Critical behavior of a water monolayer under hydrophobic confinement

The properties of water can have a strong dependence on the confinement. Here, we consider a water monolayer nanoconfined between hydrophobic parallel walls under conditions that prevent its crystallization. We investigate, by simulations of a many-body coarse-grained water model, how the properties of the liquid are affected by the confinement. We show, by studying the response functions and the correlation length and by performing finite-size scaling of the appropriate order parameter, that at low temperature the monolayer undergoes a liquid-liquid phase transition ending in a critical point in the universality class of the two-dimensional (2D) Ising model. Surprisingly, by reducing the linear size L of the walls, keeping the walls separation h constant, we find a 2D-3D crossover for the universality class of the liquid-liquid critical point for L/h=~50, i.e. for a monolayer thickness that is small compared to its extension. This result is drastically different from what is reported for simple liquids, where the crossover occurs for , and is consistent with experimental results and atomistic simulations. We shed light on these findings showing that they are a consequence of the strong cooperativity and the low coordination number of the hydrogen bond network that characterizes water.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

Speed of travelling fronts: Two-dimensional and ballistic dispersal probability distributions

The speed of traveling fronts for a two-dimensional model of a delayed reactiondispersal process is derived analytically and from simulations of molecular dynamics. We show that the one-dimensional (1D) and two-dimensional (2D) versions of a given kernel do not yield always the same speed. It is also shown that the speeds of time-delayed fronts may be higher than those predicted by the corresponding non-delayed models. This result is shown for systems with peaked dispersal kernels which lead to ballistic transport