Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation.

ABSTRACT: The present work is concerned with the study of a generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of the Langevin equation depends critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation for the drift. By further demanding time reversibility of the drift, the Langevin equation can also describe equivalent quantum-mechanical systems in

SUBMITTER: Prodanov D 

PROVIDER: S-EPMC7513018 | biostudies-literature | 2018 Jun

REPOSITORIES: biostudies-literature