One-sided broadening of frequency dependence of the velocity of a Brownian motor
DOI:
https://doi.org/10.15407/hftp10.03.227Keywords:
stochastic fluctuation processes, diffusion transport, Brownian motors, broadening of bell-shaped distributionsAbstract
It is known that widths of spectral lines provide а researcher with a variety of important information: about properties of materials, nature of particles interaction, physical parameters of an environment, etc. By analogy with a study of spectral lines, this article analyzes behavior of the width of a bell-shaped frequency dependence of the average velocity of Brownian particles described by a model of a stochastic Brownian motor with asymmetric dichotomous fluctuations of particle potential energy. The bell-shaped dependence is explained by the disappearance of the motor effect in both the low- and high-frequency limits. The relations for the average particle velocity in the adiabatic (low-frequency) and high-temperature regimes of motion allowed us to analyze the frequency dependences for different values of the temporal asymmetry parameter ? of the fluctuations and the ratio ? of potential energy amplitudes in two states of the dichotomous process. The invariance of characteristics of an adiabatic Brownian motor with respect to the asymmetry parameter allowed us to assume the effect of one-sided broadening of the frequency dependence of the velocity with changing ? and ?.
To confirm this assumption, the high-temperature behavior of a Brownian motor with a biharmonic potential energy (described by a sum of two sinusoids) is considered. Graphic dependences of the average velocity on the fluctuation frequency are obtained, which coincide in the adiabatic regime of motor functioning. Using the numerical procedure, frequencies of maxima and widths of the distributions have been calculated dependent on the temporal asymmetry parameter of fluctuations ? and the ratio ?. The calculated dependences confirmed the assumption about the one-sided broadening of the bell-shaped frequency dependence of the average velocity of a Brownian motor.References
1. Veyskopf V. Width of spectral lines in gases. Physics-Uspekhi. 1933. 13(4): 552. [in Russian].
2. Sheka E.F. Spectroscopy of amorphous substances with molecular structure. Physics-Uspekhi. 1990. 33(2): 147. [In Russian]. https://doi.org/10.1070/PU1990v033n02ABEH002546
3. Iogansen A.V. Direct proportionality of the hydrogen bonding energy and the intensification of the stretching ν(XH) vibration in infrared spectra. Optics and Spectroscopy. 1987. 63: 1186 [In Russian].
4. Iogansen A.V., Rozenberg M.Sh. Infrared bands of the OH (OD) group, hydrogen bonding, and special features of the structure of crystals of tert-butanol at 15-350 K. J. Struct. Chem. 1989. 30(1): 92. [in Russian]. https://doi.org/10.1007/BF00748186
5. Iogansen A.V. The nature of band broadening in the IR spectra of hydrogen bonds. Bull. Acad. Sci. USSR, Phys. Ser.1989. 53(9): 1741. [in Russian].
6. Rozenbaum V.M., Ogenko V.M., Chuiko A.A. Oscillatory and orientational states of surface groups of atoms. Physics-Uspekhi. 1991. 34(10): 883. [in Russian]. https://doi.org/10.1070/PU1991v034n10ABEH002525
7. Kuz'menko I.V., Klimenko V.E., Rozenbaum V.M. Shape of the local-vibration band of adsorbed hydrogen-bonded molecular complexes. Optics and Spectroscopy. 2000. 88(2): 201. [in Russian]. https://doi.org/10.1134/1.626779
8. Reimann P. Brownian Brownian motors: noisy transport far from equilibrium. Phys. Rep. 2002. 361(2-4): 57. https://doi.org/10.1016/S0370-1573(01)00081-3
9. Hänggi P., Marchesoni F. Artificial Brownian motors: Controlling transport on the nanoscale. Rev. Mod. Phys. 2009. 81(1): 387. https://doi.org/10.1103/RevModPhys.81.387
10. Schadschneider A., Chowdhury D., Nishinari K. Stochastic Transport in Complex Systems: From Molecules to Vehicles. 1st Edition. (Amsterdam: Elsevier Science, 2010).
11. Cubero D., Renzoni F. Brownian Ratchets: From Statistical Physics to Bio and Nano-motors. (Cambridge University Press., 2016). https://doi.org/10.1017/CBO9781107478206
12. Korochkova T.Ye., Shkoda N.G., Chernova A.A., Rozenbaum V.M. Exact analytical solutions in the theory of brownian motors and pumps. Surface. 2012. 4(19): 19. [in Russian].
