by Johannes Paul Blaschke
English
Asymmetric test particles can rectify thermal fluctuations of impinging particles, if the test particles are not in equilibrium with their environment. Due to this rectification, these test particles are called Brownian motors. One means of maintaining the Brownian motor out of equilibrium, is to introduce dissipation between impinging particles and Brownian motor.
So far, only Gaussian velocity distributions for the impinging particles have been considered. However, In order to maintain a steady state in the presence of dissipation, the impinging particles must have some sort of driving in order to replenish the energy that has been lost in collisions. This driving effects the velocity distribution of the impinging particles. In this dissertation, we address the question: how do non-Gaussian velocity distributions affect the motion of the Brownian motor?
By considering an anisotropic velocity distribution for the impinging particles, we where able to identify a dimensionless parameter which identifies whether the anisotropy has an effect on the motor drift. In the regime where the anisotropy dominates the drift, a dramatic violation of equipartition has been observed.
When the impinging particles all have the same speed but random orientation, we found that the direction in which the motor drifts is a function of motor mass. We where able to identify a breakdown of ergodicity for motors which are lighter than the impinging particles.
In both cases, we found that the motor drift velocity approaches a constant value, independent of motor mass, in the limit of a massive motor. We have also found that rectification occurs even when there is no dissipation, we therefore argue that an entropy current, instead of an energy current, sustains motor drift.
Keywords: Statistical Physics, Directed Motion, Drift, Non-Equilibrium, Equipartition, Brownian Motors, Thermodynamics, Non-Maxwellian Thermostat, Kramers-Moyal Expansion, Moment Expansion, Fokker-Planck Equation, Markovian Dynamics, Monte Carlo Methods, Slice Sampling, Jump Moments, Ergodicity, Swimmers, Dry Granular Gas, Shaking, Anisotropy, Granular Ratchet
Persistent Address:
http://dx.doi.org/10.53846/goediss-4403
