Regularity of the nodal set of segregated critical configurations under a weak reflection law

We deal with a class of Lipschitz vector functions U?=?(u ₁, . . . , u _h ) whose components are nonnegative, disjointly supported and verify an elliptic equation on each support. Under a weak formulation of a reflection law, related to the Pohoz?aev identity, we prove that the nodal set is a collection of C ^1,α hyper-surfaces (for every 0?<?α?<?1), up to a residual set with small Hausdorff dimension. This result applies to the asymptotic limits of reaction–diffusion systems with strong competition interactions, to optimal partition problems involving eigenvalues, as well as to segregated standing waves for Bose–Einstein condensates in multiple hyperfine spin states.     

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F∝−v^γ$F\propto -v^{\gamma }$. The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton’s second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for γ=1$\gamma =1$; (ii) exponential for γ=2$\gamma =2$; and (iii) second-degree polynomial type for γ=1.5$\gamma =1.5$. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.     

One-Step Synthesis of Aminobenzoic Acid Functionalized Graphene Oxide by Electrochemical Exfoliation of Graphite for Oxygen Reduction to Hydrogen Peroxide and Supercapacitors

Graphene-based materials have attracted considerable attention as promising electrocatalysts for the oxygen reduction reaction (ORR) and as electrode materials for supercapacitors. In this work, electrochemical exfoliation of graphite in the presence of 4-aminebenzoic acid (4-ABA) is used as a one-step method to prepare graphene oxide materials (EGO) functionalized with aminobenzoic acid (EGO-ABA). The EGO and EGO-ABAs materials were characterized by FT-IR spectroscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, X-ray diffraction and scanning electron microscopy. It was found that the EGO-ABA materials have smaller flake size and higher density of oxygenated functional groups compared to bare EGO. The electrochemical studies showed that the EGO-ABA catalysts have higher activity for the ORR to H₂O₂ in alkaline medium compared to EGO due to their higher density of oxygenated functional groups. However, bare EGO has a higher selectivity for the 2-electron process (81%) compared to the EGO-ABA (between 64 and 72%) which was related to a lower content of carbonyl groups. The specific capacitance of the EGO-ABA materials was higher than that of EGO, with an increase by a factor of 3 for the materials prepared from exfoliation in 5 mM 4-ABA/0.1 M H₂SO₄. This electrode material also showed a remarkable cycling capability with a loss of only 19.4% after 5000 cycles at 50 mVs⁻¹.     

Response Surface Modeling and Optimization of the Extraction of Phenolic Antioxidants from Olive Mill Pomace

Bioactive compounds from olive mill pomace (OMP) were extracted through a two-step solid-liquid extraction procedure considering four factors at five levels of a central composite rotatable response surface design. The influence of the process variables time of the primary extraction (2.0–4.0 h), solvent-to-sample ratio during the primary extraction (5.0–10.0 mL/g), time of the secondary extraction (1.0–2.0 h), and the solvent-to-sample ratio during the secondary extraction (3.0–5.0 mL/g) were examined. The content of bioactive compounds was determined spectrophotometrically, and the individual phenolic compounds were evaluated by reserved-phase high-performance liquid chromatography (RP-HPLC). The Derringer’s function was used to optimize the extraction process, and the best conditions were found to be 3.2 h for the primary extraction, 10.0 mL/g for the solvent-to-sample ratio and 1.3 h for the secondary extraction associated with a solvent-to-sample ratio of 3.0 mL/g, obtaining a total phenolic content of 50.0 (expressed as mg gallic acid equivalents (GAE)/g dry weight (dw). The response surface methodology proved to be a great alternative for reducing the number of tests, allowing the optimization of the extraction of phenolic antioxidants from OMP with a reduced number of experiments, promoting reductions in cost and analysis time.     

Nanoparticles positioning effect on properties of (PS-PANI/NiNPs) nanocomposite films

This work presents the effect of driven nickel nanoparticles (NiNPs) towards the surface of (PS-PANI)/NiNPs nanocomposite upon the application of a uniform magnetic field. The purpose is to obtain distinguishable optoelectronic and electrical properties. This process increases the surface roughness and its reactivity, and enables the tuning of the optical and electrical properties. Based on the results from X-ray photoelectron and Fourier-transform infrared spectroscopies, the magnetically-driven NiNPs to the surface are oxidized, forming NiONPs and NiOHNPs. This oxidation effect transforms the surface from a hydrophilic to a hydrophobic state. In addition, the optical bandgap energy decreases from 4.04 to 3.77 eV, and the electrical conductivity increases from 12.77 μS/cm to 57.80 μS/cm and 77.52 μS/cm, for 50 and 100 mT magnetic fields, respectively, which is attributed to the well-dispersed magnetic nanoparticles in the PS-PANI polymer matrix, resulting in a high homogeneous nanocomposite film.