We study the electric-field-driven translocation of polymers with ring architecture, i.e. circular polymers, in comparison with their linear counterpart. We construct the free energy landscape for ring and linear polymer translocations respectively, in the context of Fokker-Planck formalism. Non-monotonicity of translocation time as function of polymer length is observed from ring polymer, which is enhanced by pore- polymer attraction. The external electric driving force and pore-polymer interaction are the tuning parameter of relative translocation time of ring and linear polymers. We study the polyelectrolyte brush in monovalent salt using self-consistent-field- theory. We confirmed the step-function polymer profile in strong-stretched state. We examine the ion distribution and assure the trapping counterions by the brush. We also study the polyelectrolyte brush in divalent salt using explicit Donnan equi- librium and free energy minimization. We calculation the brush height and degree of ionization self-consistently as function divalent salt concentration. We explained the non-monotonic behavior of brush height versus salt concentration (observed in experiment) by charge reversal.