Dynamics of generic 2-dimensional linear differential systems

We prove that for a C⁰-generic (a dense Gδ) subset of all the 2-dimensional conservative nonautonomous linear differential systems, either Lyapunov exponents are zero or there is a dominated splitting μ almost every point.     

Automated measurement of ultrasound velocity and attenuation

A fully-automated system has been developed to measure changes in ultrasonic velocity and the attenuation coefficient resulting from changes in temperature and magnetic field. Accuracy and sensitivity comparable to the pulse-echo overlap technique have been achieved together with an increase in temperature resolution and sample throughput as a result of the automation. All components of the instrumentation are commercially available.     

Macromolecular Crowding and the Sizes of Neutral Flexible Polymer Chains: The Role of Colloids Sizes and Concentrations

In the present work, we revisit the effect of macromolecular crowding on the sizes of flexible neutral polymer chains. Motivated by recent experimental measurements on crowding effects on neutral flexible polymers chains, we perform Monte Carlo simulations on a model system consisting of hard spheres (HS) and a neutral flexible polymer chain. We find that, depending on the ratio of the sizes of the colloidal particles to the sizes of the polymer chain, and thus, on the extent of the colloid partitioning among the chain segments and the solution, the flexible polymeric coil may be either continuously compressed, or initially compressed followed by a reswelling at high enough colloid concentration. The chain behavior is thus nonmonotonic, a point which, apart from the work of Khalatur et al., has not so far been stressed in simulations of flexible polymer chains under crowding conditions. A thermodynamic model for the polymer–colloid interactions based on the Gibbs–Duhem equation and on a “Flory‐type” argument is also presented, emphasizing the indirect influence of macromolecular crowding on the monomers chemical potential. We show explicitly that under crowding conditions, the colloids are driven into the most compact coil states. These analytical results are compared with the results of the potential of mean force between the chain center of mass and the colloids obtained from the Monte Carlo simulations, and a reasonable agreement is found. The implications of the aforementioned results are further discussed in the context of biological systems, specially those for which macromolecular crowding is supposed to play the important role of including preferentially other (charged) macromolecules into the colloid‐compressed polymer phase.