Some New Features of Linear Theory for Describing Non-linear Diffusion

摘要: The non-linear flux equation, the Fokker–Planck equation (or Smoluchowski equation), and Langiven are basic equations for describing particle diffusion in non-ideal system subjected to time-dependent external fields. Nevertheless, exact solution of those is still a challenge because their inherent complexity mathematics. Li et al. found that, based on defined apparent variables, nonlinear could be transformed linear forms under condition strong friction limit or local equilibrium assumption. In this paper, some new features theory were found: (i) can obtained from irreversible thermodynamic theory; (ii) non-steady state state, which was described by derived more consistently microscopic molecular statistical (iii) theory, also bears form; (iv) For special cases, e.g. periodic total potential system, assumption not required establishing diffusion, so may important study Brown motor.