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Article

Dynamical Response of Particles in Asymmetric Ratchet Potential

by
Usman A. Marte
1,*,
Uchechukwu E. Vincent
2,3,*,†,
Abdulahi N. Njah
4,5,† and
Biodun S. Badmus
4,†
1
Department of Mathematics and Statistics, University of Maiduguri, P.M.B. 1069 Maiduguri, Nigeria
2
Department of Physics, Lancaster University of Lancaster, Lancaster LA1 4YB, UK
3
Department of Physical Sciences, Redeemer's University, P.M.B. 3005 Redemption City, Nigeria
4
Department of Physics, Federal University of Agriculture, P.M.B. 2240 Abeokuta, Nigeria
5
Department of Physics, University of Lagos, P.M.B. 56 Akoka-Yaba, Lagos, Nigeria
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2014, 6(4), 896-908; https://doi.org/10.3390/sym6040896
Submission received: 28 July 2014 / Revised: 23 September 2014 / Accepted: 15 October 2014 / Published: 27 October 2014
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Abstract

The dynamics and response of particles in an asymmetric potential of the ratchet type is considered. An approximate asymmetric ratchet potential, which allows us to apply an analytical approach to investigate the systems’ response, is proposed based on the power series interpolation scheme. The method of multiple scales (MMS) is then employed to obtain an approximate solution at the principal resonance. Comparison between results obtained from the approximated and exact potentials show excellent agreement. The frequency response curves (FRCs) for different forcing are presented. The numerically computed FRCs were compared with the theoretical result to show the extent of agreement. Furthermore, by using perturbation methods, the stable and unstable domains of the solution were obtained.
Keywords: ratchets; asymmetry potential; resonance; multiple time scale; chaos ratchets; asymmetry potential; resonance; multiple time scale; chaos
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MDPI and ACS Style

Marte, U.A.; Vincent, U.E.; Njah, A.N.; Badmus, B.S. Dynamical Response of Particles in Asymmetric Ratchet Potential. Symmetry 2014, 6, 896-908. https://doi.org/10.3390/sym6040896

AMA Style

Marte UA, Vincent UE, Njah AN, Badmus BS. Dynamical Response of Particles in Asymmetric Ratchet Potential. Symmetry. 2014; 6(4):896-908. https://doi.org/10.3390/sym6040896

Chicago/Turabian Style

Marte, Usman A., Uchechukwu E. Vincent, Abdulahi N. Njah, and Biodun S. Badmus. 2014. "Dynamical Response of Particles in Asymmetric Ratchet Potential" Symmetry 6, no. 4: 896-908. https://doi.org/10.3390/sym6040896

APA Style

Marte, U. A., Vincent, U. E., Njah, A. N., & Badmus, B. S. (2014). Dynamical Response of Particles in Asymmetric Ratchet Potential. Symmetry, 6(4), 896-908. https://doi.org/10.3390/sym6040896

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