The study of inertial brownian motor with fluctuating potential energy sign

Authors

  • Наталия Григорьевна Шкода Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164, Ukraine https://orcid.org/0000-0001-8669-7803
  • Таисия Евгеневна Корочкова Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164, Ukraine https://orcid.org/0000-0002-5110-0998
  • Виктор Михайлович Розенбаум Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164, Ukraine https://orcid.org/0000-0003-2889-3915
  • Ирина Викторовна Шапочкина Belarusian State University 4 Nezavisimosti ave, Minsk, Belarus, 220050, Belarus https://orcid.org/0000-0002-6962-7931

DOI:

https://doi.org/10.15587/1729-4061.2015.44382

Keywords:

nanomachines, nanomechanisms, Brownian motors, molecular pumps, subsurface diffusion, nonequilibrium fluctuations

Abstract

The model of a Brownian motor with potential profile fluctuating in the sign, which is described by piecewise-linear periodic function, not belonging to the classes of symmetric and antisymmetric functions was presented. The model with the potential of this type shows unidirectional motion just in the case when inertialess motion is prohibited. The simplicity of the potential profile makes the problem analytically solvable and greatly simplifies the symmetry analysis. In approximations of the adiabatic mode of fluctuations and low inertia amendments, an analytical expression for the average velocity of the Brownian motor, which is different from zero only at a non-zero mass of the particle, i.e., motor effect is purely inertial was obtained. The resulting expression depends on the mass of the particle, parameters of the nonantisymmetric potential profile, the friction coefficient of the particle and temperature. It is shown that by changing the values of the parameter characterizing the profile shape deviation from antisymmetric allows to control the motion direction, and the dependence of the average velocity on this parameter is non-monotonic.

Author Biographies

Наталия Григорьевна Шкода, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164

PhD

Scientific Associate

Department of Theory of Nanostructured Systems

Таисия Евгеневна Корочкова, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164

PhD

Senior Scientific Associate

Department of Theory of Nanostructured Systems

Виктор Михайлович Розенбаум, Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine 17 General Naumov str., Kyiv, Ukraine, 03164

Doctor of Science, Head of the Department

Department of Theory of Nanostructured Systems

Ирина Викторовна Шапочкина, Belarusian State University 4 Nezavisimosti ave, Minsk, Belarus, 220050

PhD

Associate professor of the Chair of Computer Simulations

Department of Physics

References

  1. Smoluchowski, M. (1915). Brownsche Molecularbewegung unter Einwirkung äußerer Kräfte und deren Zusammenhang mit der verallgemeinerten Diffusionsgleichung. Ann. Phys., 48, 1103–1112.
  2. Reimann, P. (2002). Brownian motors: noisy transport far from equilibrium. Physics Reports, 361 (2-4), 57–265. doi: 10.1016/s0370-1573(01)00081-3
  3. Hänggi, P., Marchesoni, F. (2009). Artificial Brownian motors: Controlling transport on the nanoscale. Reviews of Modern Physics, 81 (1), 387–442. doi: 10.1103/revmodphys.81.387
  4. Bressloff, P. C., Newby, J. M. (2013). Stochastic models of intracellular transport. Reviews of Modern Physics, 85 (1), 135–196. doi: 10.1103/revmodphys.85.135
  5. Magnasco, M. O. (1993). Forced thermal ratchets. Physical Review Letters, 71 (10), 1477–1481. doi: 10.1103/physrevlett.71.1477
  6. Klein, O. (1922). Zur statistischen Theorie der Suspensionen und Lösungen. Ark. för Mat. (German): Astron. och Fys., 16 (5), 51.
  7. Kramers, H. A. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7 (4), 284–304. doi: 10.1016/s0031-8914(40)90098-2
  8. Rozenbaum, V. M., Makhnovskii, Y. A., Shapochkina, I. V., Sheu, S.-Y., Yang, D.-Y., Lin, S. H. (2014). Inertial effects in adiabatically driven flashing ratchets. Physical Review E, 89 (5), 052131-1–052131-9. doi: 10.1103/physreve.89.052131
  9. Ghosh, P. K., Hänggi, P., Marchesoni, F., Nori, F., Schmid, G. (2012). Brownian transport in corrugated channels with inertia. Physical Review E, 86 (2), 021112. doi: 10.1103/physreve.86.021112
  10. Rozenbaum, V. M., Shapochkina, I. V. (2010). Neadiabaticheskie popravki k skorosti brounovskogo motora so slozhnym potencial'nym rel'efom. Pis'ma v ZhJeTF., 92 (2), 124–129.

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Published

2015-06-17

How to Cite

Шкода, Н. Г., Корочкова, Т. Е., Розенбаум, В. М., & Шапочкина, И. В. (2015). The study of inertial brownian motor with fluctuating potential energy sign. Eastern-European Journal of Enterprise Technologies, 3(5(75), 17–20. https://doi.org/10.15587/1729-4061.2015.44382

Issue

Vol. 3 No. 5(75) (2015): Applied physics

Section

Applied physics

License

Copyright (c) 2015 Наталия Григорьевна Шкода, Таисия Евгеневна Корочкова, Виктор Михайлович Розенбаум, Ирина Викторовна Шапочкина

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