Spatial patterns mediated by subcritical and supercritical thermal fluctuations in the splay Fréedericksz transition

The magnetically induced splay Fréedericksz transition is reexamined to look for pattern forming phenomena slightly above or below criticality. By using our traditional scheme of stochastic nematodynamic equations, situations are, respectively, found of transient and permanent predominance of transversal periodicities (wave numbers) along the direction perpendicular to the initial orientation within the sample. The relevance of these predictions in relation with recent observations in the electrically driven splay Fréedericksz transition, and in general with other pattern forming phenomena, is stressed.

Percolation and three-dimensional structure of supercritical water

It is well established that at ambient and supercooled conditions water can be described as a percolating network of H bonds. This work is aimed at identifying, by neutron diffraction experiments combined with computer simulations, a percolation line in supercritical water, where the extension of the H-bond network is in question. It is found that in real supercritical water liquidlike states are observed at or above the percolation threshold, while below this threshold gaslike water forms small, sheetlike configurations. Inspection of the three-dimensional arrangement of water molecules suggests that crossing of this percolation line is accompa- nied by a change of symmetry in the first neighboring shell of molecules from trigonal below the line to tetrahedral above.

Catalytic gasification of glycerol in supercritical water

The conversion of glycerol in supercritical water (SCW) was studied at 510-550 °C and a pressure of 350 bars using both a bed of inert and non-porous ZrO2 particles (hydrothermal experiments), and a bed of a 1% Ru/ZrO2 catalyst. Experiments were conducted with a glycerol concentration of 5 wt% in a continuous isothermal fixed-bed reactor at a residence time between 2 and 10 s. Hydrothermolysis of glycerol formed water-soluble products such as acetaldehyde, acetic acid, hydroxyacetone and acrolein, and gases like H2, CO and CO2. The catalyst enhanced the formation of acetic acid, inhibited the formation of acrolein, and promoted gasification of the glycerol decomposition products. Hydrogen and carbon oxides were the main gases produced in the catalytic experiments, with minor amounts of methane and ethylene. Complete glycerol conversion was achieved at a residence time of 8.5 s at 510 °C, and at around 5 s at 550 °C with the 1 wt% Ru/ZrO2 catalyst. The catalyst was not active enough to achieve complete gasification since high yields of primary products like acetic acid and acetaldehyde were still present. Carbon balances were between 80 and 60% in the catalytic experiments, decreasing continuously as the residence time was increased. This was attributed partially to the formation of methanol and acetaldehyde, which were not recovered and analyzed efficiently in our set-up, but also to the formation of carbon deposits. Carbon deposition was not observed on the catalyst particles but on the surface of the inert zirconia particles, especially at high residence time. This was related to the higher concentration of acetic acid and other acidic species in the catalytic experiments, which may polymerize to form tar-like carbon precursors. Because of carbon deposition, hydrogen yields were significantly lower than expected; for instance at 550 °C the hydrogen yield potential was only 50% of the stoichiometric value.

The role of fixed delays in neuronal rate models

Fixed delays in neuronal interactions arise through synaptic and dendritic processing. Previous work has shown that such delays, which play an important role in shaping the dynamics of networks of large numbers of spiking neurons with continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay. Here we extend this work to account for arbitrary symmetric patterns of synaptic connectivity and generic nonlinear transfer functions. Specifically, we conduct a weakly nonlinear analysis of the dynamical states arising via primary instabilities of the stationary uniform state. In this way we determine analytically how the nature and stability of these states depend on the choice of transfer function and connectivity. While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance. These are: 1 - fast oscillations are always supercritical for realistic transfer functions. 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.

Bifurcations and chaos in single-roll natural convection with low Prandtl number

Convective flows of a small Prandtl number fluid contained in a two-dimensional cavity subject to a lateral thermal gradient are numerically studied by using different techniques. The aspect ratio (length to height) is kept at around 2. This value is found optimal to make the flow most unstable while keeping the basic single-roll structure. Two cases of thermal boundary conditions on the horizontal plates are considered: perfectly conducting and adiabatic. For increasing Rayleigh numbers we find a transition from steady flow to periodic oscillations through a supercritical Hopf bifurcation that maintains the centrosymmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation the system initiates a complex scenario of bifurcations. In the conductive case these include a quasiperiodic route to chaos. In the adiabatic one the dynamics is dominated by the interaction of two Neimark-Sacker bifurcations of the basic periodic solutions, leading to the stable coexistence of three incommensurate frequencies, and finally to chaos. In all cases, the complex time-dependent behavior does not break the basic, single-roll structure.

Self-organized criticality induced by diversity

We have studied the collective behavior of a population of integrate-and-fire oscillators. We show that diversity, introduced in terms of a random distribution of natural periods, is the mechanism that permits one to observe self-organized criticality (SOC) in the long time regime. As diversity increases the system undergoes several transitions from a supercritical regime to a subcritical one, crossing the SOC region. Although there are resemblances with percolation, we give proofs that criticality takes place for a wide range of values of the control parameter instead of a single value.