Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Probing the relationships between molecular conformation and intermolecular contacts in N,N-dibenzyl-N '-(furan-2-carbonyl)thiourea

In the crystal structure of the title compound, C20H18N2O2S, molecules are linked by bifurcated C-H center dot center dot center dot O hydrogen-bond interactions, giving rise to chains whose links are composed of alternating centrosymmetrically disposed pairs of molecules and characterized by R-2(2)(10) and R-2(2)(20) hydrogen-bonding motifs. Also, N-H center dot center dot center dot S hydrogen bonds form infinite zigzag chains along the [010] direction, which exhibit the C(4) motif. Hirshfeld surface and fingerprint plots were used to explore the intermolecular interactions in the crystal structure. This analysis confirms the important role of C-H center dot center dot center dot O hydrogen bonds in the molecular conformation and in the crystal structure, providing a potentially useful tool for a full understanding of the intermolecular interactions in acylthiourea derivatives.

Size-dependent phase transitions in nanostructured zirconia-scandia solid solutions.

Size effects on phase stability and phase transitions in technologically relevant materials have received growing attention. Several works reported that metastable phases can be retained at room temperature in nanomaterials, these phases generally corresponding to the high-temperature polymorph of the same material in bulk state. Additionally, size-dependent shifts in solubility limits and/or in the transition temperatures for on heating or on cooling cycles have been observed. ZrO2-Sc2O3 (zirconia-scandia) solid solutions are known to exhibit very high oxygen ion conductivity provided their structure is composed of cubic and/or pseudocubic tetragonal phases. Unfortunately, for solid zirconia-scandia polycrystalline samples with typical micrometrical average crystal sizes, the high-conductivity cubic phase is only stable above 600°C. Depending on composition, three low-conductivity rhombo-hedral phases (β, γ and δ) are stable below 600°C down to room temperature, within the compositional range of interest for SOFCs. In previous investigations, we showed that the rhombohedral phases can be avoided in nanopowders with average crystallite size lower than 35 nm.