Hydrodynamic interactions in self similar structures, such as polymers

Abstract

We study the hydrodynamic properties of polymers and more generally self-similar structures using a new recursion model. The hydrodynamic interaction between monomers is modeled by the standard Green's function of Stokes flow in which an ultrametric distance is substituted for the usual Euclidean distance. This leads to a model where the long-range hydrodynamic interactions and the long-range correlations of the polymer conformation can both be accounted for and yet allow for analytical solutions. We explore the asymptotic as well as the finite size corrections to the scaling behavior with this model. In order to compare the results of the present scheme with more conventional techniques a generalized version of the existing mean field results by Kirkwood and Riseman for the hydrodynamic drag is introduced.PACS. 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling -47.11.+j Computational methods in fluid dynamics 36.20.-r Macromolecules and polymer molecules

Translation Drag Coefficient of a Self-Similar Assembly of Spheres Immersed in an Incompressible Fluid

“…a and finite screening for D , a. A similar conclusion has been drawn by using the idea of ultrametric distance [18].…”

“…1 have been theoretically studied by the generalized Kirkwood-Riseman preaveraging approach (KR) and the recursion model (RM) [18]. The former approach replaces the interaction tensor in Eq.…”

Attractive asymmetric inclusions in elastic membranes under tension: cluster phases and membrane invaginations

“…Having in mind the elucidation of the physical laws governing assemblies of proteins embedded in lipidic biomembranes [1], the statistical mechanics of membrane inclusions has been the focus of active and plethoric research in the two past decades . Several complementary theoretical and numerical developments have been proposed to study these soft matter systems, among which mechanical approaches in the zero-temperature limit [3,6,11,14], field-theorectical studies taking explicitly membrane fluctuations into account [3,9,13,23], Molecular Dynamics [16,18,21,27] or mesoscopic-scale Monte Carlo simulations [13,17,24]. However, at this stage, no consensual view of the dynamical membrane organization exists that is fully recognized by both biologists and physicists.…”

“…The present works adopts a field-theoretical formulation [3,9,13,23] because it efficiently and elegantly provides exact results without requiring too tedious calculations. It is pseudo-analytical: after integrating Gaussian functional integrals, free-energies can be expressed in terms of inverses and determinants of large matrices.…”

Saffman-Delbrück and beyond: A pointlike approach

“…However, since the particle's radius appears within a logarithm in the SD law, it turns out to be excellent. Pointlike ap-proximations are standard in soft matter to calculate interactions among particles [7][8][9][10][11] and dynamical behaviors such as mobility and diffusion [12][13][14][15][16][17]. Either sharp cutoffs are used, with excellent approximate results [8][9][10][11]13], or smooth cutoffs in numerical works that have the effect of distributing the applied forces over small finite regions [12,[14][15][16][17].…”