A colored-noise approach to Brownian motion in position space. Corrections to the Smoluchowski equation

Statistical properties of nanosized clusters on a surface in overdamped stochastic reaction-Cattaneo systems

“…However, under certain conditions one can make a transition to overdamped stochastic limit and consider dynamics of the corresponding stochastic system (see, for example, discussions in Refs. [40][41][42][43]). …”

Fluctuating hydrodynamics for a rarefied gas based on extended thermodynamics

“…In comparison with the conserved quantities (mass, momentum and energy), the rapidly changing modes usually have much smaller relaxation times, and decay quickly. Therefore the elimination can be done by retaining one or a few terms in the expansion of the general solution with respect to the characteristic times of the rapidly changing modes, λ −1 1 and λ −1 2 [29][30][31]. More explicitly, we apply to (23) the following kind of approximation obtained by successive integrations by parts and by neglecting transient terms:…”

Response to “Comment on ‘Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker–Planck equation’ ” [J. Chem. Phys. 132, 017103 (2010)]

“…͑1͒ of the Comment 7 ͔, which was also obtained through a different method by San Miguel and Sancho in a paper 11 which cites the article by Chaturvedi and Shibata. 6 But, in spite of the fact that, at first sight, our general Eq.…”

“…͑1͒ ͑as well as Eq. ͑4͒͒ can be employed as a first useful test of the reliability of the corrections to the Smoluchowski equation which were found in the past [3][4][5]11,12 for particles subject to positiondependent forces. An example of the discussion on this point is given in Paper I.…”