13. Korochkova T.Ye., 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
14. Rozenbaum V.M., Shapochkina I.V., Trakhtenberg L.I. The method of green's functions in the theory of Brownian motors. Physics-Uspekhi. 2019. 189(5): 529. [in Russian]. https://doi.org/10.3367/UFNe.2018.04.038347
15. Rousselet J., Salome L., Ajdari A. Directional motion of brownian particles induced by a periodic asymmetric potential. J. Nature. 1994. 370: 446. https://doi.org/10.1038/370446a0
16. Gorre-Talini L., Spatz J.P., Silberzan P. Dielectroscopic ratchets. Chaos. 1998. 8: 650. https://doi.org/10.1063/1.166347
17. de Souza Silva C.C., de Vondel J.V., Morelle M., Moshchalkov V.V. Controlled multiple reversals of a ratchet effect. Nature. 2006. 440: 651. https://doi.org/10.1038/nature04595
18. Gommers R., Bergamini S., Renzoni F. Dissipation-induced symmetry breaking in a driven optical lattice. Phys. Rev. Lett. 2005. 95: 073003. https://doi.org/10.1103/PhysRevLett.95.073003
19. Kedem O., Lau B., Weiss E.A. Mechanisms of symmetry breaking in a multidimensional flashing particle rattchet. ACS Nano Lett. 2017. 11(7): 7148. https://doi.org/10.1021/acsnano.7b02995
20. Rozenbaum V.M., Chernova A.A. Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force. Surf. Sci. 2009. 603(22): 3297. [in Russian]. https://doi.org/10.1016/j.susc.2009.09.019
21. Romanovskiy Yu.L., Tikhonov A.N. Molecular energy transducers of the living cell. Proton ATP synthase: a rotating molecular motor. Physics-Uspekhi. 2010. 53(7): 893. [in Russian]. https://doi.org/10.3367/UFNe.0180.201009b.0931
22. Romanovskiy Yu.L., Trifonenkov V.P. Energetics and stochastic dynamics of intraneuron transport. Physics-Uspekhi. 2016. 59(2): 121. [in Russian]. https://doi.org/10.3367/UFNe.0186.201602b.0125
23. Zakharov P.N., Arzhanik V.K., Ul'yanov Ye.V., Gudimchuk N.B., Ataullakhanov F.I. Microtubule: a dynamically unstable stochastic phase switching polymer. Physics-Uspekhi. 2016. 59(8): 773. [in Russian]. https://doi.org/10.3367/UFNe.2016.04.037779
24. Astumian R.D., Bier M. Fluctuation driven ratches: Molecular motors. Phys. Rev. Lett. 1994. 72(11): 1766. https://doi.org/10.1103/PhysRevLett.72.1766
25. Van der Broeck C., Hänggi P. Activation rates for nonlinear stochastic flows driven by non-Gaussian noise. Phys. Rev. A. 1984. 30(5): 2730. https://doi.org/10.1103/PhysRevA.30.2730
26. Riskin H. The Fokker-Plank Equation. Methods of Solution and Applications. (Berlin: Springer-Verlag, 1989).
27. Rozenbaum V.M., Korochkova T.Ye., Chernova A.A., Dekhtyar M.L. Brownian motor with competing spatial and temporal asymmetry of potential energy. Phys. Rev. E. 2011. 83: 051120. https://doi.org/10.1103/PhysRevE.83.051120
28. Rozenbaum V.M. Brownian motion and surface diffusion. In: Physics and chemistry of the surface. Book 1. Physics of the surface. (Part VI, Chapter 23). (Kyiv: Chuiko Institute of Surface Chemistry of National Academy of Sciences of Ukraine, Interservis, 2015). P. 806. [in Russian].
29. Parrondo J.M.R. Reversible ratchets as Brownian particles in an adiabatically changing periodic potential. Phys. Rev. E. 1998. 57(6): 7297. https://doi.org/10.1103/PhysRevE.57.7297
30. Parrondo J.M.R., Blanco J.M., Cao F.J., Brito R. Efficiency of Brownian motors. Europhys. Lett. 1998. 43(3): 248. https://doi.org/10.1209/epl/i1998-00348-5
31. Rozenbaum V.M High-temperature Brownian motors: deterministic and stochastic fluctuations of a periodic potential. JETP Lett. 2008. 88(5): 342. [in Russian]. https://doi.org/10.1134/S0021364008170128
32. Rozenbaum V.M., Dekhtyar M.L., Lin S.H., Trakhtenberg L.I. Photoinduced diffusion molecular transport. J. Chem. Phys. 2016. 145(6): 064110. https://doi.org/10.1063/1.4960622
Downloads
How to Cite
Issue
Section
License
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
