Mean curvature flow in an extended Ricci flow background

In this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background. One of them is a weighted extended version of the Gibbons-Hawking-York action on Riemannian metrics in compact manifolds with boundary. We compute its variational properties from which naturally arise boundary conditions to the analysis of its time-derivative under Perelman's modified extended Ricci flow. For instance, the boundary integrand term provides an extension of Hamilton's differential Harnack expression for mean curvature flows in Euclidean space. We also derive the evolution equations for both the second fundamental form and the mean curvature under mean curvature flow in an extended Ricci flow background. In the special case of gradient solitons to the extended Ricci flow, we discuss mean curvature solitons and establish a Huisken's monotonicity-type formula. We show how to construct a family of mean curvature solitons and establish a characterization of such a family. Also, we show how for constructing examples of mean curvature solitons in an extended Ricci flow background.Comment: 24 pages. Suggestions and comments are welcom

Synthesis and characterization of analogues of glycine-betaine ionic liquids and their use in the formation of aqueous biphasic systems

A series of novel analogues of glycine-betaine ionic liquids (AGB-ILs), viz. 1-(4-ethoxy-4-oxobutyl)-1-methylpyrrolidin-1-ium, N,N,N-tri(n-butyl)(4-ethoxy-4-oxobutyl)-1-phosphonium and N,N,N-trialkyl(4-ethoxy-4-oxobutyl)-1-aminium cations with ethyl, n-propyl and n-butyl alkyl chains, combined with the bromide anion, have been synthesized and characterized. Their synthesis and characterization by spectroscopic methods and elemental analysis is here reported. These ILs were further characterized in what concerns their thermal properties and ecotoxicity against Allvibrio fischeri, and compared with the commercial tetra(n-butyl)ammonium and tetra(n-butyl)phosphonium bromide. The novel AGB-ILs described in this work have low melting points, below 100 °C, display high degradation temperatures (180–310 °C), and low toxicity as shown by being harmless or practically harmless towards the marine bacteria Allvibrio fischeri. Finally, the ability of the synthesized AGB-ILs to form aqueous biphasic systems with potassium citrate/citric acid (at pH 7) was evaluated, and the respective ternary phase diagrams were determined. It is shown that the increase of the cation alkyl chain length facilitates the creation of ABS, and that phosphonium-based ILs present a slightly better separation performance in presence of aqueous solutions of the citrate-based salt.publishe

Raman evidence for pressure-induced formation of diamondene.

Despite the advanced stage of diamond thin-film technology, with applications ranging from superconductivity to biosensing, the realization of a stable and atomically thick two-dimensional diamond material, named here as diamondene, is still forthcoming. Adding to the outstanding properties of its bulk and thin-film counterparts, diamondene is predicted to be a ferromagnetic semiconductor with spin polarized bands. Here, we provide spectroscopic evidence for the formation of diamondene by performing Raman spectroscopy of double-layer graphene under high pressure. The results are explained in terms of a breakdown in the Kohn anomaly associated with the finite size of the remaining graphene sites surrounded by the diamondene matrix. Ab initio calculations and molecular dynamics simulations are employed to clarify the mechanism of diamondene formation, which requires two or more layers of graphene subjected to high pressures in the presence of specific chemical groups such as hydroxyl groups or hydrogens