Biological molecular motors achieve directed motion and perform work in an environment dominated by thermal noise and in most cases incorporate thermally driven motion into the motor process. Inspired by bio-molecular motors, many other motor systems that incorporate thermal motion have been developed and studied. These motors are broadly referred to as Brownian motors. This dissertation presents simulation studies of two particular Brownian motors, the feedback-controlled flashing ratchet and an artificial molecular motor concept, the results of which not only drive experimental considerations but also illuminate physical behaviors that may be applicable to other Brownian motors.

A flashing ratchet rectifies the motion of diffusive particles using a time dependent, asymmetric potential energy landscape, and the transport speed of the ratchet can be increased if information about the particle distribution is incorporated as feedback in the time dependency of the landscape. Using a Langevin Dynamics simulation, we compare two implementations of feedback control, a discrete algorithm and a continuous algorithm, and find that the discrete algorithm is less sensitive to fluctuations in the particle distribution. We also model an experimental system with time delay and find that the continuous algorithm can be improved by adjusting the feedback criteria to react to the expected state of the system after the delay time rather than the real-time state of the system.

Motivated by the desire to understand bio-molecular linear stepping motors, we present a bottom-up approach of designing an artificial molecular motor. We develop a coarse-grained Molecular Dynamics model that is used to understand physical contributions to the diffusive stepping time of the motor and discover that partially reducing the diffusional space from 3D to 1D can dramatically increase motor speed. We also develop a stochastic model based on the classical Master equation for the system and explore the sensitivity of the motor to currently undetermined experimental parameters. We find that a reduced diffusional stepping time is critical to maintain motor attachment for many successive steps and explore an experimental design effect that leads to motor misstepping.