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Studying the transport characteristics of carriers in quantum dot (QD) film provides theory support for the structure design and performance improvement of QD film device. However, time of flight experiment can only test the global optoelectric current signal brought by the carrier transport, and cannot analyze the carrier transport in the transport layer. Here, the hopping transport model of photogenerated carriers in QD films was established to study the expansion and drift movement of carriers in the PDE module of COMSOL. According to the material properties of the actual QD films, the carrier transport in single-size QD films was studied.

The motion of molecular motor is essential to the biophysical functioning of living cells. This motion can be regarded as a multiple chemical state process. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping processes or by several coupled Fokker–Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest case in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, one can see that the mean velocity of molecular motor might be non-zero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is non-trivial energy input. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two chemical states, but also on the transition rates between them.