Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical approaches to these exponents so far can be divided into two groups, macroscopically oriented approaches, using kinetic theory or hydrodynamics, and more microscopically oriented random-matrix approaches in quasi-one-dimensional systems. In this paper, I present an approach using random matrices and weak disorder expansion in an arbitrary number of dimensions. Correlations between subsequent collisions of a particle are taken into account. It is shown that the results are identical to those of a previous approach based on an extended Enskog-equation. I conclude that each approach has its merits, and provides different insights into the approximations made, which include the Sto{\ss}zahlansatz, the continuum limit, and the long-wavelength approximation. The comparison also gives insight into possible connections between Lyapunov exponents and fluctuations

Stability of low-friction surface sliding of nanocrystals with rectangular symmetry and application to W on NaF(001)

We investigate the stability of low-friction sliding of nanocrystal with rectangular atomic arrangement on rectangular lattices, for which analytical results can be obtained. We find that several incommensurate periodic orbits exist and are stable against thermal fluctuations and other perturbations. As incommensurate orientations lead to low corrugation, and therefore low friction, such incommensurate periodic orbits are interesting for the study of nanotribology. The analytical results compare very well with simulations of W nanocrystals on NaF(001). The geometry and high typical corrugation of substrates with square lattices increase the robustness compared to typical hexagonal lattices, such as graphite

Understanding and Controlling Regime Switching in Molecular Diffusion

Diffusion can be strongly affected by ballistic flights (long jumps) as well as long-lived sticking trajectories (long sticks). Using statistical inference techniques in the spirit of Granger causality, we investigate the appearance of long jumps and sticks in molecular-dynamics simulations of diffusion in a prototype system, a benzene molecule on a graphite substrate. We find that specific fluctuations in certain, but not all, internal degrees of freedom of the molecule can be linked to either long jumps or sticks. Furthermore, by changing the prevalence of these predictors with an outside influence, the diffusion of the molecule can be controlled. The approach presented in this proof of concept study is very generic, and can be applied to larger and more complex molecules. Additionally, the predictor variables can be chosen in a general way so as to be accessible in experiments, making the method feasible for control of diffusion in applications. Our results also demonstrate that data-mining techniques can be used to investigate the phase-space structure of high-dimensional nonlinear dynamical systems.Comment: accepted for publication by PR

A criterion for condensation in kinetically constrained one-dimensional transport models

We study condensation in one-dimensional transport models with a kinetic constraint. The kinetic constraint results in clustering of immobile vehicles; these clusters can grow to macroscopic condensates, indicating the onset of dynamic phase separation between free flowing and arrested traffic. We investigate analytically the conditions under which this occurs, and derive a necessary and sufficient criterion for phase separation. This criterion is applied to the well-known Nagel-Schreckenberg model of traffic flow to analytically investigate the existence of dynamic condensates. We find that true condensates occur only when acceleration out of jammed traffic happens in a single time step, in the limit of strong overbraking. Our predictions are further verified with simulation results on the growth of arrested clusters. These results provide analytic understanding of dynamic arrest and dynamic phase separation in one-dimensional traffic and transport models

Emergent friction in two-dimensional Frenkel-Kontorova models

Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature-dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.Comment: 14 pages, 13 figure

Nano-apatite/polymer composites: mechanical and physicochemical characteristics

Hydrothermally synthesized acicular nano-apatite (Nap) was used as filler to make composites with a polyethylene glycol/poly(butylene terephthalate) (PEG/PBT) block copolymer (Polyactive™70:30). The Nap had a particle diameter of 9–25 nm and a length of 80–200 nm. The mechanical properties and the physiochemical characteristics of the composites, such as Young's modulus, swelling degree in water and the calcification behaviour, have been determined. It was found that Nap had a strong ability to promote the calcification of composites when incorporated into Polyactive 70:30, while poly(acrylic acid) (PAA) coating of Nap had an adverse effect on the calcification of composites, presumably due to the formation of complexes between PAA and PEG segments. Nap had a prominent stiffening effect for Polyactive 70:30 in the dry state, but had a poor stiffening effect for composites in an aqueous environment due to the hygroscopic nature and/or the formation of aggregates. PAA coating on Nap had almost no additional effect on the mechanical properties of composites either in the dry state or in an aqueous environment. To reinforce the polymer by Nap, achieving a more homogeneous dispersion of Nap in the polymer matrix and surface modifications to render the powders less hygroscopic appear to be necessary