The geometric stochastic resonance and rectification of active particles

This thesis describes the work of three research projects, the background research that motivated the work, and the resultant project findings. The three projects concerned: (i) Geometric stochastic resonance in a double cavity, (ii) Synchronisation of geometric stochastic resonance by a bi-harmonic drive, and (iii) Rectification of Brownian particles with oscillating radii in asymmetric corrugated channels. In the project 'Geometric stochastic resonance in a double cavity', we investigated synchronisation processes for the geometric stochastic resonance of particles diffusing across a porous membrane and subject to a periodic driving force. Non-interacting particle currents were driven through a symmetric membrane pore either parallel or perpendicular to the membrane. Then, harmonic mixing spectral current components were generated by the combined action of parallel and perpendicular drives. The role of the repulsive interaction of particles as a controlling factor with potential applications to the transport of colloids and biological molecules through narrow pores was also investigated. In 'Synchronisation of geometric stochastic resonance by a bi-harmonic drive', we simulated the stochastic dynamics of an elliptical particle using the Langevin equation. The particle was simultaneously driven by low and high frequency harmonic drives across a porous inter-cavity membrane. It was observed that the particle oscillated out of phase with the low frequency drive. This effect was due to the absolute negative mobility the particle would have exhibited if the low frequency drive had been replaced by a dc static force. It was also observed that the magnitude of this out-of-phase stochastic resonance depends on how the combined action of the driving forces and noise fluctuations affect the particle orientation, and as such was shown to be sensitive to the particle shape. This emphasises the importance of particle geometry, in addition to chamber geometry, to the realisation and optimisation of geometric stochastic resonance. In the project 'Rectification of Brownian particles with oscillating radii in asymmetric corrugated channels', we simulated the transport of a Brownian particle with an oscillating radius freely diffusing in an asymmetric corrugated channel over a range of driving forces for a series of temperatures and angular frequencies of radial oscillation. It was observed that there was a strong influence of self-oscillation frequency upon the average particle velocity. This effect can be used to control rectification of biologically active particles as well as for their separation according to their activity, for instance in the separation of living and dead cells. The background research is described in Chapter One and the research findings are described along with their related projects in Chapters Two and Three.