arXiv subjects

C. P. Lowe

Publications and source records attributed to C. P. Lowe.

3 recordsLinked to original sources

arXiv2008

Simplicity and scaling - size of a real polymer in three (or any) dimensions

We examine the scaling of the linear dimension of the system size of a real polymer solution at constant excess free energy and in two different spacial dimensionalities, d=d0 and d=d1. Standard results for the functional form of the excess free energy lead to the conclusion that the scaling exponent nu(d) satisfies nu(d0) - nu(d1) = 1/d0 - 1/d1. Taking the critical dimensionality as a point of reference (nu(4)=1/2) gives a scaling exponent nu(d) = 1/4 +1/d, in agreement with the accepted result for two-dimensions (nu(2) = 3/4) and the first term in the epsilon (d-4) expansion. For the unsolved case of three dimensions it predicts nu(3)=7/12. Several simplifying features of this result are pointed out.

cond-mat.soft↗

arXiv2005

Hydrodynamic induced deformation and orientation of a microscopic elastic filament

We describe simulations of a microscopic elastic filament immersed in a fluid and subject to a uniform external force. Our method accounts for the hydrodynamic coupling between the flow generated by the filament and the friction force it experiences. While models that neglect this coupling predict a drift in a straight configuration, our findings are very different. Notably, a force with a component perpendicular to the filament axis induces bending and perpendicular alignment. Moreover, with increasing force we observe four shape regimes, ranging from slight distortion to a state of tumbling motion that lacks a steady state. We also identify the appearance of marginally stable structures. Both the instability of these shapes and the observed alignment can be explained by the combined action of induced bending and non-local hydrodynamic interactions. Most of these effects should be experimentally relevant for stiff micro-filaments, such as microtubules.

cond-mat.soft↗

arXiv2002

A simulation study of the dynamics of a driven filament in an Aristotelian fluid

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more realistic case of large amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For realistic amplitudes we show that the one armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one armed swimmers in nature?

physics.bio-ph↗