A new high order compact off-step discretization for the system of 3D quasi-linear elliptic partial differential equations

We present a new fourth order compact finite difference scheme based on off-step discretization for the solution of the system of 3D quasi-linear elliptic partial differential equations subject to appropriate Dirichlet boundary conditions. We also develop new fourth order methods to obtain the numerical solution of first order normal derivatives of the solution. In all the cases, we use only 19-grid points of a single computational cell to compute the problem. The proposed methods are directly applicable to singular problems and the problems in polar coordinates, without any modification required unlike the previously developed high order schemes of [14] and [30]. We discuss the convergence analysis of the proposed method in details. Many physical problems are solved and comparative results are given to illustrate the usefulness of the proposed methods.     

Modifications of 5,12-dihydroindolo[3,2-a]carbazole scaffold via its regioselective C2,9-formylation and C2,9-acetylation

The effective approaches for regioselective double formylation and acetylation of 5,12-dialkyl-6,7-diaryl-substituted 5,12-dihydroindolo[3,2-a]carbazoles by their treatment with dichloromethyl methyl ether in the presence of SnCl₄ or with acetyl chloride in the presence of AlCl₃ to afford the 2,9-diformyl or 2,9-diacetyl derivatives, respectively, were developed. Furthermore, new 2,9-bis(2,2-dicyanovinyl) derivatives were synthesized by the Knoevenagel condensation of diformyl-containing substrates with malononitrile, when new 2,9-bis(quinoxaline-2-yl)- and 2,9-bis(benzo[g]quinoxaline-2-yl) derivatives were formed via microwave-promoted oxidation of diacetyl-containing substrates with SeO₂ to the corresponding diglyoxals, followed by the reaction of these intermediates with o-phenylendiamine or 2,3-diaminonaphthalene, respectively. The basic optical and electrochemical properties of some 5,12-dihydroindolo[3,2-a]carbazoles were investigated.     

Planar Chiral Rhodium Complexes of 1,4-Benzoquinones

Diene rhodium complexes are important catalysts in modern organic synthesis. Herein, we report a new approach to such complexes with the uncommon planar chirality. The synthesis is achieved by face-selective coordination of the prochiral 2,5-disubstituted-1,4-benzoquinones (R₂-Q) with rhodium precursors containing the chiral auxiliary ligand S-salicyl-oxazoline (S-Salox). Such coordination leads to the formation of (R,R-R₂-Q)Rh(S-Salox) complexes in high yields and with exceptional diastereoselectivity (d. r.>20 : 1). Subsequent replacement of the auxiliary ligand provides various benzoquinone rhodium complexes with retention of the planar chirality. Combined theoretical and experimental studies show that due to their electron-withdrawing nature benzoquinones bind metals stronger than the related 1,4-cyclohexadiene, but weaker than other common diene ligands, such as cyclooctadiene.     

Multifunctional Sulfur-Hyperdoped Silicon Nanoparticles with Engineered Mid-Infrared Sulfur-Impurity and Free-Carrier Absorption

Si nanoparticles (NPs), which are innovative promising light-harvesting components of thin-film solar cells and key-enabling biocompatible theranostic elements of infrared-laser and radiofrequency hyperthermia-based therapies of cancer cells in tumors and metastases, are significantly advanced in their near/mid-infrared band-to-band and free-carrier absorption via donor sulfur-hyperdoping during high-throughput facile femtosecond-laser ablative production in liquid carbon disulfide. High-resolution transmission electron microscopy and Raman microscopy reveal their mixed nanocrystalline/amorphous structure, enabling the extraordinary sulfur content of a few atomic percents and very minor surface oxidation/carbonization characterized by energy-dispersive X-ray spectroscopy and X-ray photoelectron spectroscopy. A 200-nm thick layer of the nanoparticles exhibits near−mid-infrared absorbance, comparable to that of the initial 380-micron thick n-doped Si wafer (phosphor-dopant concentration ≈10¹⁵ cm⁻³), with the corresponding extinction coefficient for the hyperdoped NPs being 4–7 orders higher over the broadband spectral range of 1–25 micrometers. Such ultimate, but potentially tunable mid-IR structured, multi-band absorption of various sulfur-impurity clusters and smooth free-carrier absorption are break through advances in mid-infrared (mid-IR) laser and radiofrequency (RF) hyperthermia-based therapies, as envisioned in the RF-heating tests, and in fabrication of higher-efficiency thin-film and bulk photovoltaic devices with ultra-broad (UV−mid-IR) spectral response.     

