Confinement–deconfinement transitions for two-dimensional Dirac particles

We consider a two-dimensional massless Dirac operator coupled to a magnetic field B and an electric potential V growing at infinity. We find a characterization of the spectrum of the resulting operator H in terms of the relation between B and V at infinity. In particular, we give a sharp condition for the discreteness of the spectrum of H beyond which we find dense pure point spectrum.     

An Extension of a Theorem of Yao and Yao

In this paper we study N _d (k), the smallest positive integer such that any nice measure μ in $\mathbb{R}^{d}$ can be partitioned into N _d (k) convex parts of equal measure so that every hyperplane avoids at least k of them. A theorem of Yao and Yao states that N _d (1)≤2 ^d . Among other results, we obtain the bounds N _d (2)≤3?2 ^d?1 and N _d (1)≥C?2 ^d/2 for some constant C. We then apply these results to a problem on the separation of points and hyperplanes.     

Evaluation of different PAMAM dendrimers as molecular vehicle of 1,2,4-triazine N-oxide derivative with potential antitumor activity

The interaction between a 1,2,4-triazine N-oxide derivative, that holds potential antitumor activity under hypoxic conditions, and diverse polyamidoamine (PAMAM) dendrimers were investigated with the purpose of select the most appropriate macromolecule to act as potential molecular carrier of this active compound. The results shows that dendrimers with amine terminal groups (PAMAM-AT G = 3) and dendrimers with carboxylate terminal groups (PAMAM-CT G2.5 and G4.5) produces triazine derivative hydrolysis, even in buffered medium, and are not suitable as carriers. In contrast, dendrimers with neutral end groups (PAMAM-OHT) shows stable association with the active compound, making this dendrimer a possible medium for triazine carriage.     

Co-doped ZnO nanoparticles synthesized by an adapted sol–gel method: effects on the structural,optical, photocatalytic and antibacterial properties

Pure and Co-doped ZnO nanoparticles were synthesized with different cobalt levels (1–10 mol%) via adapted sol–gel method using water as solvent and characterized by X-ray diffraction, transmission electron microscopy, Raman spectroscopy and photoacoustic absorption spectroscopy. The results showed that all the samples have hexagonal wurtzite structure, with no evidence of any secondary phases until 10 mol% of the dopant. The average crystallite size of the samples was in the range of 25–50 nm, do not showing significant differences with the increase of the dopant level. However, the band gap energy of the nanoparticles decreases from 2.98 eV (pure ZnO) to 1.95 eV (10 mol% of Co). The photocatalytic activity of the samples was evaluated on the removal of methylene blue under visible light irradiation, which revealed an efficiency reduction by Co-doping ZnO. The antibacterial property was carried out indicating activity of the prepared samples against gram-positive bacteria.     

Erdős–Szekeres Theorem for Lines

According to the Erd?s–Szekeres theorem, for every n, a sufficiently large set of points in general position in the plane contains n in convex position. In this note we investigate the line version of this result, that is, we want to find n lines in convex position in a sufficiently large set of lines that are in general position. We prove almost matching upper and lower bounds for the minimum size of the set of lines in general position that always contains n in convex position. This is quite unexpected, since in the case of points, the best known bounds are very far from each other. We also establish the dual versions of many variants and generalizations of the Erd?s–Szekeres theorem.     

ZnSe Etching of Zn‐Rich Cu2ZnSnSe4: An Oxidation Route for Improved Solar‐Cell Efficiency

Cu₂ZnSnSe₄ kesterite compounds are some of the most promising materials for low‐cost thin‐film photovoltaics. However, the synthesis of absorbers for high‐performing devices is still a complex issue. So far, the best devices rely on absorbers grown in a Zn‐rich and Cu‐poor environment. These off‐stoichiometric conditions favor the presence of a ZnSe secondary phase, which has been proved to be highly detrimental for device performance. Therefore, an effective method for the selective removal of this phase is important. Previous attempts to remove this phase by using acidic etching or highly toxic organic compounds have been reported but so far with moderate impact on device performance. Herein, a new oxidizing route to ensure efficient removal of ZnSe is presented based on treatment with a mixture of an oxidizing agent and a mineral acid followed by treatment in an aqueous Na₂S solution. Three different oxidizing agents were tested: H₂O₂, KMnO₄, and K₂Cr₂O₇, combined with different concentrations of H₂SO₄. With all of these agents Se^2? from the ZnSe surface phase is selectively oxidized to Se⁰, forming an elemental Se phase, which is removed with the subsequent etching in Na₂S. Using KMnO₄ in a H₂SO₄‐based medium, a large improvement on the conversion efficiency of the devices is observed, related to an improvement of all the optoelectronic parameters of the cells. Improvement of short‐circuit current density (J_sc) and series resistance is directly related to the selective etching of the ZnSe surface phase, which has a demonstrated current‐blocking effect. In addition, a significant improvement of open‐circuit voltage (V_oc), shunt resistance (R_sh), and fill factor (FF) are attributed to a passivation effect of the kesterite absorber surface resulting from the chemical processes, an effect that likely leads to a reduction of nonradiative‐recombination states density and a subsequent improvement of the p–n junction.     

A Solution-Generating Method in Einstein-Scalar Gravity

We present a method to generate static, spherically symmetric, solutions of Einstein gravity in \(d+2\) dimensions minimally coupled to a real scalar field with a self-interacting potential. The solutions can be fully parametrised by a single function, whose behaviour encodes all the information about the local and global behaviour of the spacetime. We give several explicit applications of our solution-generating method that describe black holes, naked singularities and solitonic configurations.

     

Hysteresis in $$\eta /s$$ for QFTs dual to spherical black holes

We define and compute the (analog) shear viscosity to entropy density ratio \(\tilde{\eta }/s\) for the QFTs dual to spherical AdS black holes both in Einstein and Gauss–Bonnet gravity in five spacetime dimensions. Although in this case, owing to the lack of translational symmetry of the background, \(\tilde{\eta }\) does not have the usual hydrodynamic meaning, it can be still interpreted as the rate of entropy production due to a strain. At large and small temperatures it is found that \(\tilde{\eta }/s\) is a monotonic increasing function of the temperature. In particular, at large temperatures it approaches a constant value, whereas at small temperatures, when the black hole has a regular, stable extremal limit, \(\tilde{\eta }/s\) goes to zero with scaling law behavior. Whenever the phase diagram of the black hole has a Van der Waals-like behavior, i.e. it is characterized by the presence of two stable states (small and large black holes), connected by a meta-stable region (intermediate black holes), the system evolution must occur through the meta-stable region- and temperature-dependent hysteresis of \(\tilde{\eta }/s\) is generated by non-equilibrium thermodynamics.