Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

Nonuniform reinjection probability density function in type V intermittency

Nonlinear Dynamics - In this paper, type V intermittency is studied using the M function methodology developed in the last years. This methodology is applied on two different maps to evaluate the...     

Enantioselective Organocatalytic Reduction of β‐Trifluoromethyl Nitroalkenes: An Efficient Strategy for the Synthesis of Chiral β‐Trifluoromethyl Amines

An efficient organocatalytic stereoselective reduction of β‐trifluoromethyl‐substituted nitroalkenes, mediated by 3,5‐dicarboxylic ester‐dihydropyridines (Hantzsch ester type), has been successfully developed. A multifunctional thiourea‐based (S)‐valine derivative was found to be the catalyst of choice, promoting the reaction in up to 97 % ee. The methodology has been applied to a wide variety of substrates, leading to the formation of differently substituted precursors of enantiomerically enriched β‐trifluoromethyl amines. The mechanism of the reaction and the mode of action of the metal‐free catalytic species were computationally investigated; on the basis of DFT transition‐state (TS) analysis, a model of stereoselection was also proposed.     

1,2‐Dimethoxyethane Degradation Thermodynamics in Li−O2 Redox Environments

The reaction thermodynamics of the 1,2‐dimethoxyethane (DME), a model solvent molecule commonly used in electrolytes for Li?O₂ rechargeable batteries, has been studied by first‐principles methods to predict its degradation processes in highly oxidizing environments. In particular, the reactivity of DME towards the superoxide anion O₂^? in oxygen‐poor or oxygen‐rich environments is studied by density functional calculations. Solvation effects are considered by employing a self‐consistent reaction field in a continuum solvation model. The degradation of DME occurs through competitive thermodynamically driven reaction paths that end with the formation of partially oxidized final products such as formaldehyde and methoxyethene in oxygen‐poor environments and methyl oxalate, methyl formate, 1‐formate methyl acetate, methoxy ethanoic methanoic anhydride, and ethylene glycol diformate in oxygen‐rich environments. This chemical reactivity indirectly behaves as an electroactive parasitic process and therefore wastes part of the charge exchanged in Li?O₂ cells upon discharge. This study is the first complete rationale to be reported about the degradation chemistry of DME due to direct interaction with O₂^?/O₂ molecules. These findings pave the way for a rational development of new solvent molecules for Li?O₂ electrolytes.     

Probing the Catalytic Activity of Reduced Graphene Oxide Decorated with Au Nanoparticles Triggered by Visible Light

Hybrid materials in which reduced graphene oxide (rGO) is decorated with Au nanoparticles (rGO–Au NPs) were obtained by the in situ reduction of GO and AuCl₄^?_(aq) by ascorbic acid. On laser excitation, rGO could be oxidized as a result of the surface plasmon resonance (SPR) excitation in the Au NPs, which generates activated O₂ through the transfer of SPR‐excited hot electrons to O₂ molecules adsorbed from air. The SPR‐mediated catalytic oxidation of p‐aminothiophenol (PATP) to p,p′‐dimercaptoazobenzene (DMAB) was then employed as a model reaction to probe the effect of rGO as a support for Au NPs on their SPR‐mediated catalytic activities. The increased conversion of PATP to DMAB relative to individual Au NPs indicated that charge‐transfer processes from rGO to Au took place and contributed to improved SPR‐mediated activity. Since the transfer of electrons from Au to adsorbed O₂ molecules is the crucial step for PATP oxidation, in addition to the SPR‐excited hot electrons of Au NPs, the transfer of electrons from rGO to Au contributed to increasing the electron density of Au above the Fermi level and thus the Au‐to‐O₂ charge‐transfer process.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.