Equilibrium route to colloidal gellation: mixtures of hard sphere-like colloids

The binodals and the non-ergodicity lines of a binary mixture of hard sphere-like particles with large size ratio are computed for studying the interplay between dynamic arrest and phase separation in depletion-driven colloidal mixtures. Contrarily to the case of hard core plus short range effective attraction, physical gellation without competition with the fluid-phase separation can occur in such mixtures. This behavior due to the oscillations in the depletion potential should concern all simple mixtures with non-ideal depletant, justifying further studies of their dynamic properties

Synchronization hypothesis in the Winfree model

We consider $N$ oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength $\kappa$ and the spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled regime, $\kappa=0$, each oscillator possesses its own natural frequency, and the difference between the phases of any two oscillators grows linearly in time. We say that $N$ oscillators are synchronized if the difference between any two phases is uniformly bounded in time. We identify a new hypothesis for the existence of synchronization. The domain in $(\gamma,\kappa)$ of synchronization contains coupling values that are both weak and strong. Moreover the domain is independent of the number of oscillators and the distribution of the frequencies. We give a numerical counter-example which shows that this hypothesis is necessary for the existence of synchronization