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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 731358, 17 pages
Research Article

A New Mechanical Model for Particle Transport by Surface Waves and Applications

1Department of Mathematical Research in Systems, Kaunas University of Technology, Studentu 50-222, 51638 Kaunas, Lithuania
2Nonlinear Dynamics, Chaos and Complex Systems Group, Department of Physics, University Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

Received 3 December 2008; Revised 17 April 2009; Accepted 2 June 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 Minvydas Ragulskis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a study of the behavior of a ball under the influence of gravity on a platform. A propagating surface wave travels on the surface of the platform while the platform remains motionless. This is a modification of the classical bouncing ball problem and describes the transport of particles by surface waves. Phase and velocity maps cannot be expressed in the explicit form due to implicit formulations, and no formal analytical analyses is possible. Numerical analysis shows that the transition to chaos is produced via a period doubling route which is a common property for classical bouncers. These numerical analysis have been carried out for the conservative and for the viscous cases and also for elastic and for inelastic collisions. The bouncing process can be sensitive to the initial conditions and can be useful for control techniques which can dramatically increase the effectiveness of particle transport in practical applications. Finally, we also consider the mechanical model of a particle sliding on a surface which is also important because it has important physical implications such as the transportation of thin films in biomedical applications, among others.