Email the author Ratchet effect modeling by method of paradoxical games for stochastic fluctuations of double-well potential
DOI: https://doi.org/10.15407/hftp13.03.338
Abstract
The ratchet effect is a directed nanoparticle flux phenomenon induced by nonequilibrium fluctuations in a system with spatial and (or) temporal asymmetry. One is used as the way to create a controlled nanotransport and is the basis of the theory of Brownian motors. Fluctuation motion simulation is a promising way to calculate the main characteristics of Brownian motors, it avoids complex calculations and quickly obtains predictions about the appearance or absence of generated directional motion in a specific model. Nonequilibrium fluctuations are usually introduced into the system by a dichotomous process that switches two periodic asymmetric potential profiles at certain fixed intervals (deterministic process), or randomly with average potential lifetimes (stochastic process). We investigate the modeling of the process of the ratchet effect in the framework of the Brownian motor jump-like model by the method of Parrondo’s paradoxical game for the stochastic dichotomous process and compare results with a similar deterministic process. A calculus method for the main characteristics obtaining of the motor with stochastic dichotomous process is proposed, it is shown correspondence to the analytical description of this model in extreme cases. It is shown that the stochasticity of the process directly affects the characteristics of the ratchet effect: the trajectories of the average displacements of nanoparticles fundamentally differs in the deterministic description, and a gradual difference in these processes is observed at low values. The study of asymmetric dichotomous processes for different temperature modes of motor operation is carried out. The model allows one to analyze the peculiarities of the directional motion starting at the level of single jumps, as well as to formulate recommendations for possible improvement of motor efficiency for different temperatures. For high-temperature mode, it is advisable to reduce the lifetime of the state with the active potential, and for low-temperature mode, arbitrary, it should be increased.
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References
Reimann P. Brownian Motors: Noisy Transport far from Equilibrium. Phys. Rep. 2002. 361(2-4): 57. https://doi.org/10.1016/S0370-1573(01)00081-3
Astumian R.D. Thermodynamics and kinetics of a Brownian motor. Science. 1997. 276(5314): 917. https://doi.org/10.1126/science.276.5314.917
Cubero D., Renzoni F. Brownian Ratchets: From Statistical Physics to Bio and Nanomotors. (Cambridge, UK: Cambridge University Press, 2016). https://doi.org/10.1017/CBO9781107478206
Hanggi P. Organic electronics: Harvesting randomness. Nat. Mater. 2011. 10: 6. https://doi.org/10.1038/nmat2925
Astumian R.D. Adiabatic Theory for Fluctuation-Induced Transport on a Periodic Potential. J. Phys. Chem. 1996. 100(49): 19075. https://doi.org/10.1021/jp961614m
Kay E. R., Leigh D. A., Zerbetto F. Synthetic Molecular Motors and Mechanical Machines. Angew. Chem. Int. Ed. Engl. 2007. 46(1-2): 72. https://doi.org/10.1002/anie.200504313
Cheetham M.R., Bramble J.P., McMillan D.G.G., Bushby R.J., Olmsted P.D., Jeuken L.J.C., Evans S.D. Manipulation and sorting of membrane proteins using patterned diffusion-aided ratchets with AC fields in supported bilayers. Soft Matter. 2012. 8(20): 5459. https://doi.org/10.1039/c2sm25473e
Drexler K.E. Nanosystems: Molecular Machinery, Manufacturing and Computation. (New York: Wiley, 1992).
Howard J. Mechanics of Motor Proteins and the Cytoskeleton. (Sunderland, MA: Sinauer Associates, 2001).
Lipowsky R., Klumpp S. 'Life is Motion' - Multiscale Motility of Molecular. Motor. Physica A. 2005. 352(1): 53. https://doi.org/10.1016/j.physa.2004.12.034
Krogh A., Larsson B., von Heijne G., Sonnhammer E. Predicting transmembrane protein topology with a hidden Markov model. Application to complete genomes. J. Mol. Biol. 2001. 305(3): 567. https://doi.org/10.1006/jmbi.2000.4315
Vale R.D. The molecular motor toolbox for intracellular transport. Cell. 2003. 112(4): 467. https://doi.org/10.1016/S0092-8674(03)00111-9
Kramers H.A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica VII. 1940. 7(4): 284. https://doi.org/10.1016/S0031-8914(40)90098-2
Derrida B. Velocity and diffusion constant of a periodic one-dimensional hopping model. J. Stat. Phys. 1983. 31: 433. https://doi.org/10.1007/BF01019492
Gardiner C.R. Handbook of Stochastic Methods. 2nd ed (Berlin: Springer, 1985).
Parrondo J.M.R., Harmer G.P., Abbott D. New paradoxical games based on Brownian ratchets. Phys. Rev. Lett. 2000. 85(4): 5226. https://doi.org/10.1103/PhysRevLett.85.5226
Gorre-Talini L., Jeanjean S., Silberzan P. Sorting of Brownian particles by pulsed application of an asymmetric potential. Phys. Rev. E. 1997. 56(2): 2025. https://doi.org/10.1103/PhysRevE.56.2025
Okada Y., Hirokawa N. A Processive Single-Headed Motor: Kinesin Superfamily Protein KIF1A. Science. 1999. 283(5405): 1152. https://doi.org/10.1126/science.283.5405.1152
Dekhtyar M.L., Ishchenko A.A., Rozenbaum V.M. Photoinduced molecular transport in biological environments based on dipole moment fluctuations. J. Phys. Chem. B. 2006. 110(41): 20111. https://doi.org/10.1021/jp063795q
Rozenbaum V.M. High-temperature brownian motors: Deterministic and stochastic fluctuations of a periodic potential. JETP Lett. 2008. 88(5): 342. https://doi.org/10.1134/S0021364008170128
Rozenbaum V.M. Constructive role of chaos: Brownian motors and winning strategies in game theory. Him. Fiz. Tehnol. Poverhni. 2020. 11(1): 100. [in Russian]. https://doi.org/10.15407/hftp11.01.100
Terets A.D., Korochkova T.Ye., Rozenbaum V.M., Mashira V.A., Shapochkina I.V., Furs A.N., Ikim M.I., Gromov V.F. Motion reversal modeling for a Brownian particle affected by nonequilibrium fluctuations. Him. Fiz. Tehnol. Poverhni. 2020. 11(3): 395. [in Russian]. https://doi.org/10.15407/hftp11.03.395
Korochkova T.E., Shkoda N.G., Rozenbaum V.M., Kamysh Yu.A., Shapochkina I.V., Ikim M.I., Gerasimov G.N., Gromov V.F. General solution of Pauli master equation and applications to diffusive transport. Surface. 2018. 10(25): 3. [in Russian]. https://doi.org/10.15407/Surface.2018.10.003
Rozenbaum V.M., Shapochkina I.V., Teranishi Y., Trakhtenberg L.I. Symmetry of deterministic ratchets. Phys. Rev. E. 2019. 100(2): 022115-1-16. https://doi.org/10.1103/PhysRevE.100.022115
Rozenbaum V.M., Yang D.-Y., Lin S.H., Tsong T.Y. Catalytic Wheel as a Brownian Motor. J. Phys. Chem. B. 2004. 108(40): 15880. https://doi.org/10.1021/jp048200a
DOI: https://doi.org/10.15407/hftp13.03.338
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