Ard Louis

Abstract:

The crossover from single-file diffusion, where the mean-square displacement scales as (x2) to approximately t(1/2), to normal Fickian diffusion, where (x2) to approximately t, is studied as a function of channel width for colloidal particles. By comparing Brownian dynamics to a hybrid molecular dynamics and mesoscopic simulation technique, we can study the effect of hydrodynamic interactions on the single file mobility and on the crossover to Fickian diffusion for wider channel widths. For disc-like particles with a steep interparticle repulsion, the single file mobilities for different particle densities are well described by the exactly solvable hard-rod model. This holds both for simulations that include hydrodynamics, as well as for those that do not. When the single file constraint is lifted, then for particles of diameter sigma and pipe of width L such that (L - 2sigma)/sigma = deltac << 1, the particles can be described as hopping past one-another in an average time t(hop). For shorter times t << t(hop) the particles still exhibit sub-diffusive behaviour, but at longer times t >> t(hop), normal Fickian diffusion sets in with an effective diffusion constant Dhop to approximately 1/ mean square root of t(hop). For the Brownian particles, t(hop) to approximately deltac(-2) when deltac << 1, but when hydrodynamic interactions are included, we find a stronger dependence than deltac(-2). We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels.

Abstract:

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type of physical system. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favoured in biological self-assembly, for example of protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful distance measure between physical structures.