Abstract:
Motivated by biological transport phenomena and vehicular traffic flow we investigate the dynamics of
interacting molecular motors or interacting vehicles that move along linear filaments (tracks) and can reversibly
associate or dissociate from them. To analyze these processes, we introduced a model assimilating the
interactions in a totally asymmetric simple exclusion process coupled with nonconserving Langmuir kinetics.
The model is analyzed first using the continuum version of the simple mean-field approach that neglects the
correlations between the particles. It is shown that even for weak interactions theoretical predictions deviate
significantly from computer simulation results. To alleviate the problems, we developed a theoretical method
that takes into account some correlations in the system. The effect of interactions on stationary phase diagrams,
particle currents, and densities are explicitly evaluated. The analysis of two-point correlation function on the
lattice indicates that the correlations are stronger at the locations of localized shocks. Our theoretical calculations
are in excellent agreement with Monte Carlo computer simulations.
