Volume-preserving mean curvature flow of revolution hypersurfaces in a Rotationally Symmetric Space

In an ambient space with rotational symmetry around an axis (which include the Hyperbolic and Euclidean spaces), we study the evolution under the volume-preserving mean curvature flow of a revolution hypersurface M generated by a graph over the axis of revolution and with boundary in two totally geodesic hypersurfaces (tgh for short). Requiring that, for each time t ≥ 0, the evolving hypersurface M _t meets such tgh orthogonally, we prove that: (a) the flow exists while M _t does not touch the axis of rotation; (b) throughout the time interval of existence, (b1) the generating curve of M _t remains a graph, and (b2) the averaged mean curvature is double side bounded by positive constants; (c) the singularity set (if non-empty) is finite and lies on the axis; (d) under a suitable hypothesis relating the enclosed volume to the n-volume of M, we achieve long time existence and convergence to a revolution hypersurface of constant mean curvature.     

Competitive binding of cadmium by plant thiols: an electrochemical study assisted by multivariate curve resolution

Multivariate curve resolution with alternating least squares (MCR-ALS) has been applied to voltammetric data obtained from analysis of the competitive binding of cysteine (Cys) and cysteine–glycine (Cys-Gly) by Cd(II) as a first approach towards mixtures of phytochelatins and related compounds in natural media. From different starting points, the possibilities of formation of mixed complexes and/or displacements between ligands are investigated. Analysis of the resulting unitary voltammograms and concentration profiles of the resolved components by MCR-ALS suggests that the strongest ligand (Cys-Gly) is able to displace the weakest (Cys) from its metal complexes, whereas this does not happen in the opposite direction. On the other hand, no evidence of Cd mixed-ligand complexes was found. Figure Differential pulse polarograms measured in the independent titrations of 1 × 10^-5 mol L^-1 Cys, 1 × 10^-5 mol L^-1 Cys-Gly, and a mixture of Cys-Gly (0.5 × 10^-5 mol L^-1) and Cys (1 × 10^-5 mol L^-1) with Cd²⁺, at TRIS-HNO₃ buffer (0.1 mol L^-1 and PH 7.5) in the presence of 0.1 mol L^-1 KNO₃     

Volume preserving mean curvature flow of revolution hypersurfaces between two equidistants

In a rotationally symmetric space ${{\overline M}}$ around an axis ${\mathcal{A}}$ (whose precise definition is satisfied by all real space forms), we consider a domain G limited by two equidistant hypersurfaces orthogonal to ${\mathcal{A}}$ . Let ${M \subset {\overline M}}$ be a revolution hypersurface generated by a graph over ${\mathcal{A}}$ , with boundary in ?G and orthogonal to it. We study the evolution M _t of M under the volume-preserving mean curvature flow requiring that the boundary of M _t rests on ?G and stays orthogonal to it. We prove that: (a) the generating curve of M _t remains a graph; (b) the flow exists as long as M _t does not touch the rotation axis; (c) under a suitable hypothesis relating the enclosed volume and the area of M, the flow is defined for every ${t\in [0,\infty[}$ and a sequence of hypersurfaces ${M_{t_n}}$ converges to a revolution hypersurface of constant mean curvature. Some key points are: (i) the results are true even for ambient spaces with positive curvature, (ii) the averaged mean curvature does not need to be positive and (iii) for the proof it is necessary to carry out a detailed study of the boundary conditions.     

Model analysis of the world data on the pion transition form factor

The evolution of neck for the asymmetric system ⁵⁸Fe + ²⁴⁴Pu at E _c.m. = 260 MeV has been studied with the coupled Langevin equations in two-dimensional collective space and the results compared to those obtained with a one-dimensional approach under the frozen assumption. It is found that the coupling between the radial and neck degrees of freedom reduces the drift velocity of neck growth and delays the transition from dinucleus to mononucleus. Besides, the coupling brings the system into a somehow elongated shape when the injection into the asymmetric fission valley takes place, hence, the fusion probability and the relevant evaporation residue (ER) cross-sections decrease. For the system ⁵⁸Fe + ²⁴⁴Pu , the ER cross-sections decrease by about 30% as compared to those obtained under the frozen approximation. Therefore, we may arrive at the conclusion that for the heavy asymmetric systems such as ⁵⁸Fe + ²⁴⁴Pu the coupling between different degrees of freedom has important effects on the evolution from dinucleus to mononucleus and the frozen approximation is basically not satisfied as far as the neck dynamics is concerned. However, as compared to the symmetric reactions, the influence of the neck dynamics on the fusion hindrance factor of heavy systems is much weaker for the asymmetric reactions.     

Photochemistry of Thymine in Protic Polar Nanomeric Droplets Using Electrostatic Embeding TD-DFT/MM

Thymine photochemistry is important for understanding DNA photodamage. In the gas phase, thymine undergoes a fast non-radiative decay from S 2 to S 1 . In the S 1 state, it gets trapped for several picoseconds until returning to the ground-state S 0 . Here, we explore the electrostatic effects of nanomeric droplets of methanol and water on the excited states of thymine. For this purpose, we develop and implement an electrostatic embedding TD-DFT/MM method based on a QM/MM coupling defined through electrostatic potential fitting charges. We show that both in methanol and water, the mechanism is similar to the gas phase. The solvent molecules participate in defining the branching plane of S 0 /S 1 intersection and have a negligible effect on the S 1 /S 2 intersection. Despite the wrong topology of the ground/excited state intersections, electrostatic embedding TD-DFT/MM allows for a fast exploration of the potential energy surfaces and a qualitative picture of the photophysics of thymine in solvent droplets.     

Solid-phase extraction and field-amplified sample injection–capillary zone electrophoresis for the analysis of benzophenone UV filters in environmental water samples

A field-amplified sample injection–capillary zone electrophoresis (FASI-CZE) method for the analysis of benzophenone (BP) UV filters in environmental water samples was developed, allowing the separation of all compounds in less than 8 min. A 9- to 25-fold sensitivity enhancement was obtained with FASI-CZE, achieving limits of detection down to 21–59 μg/L for most of the analyzed BPs, with acceptable run-to-run and day-to-day precisions (relative standard deviations lower than 17 %). In order to remove water sample salinity and to enhance FASI sensitivity, an off-line solid-phase extraction (SPE) procedure using a Strata X polymeric reversed-phase sorbent was used and afforded recoveries up to 72–90 % for most BPs. With the combination of off-line SPE and FASI-CZE, limits of detection in the range 0.06–0.6 μg/L in a river water matrix, representing a 2,400- to 6,500-fold enhancement, were obtained. Method performance was evaluated by quantifying a blank river water sample spiked at 1 μg/L. For a 95 % confidence level, no statistical differences were observed between found concentrations and spiked concentrations (probability at the confidence level, p value, of 0.60), showing that the proposed off-line SPE-FASI-CZE method is suitable for the analysis of BP UV filters in environmental water samples at low microgram per liter levels. The method was successfully applied to the analysis of BPs in river water samples collected up- and downstream of industrialized and urban areas, and in some drinking water samples.