The Smoluchowski diffusion equation for structured macromolecules near structured surfaces

Abstract

Beginning with the molecular-based Fokker-Planck equation obtained previously ͓M. H. Peters, J. Chem. Phys. 110, 528 ͑1999͒; J. Stat. Phys. 94, 557 ͑1999͔͒, the Smoluchowski diffusion equation is derived here to describe the spatial and orientational dynamics of molecularly structured macromolecules near molecularly structured surfaces. The formal scaling and perturbation methods employed allow the establishment of definite limits on the use of the Smoluchowski equation when surfaces are present. It is shown that the Smoluchowski equation reduces to that given previously ͓D. W. Condiff and J. S. Dahler, J. Chem. Phys. 44, 3988 ͑1966͔͒ in the absence of external surfaces. A specific example application is given involving a spherical macromolecule with electrostatic charge segments near a planar surface with an arbitrary charge distribution. Finally, we show that the short-time solution to the Smoluchowski equation obtained here yields a Brownian dynamics method consistent with that given previously ͓E. Dickinson, S. A. Allison, and J. A. McCammon, J. Chem. Soc. Faraday Trans. 2 81, 591 ͑1985͔͒ for orientable, interacting Brownian particles.This study has applications to problems involving site-specific adsorption of orientable, structured Brownian particles, such as association or adsorption of biological macromolecules to cellular surfaces and enzyme-substrate docking kinetics, to name a few.

General framework for fluctuating dynamic density functional theory

“…For this reason, the functional  r [ ]can be identified as the classical Helmholtz free-energy functional [21,22] where the first term on the right-hand side of equation (54) accounts for the ideal gas contribution and the last one is the excess over-ideal term containing the contribution due to interactions. Upon substitution of equations (50)-(56) into (49), and using equation (48), the mesoscopic fluctuating DDFT equation is finally obtained, which constitutes the main result of this work. To understand the connection between the fluctuating DDFT (57) and the fluctuating Navier-Stokes (NS) equations of Landau and Lifshitz [36], we need to discuss first the connection between local pressure and the free-energy functional.…”

Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative

“…The solutions (15) and (36) correspond to space-time generalized solutions of the DAE. Figures 5 and 6 show the case where both derivatives are considered (time-space) simultaneous; besides, it was shown that when and are less than 1, the concentration behaves like a concentration with spatial-temporal-decaying amplitude with respect to time and the space .…”

“…The sedimentation phenomena describe the response of the system to the action of an external force (usually centrifugal). The hydrodynamical problem of one particle falling through a fluid has been solved by Einstein, for Smoluchowski and many others [14,15]. A random walk is a mathematical formalization of a path that consists of a succession of random steps.…”

Langevin dynamics for rigid bodies of arbitrary shape

“…Other than the fluctuation-dissipation formulas given by Peters, [32][33][34] there are no analytic solutions for the friction tensor for rigid molecules of arbitrary shape. The ellipsoid of revolution and general triaxial ellipsoid models have been widely used to approximate the hydrodynamic properties of rigid bodies.…”