Directed transport without net bias in physics and biology

Ratchets allow for directed transport without net bias. In this context, 'no net bias' means that net potential gradients on the system or non-zero initial velocities are not necessary to achieve a long-term non-zero average velocity. One type of a ratchet is the rocking ratchet, where a particle is subject to a periodic but asymmetric spatial potential, such as a sawtooth. If the particle is in addition subject to an alternating time-dependent force of zero mean, the average velocity of the particle is generally non-zero. Neither the potential nor the force would generate transport by themselves, but provided that the appropriate symmetries of the system are broken directed transport does occur. Ratchets have been implemented in a variety of physical systems, and are promising candidates for nanotechnological transport. Optimisation of ratchets has generally focused on variation of a single parameter of the ratchet. This thesis first considers the optimisation of the average velocity of the particle in a rocking ratchet with respect to the functional form of the rocking force. Specifically, an adiabatic, overdamped rocking ratchet is considered. It is proved that the optimal rocking force is dichotomous, that is, takes only two values. A ratchet approach, it is proposed, can produce directed transport of cold atoms in atom wires, the emerging field of trapping and manipulating cold atoms with magnetic fields. The directed transport is predicted by symmetry analysis and demonstrated by direct numerical simulation. The resulting 'magnetic micropump', unlike other transport methods, requires only minor modification of the basic atom wire configuration. Molecular motors also generate directed transport without net bias. The processive molecular motors, of which myosin-V and kinesin are the most well known, 'walk' along the cytoskeleton, the internal skeleton of the cell. Both myosin-V and kinesin are known to walk in a 'hand over hand' manner, fuelled by ATP, adenosine triphosphate. Unresolved questions about their walking mechanisms generally concern short temporal or spatial scales, for example the existence of substeps or short-lived intermediate states. Molecular motors can be tracked by modern single molecule assays. The improving spatial and temporal resolution of these assays permits more precise analysis and characterisation of motor behaviour than was previously possible. This thesis extends a method of stochastic time series analysis, that of the Kramers-Moyal coefficients, to take into account finite sampling interval and geometric projection effects. Its utility is demonstrated by analysing time series generated by simple models of molecular motors. Many single-molecule motor assays rely on a bead attached to the motor, which in turn interacts with an optical force, to both control and monitor the motion of the motor. The bead, however, is often much larger than the motor itself. This can render difficult the observation of small-scale motor dynamical features. Performance measures of a bead assay are quantified, and their dependence on experimental parameters explored, to aid the design of future bead assays. The analysis is undertaken with two numerical models and by comparison against experimental data for the molecular motor myosin-V. The models are compared and validated against each other and against this experimental data with their Kramers-Moyal coefficients. Unexpectedly, this reveals evidence for previously unobserved substates within the motor waiting periods