammond, R.W., Henck, S.A., Deem, M.W., McDermott, G.A., Bustillo, J.M.,
Simpson, J.W., Mulhern, G.T., Rothberg, J.M.: DNA transport by a micromachined Brownian
ratchet device. Proc. Natl. Acad. Sci. U. S. A. 96, 13165 (1999)
12. Doering, C.R.: Randomly rattled ratchets. IL Nuovo Cimento D. 17(7–8), 685–697 (1995)
13. Reimann, P.: Brownian motors: noisy transport far from equilibrium. Phys. Rep. 361(2–4),
57–265 (2002)
14. Mogilner, A., Elston, T., Wang, H., Oster, G.: Molecular motors: examples. In: Fall, C.,
Marland, E., Tyson, J., Wagner, J. (eds.) Joel Keizer’s Computational Cell Biology, Chapter 13.
A motor driven by a “flashing potential”, vol. 13.2, p. 361 (2002). https://doi.org/10.1016/
S0370-1573(01)00081-3