Diffusion-drift equation

In the case of electron transport where d> = eV + kBT In (p) is the electrochemical potential, one can derive the familiar drift-diffusion equation [11] ... 

Device Models of Bulk Heterojunction Solar Cells. 10-27 The Equivalent Circuit Model Extended One-Diode Model Electric Field-Dependent Dissociation of the Coulomb-Coupled E-H Pairs Numerical Solution to the Drift-Diffusion Equations... 

If magnetic field is equal to zero, we obtain directly from the above expression of the drift-diffusion equation for current density in a semiconductor device. 

For I and St very small, the trajectory of the walk can be represented as a continuous curve as shown in Figure 6.1b. The probability distribution given by Equation 6.20 obeys the drift-diffusion equation,... 

The probability distribution function obeys the simple drift-diffusion equation (Equations 6.25 and 6.63),... 

In the present simple model, both the translocation force arising from the free energy profile and the diffusion constant of the translocating monomer are constants. Substituting the above equations in Equation 10.21, we get the familiar drift-diffusion equation. 

It must be mentioned that the model of translocation as a ratchet is a subset of the one-dimensional drift-diffusion process (Peskin et al. 1993). In the ratchet model, every monomer being translocated gets reflected back at every site along the pore in the direction of translocation and undergoes drift-diffusion between successive sites along the pore. The final results of this model are readily derived from the same drift-diffusion equation (Equation 10.39). 

The shape of the distribution function for the translocation time given by the drift-diffusion equation (Figure 10.11b) is similar to experimentally observed histograms, as long as the multiple peaks of Figure 10.1a are deconvoluted. When the reflecting boundary condition is used at the pore entry, theory yields only one peak in the distribution function of the translocation time. On the other hand, experiments show that there are two peaks, after the first peak corresponding to faster collisions between the polymer and pore is deleted. This feature is particular to the aHL protein pore and ssDNA, and is also based on the way the data are analyzed. 

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