Hydrodynamic interactions effects on the dipole-induced self-assembly of $\beta$-peptides and Brownian-induced polymer pore translocation

A novel method that scales linearly with the number of particles is used to study Brownian-systems considering fluctuating hydrodynamic interactions. The method is demostrated in the concept of two applications: the dipole-induced self-assembly of $\beta$-peptides and the Brownian-motion-induced translocation of a polymer thought a rectangular pore. The method includes the long-range interactions by the Green's function formalism. It allows the consideration of peptides at intermediate concentrations and the inclusion of the non-periodic domain of the translocation. The hydrodynamics interactions affect the dynamics of the peptides agglomeration and the mean-squared-displacement indicates significant changes in the long-time diffusion coefficient. The polymer translocation is study using a transition path sampling based methodology. In particular it is used to calculate the translocation rate constant. Even for a single bead there are differences once hydrodynamics are included. These differences are due to the changes of mobility near walls and the change in polymer chain diffusion coefficient.