Seeing the Unseen: Experimental Observation of Magnetic Anapole State Inside a High-Index Dielectric Particle

The existence of non-radiating electromagnetic sources attracts much attention in photonic community and gives rise to extensive discussions of various applications in lasing, medical imaging, sensing, and nonlinear optics. In this article, the existence of magnetic anapole states (or magnetic-type non-radiating sources) characterized by a suppressed magnetic dipole radiation in a dielectric cylindrical particle is theoretically predicted and experimentally demonstrated. The specific features of the magnetic anapole state under ideal conditions are identified, followed by a demonstration of how their existence can be detected in practical structures. The concept is valid in various frequency bands from visible range for nanoparticles to microwave range for millimeter size objects. The experimental study is performed in microwave frequency range which allows not only to measure the far-field (scattered field) characteristics, but also to probe the peculiar field profile directly inside the dielectric particle. The experimental results agree well with the analytical ones and pave the way to detect and identify nontrivial different-type anapole states.     

Inorganic Molecular Electride Mg4O3: Structure,Bonding, and Nonlinear Optical Properties

Growing demands of material science and, in particular, in the field of nonlinear optics (NLO) encourage us to look for stable highly polarizable molecules with excess diffuse electrons. An unusual class of compounds called electrides comply with these requirements. Many attempts have been made, yet only few electrides have been synthesized as solids and none of them as molecular species. In this paper, a new theoretically designed molecular species with electride characteristics is reported. The idea of this molecular electride comes from the formation of electride-like features in the MgO crystal with defect F-centers. The geometry of the investigated molecule can be described as a Mg₄O₄ cube with one oxygen atom removed. In Mg₄O₃, two 3s electrons are pushed out from the inner area of the molecule forming a diffuse electride multicentered bond. Our calculations show that this electride-like cluster possesses a noticeably large first hyperpolarizability β=5733 au. At the same time, a complete cube Mg₄O₄ and Mg₄O₃²⁺ without electride electron pair have much smaller β: 0 au and 741 au, respectively. This fact indicates the decisive role of the electride electron pair in NLO properties. Additionally, vertical detachment energies of isomers (VDE), excitation energies ΔE, polarizabilities α, and IR spectra were calculated. These properties, including β, are supposed to be observable experimentally and can serve as indirect evidence of the stable molecular electride formation.     

Structure and conductivity of AOT solutions in n-hexadecane-chloroform mixtures

The structure and conductivity of AOT (sodium bis(2-ethylhexyl) sulfosuccinate) solutions (2.5 × 10⁻⁴–2.5 × 10⁻¹ M) in n-hexadecane-chloroform mixture at the chloroform concentration from 50 to 100 vol% were studied. The diffusion ordered spectroscopy NMR study revealed that in the indicated range, the observed hydrodynamic diameter of micelles depends only on the AOT concentration and does not depend on the chloroform content. Molar fractions of free AOT molecules and those aggregated into micelles were calculated using the Lindman's law: at concentrations above 2.5 × 10⁻¹ М, the solutions contain mostly the micelles, whereas at concentrations below 2.5 × 10⁻⁴ M, the solutions contain AOT molecules. The transition region contains both the AOT molecules and the micelles. Conductivity measurements were used to determine free charge carriers in the bulk of solutions and their contributions to conductivity.