Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

Cyanide-Free One-Pot Synthesis of Methacrylic Esters from Acetone

Methacrylic esters, represented by methyl methacrylate (MMA), are widely used as commodity chemicals. Here, the one-pot synthesis of methacrylic esters from acetone, a haloform and alcohols in the presence of an organic base is described. Using DBU as the organic base for the reaction of acetone, chloroform and methanol in acetonitrile afforded MMA in 66 % yield. When the solvent was replaced by benzonitrile, the product MMA was successfully purified by distillation. Applicability of this process to various alcohols was also investigated to show ethyl, phenyl, CF₃CH₂, and n-C₆F₁₃CH₂CH₂ esters were obtained in moderate yields. The use of bromoform instead of chloroform resulted in the improvement of the yield, for example, methyl and n-C₆F₁₃CH₂CH₂ esters up to 81 and 70 %, respectively. The reaction with deuterated starting materials acetone-d₆ and MeOH-d₄, with DBU in acetonitrile afforded deuterated MMA (MMA-d₈) in 70 % yield.     

Synthesis of nonplanar bipyridyls bridged by disilane and disiloxane and their phosphorescent copper complexes

Disilane- and disiloxane-bridged bipyridyls ( DSBPy and DSOBPy ) were prepared and their optical properties were investigated in comparison with those of previously reported monosilane- and monogermane-bridged counterparts. The UV–visible absorption and photoluminescence bands of DSBPy and DSOBPy were blue-shifted as a result of elongation of the bridging units from monosilane and monogermane to disilane and disiloxane, likely due to the enhanced twisting of the bipyridyl units. Phosphorescent complexes DSBPy–Cu and DSOBPy–Cu were prepared by the interaction of DSBPy and DSOBPy with Cu₂I₂(PPh₃)₂. X-ray diffraction studies of their single-crystal structures revealed polymeric structures composed of repeat units of DSBPy or DSOBPy and [Cu^II(PPh₃)]₂. Organic light-emitting diodes with the ITO/PEDOT:PSS/ DSBPy–Cu or DSOBPy–Cu :PCTSQ/TAZ/Al structure were fabricated to examine the applications of the complexes as electroluminescent materials. The devices emitted yellow light with emission maxima at approximately 600 nm, and maximal luminance reached 120 and 190 cd m⁻² for devices based on DSBPy–Cu and DSOBPy–Cu , respectively. The performance of the DSOBPy–Cu -based device was improved by using TAZ as the dopant of the emissive layer, and luminance was increased to 390 cd m⁻².     

Electrochemical Characteristics of a Triphenylamine Derivative by Microelectrode Voltammetry

With the objective of understanding the kinetic redox properties of triphenylamine derivatives in association with chemical reactions, for their future application in functional organic semiconductor devices, the electrochemical characteristics of 4‐(2,2‐diphenylethenyl)‐N,N‐bis(4‐methylphenyl)‐benzenamine (TPA) were evaluated. Based on cyclic voltammograms of TPA on Pt disk electrodes with diameters of 300 μm and 10 μm at slow and fast scan rates in an acetonitrile solution, the TPA^.+ is stable, while the TPA²⁺ is unstable. Importantly, the unstable TPA²⁺ appears to break down by a subsequent chemical reaction. A Cottrell plot analysis from chronoamperometry of a solution containing TPA reveals that both the first and second oxidations are one‐electron reactions. Concerning the stabilization mechanism of the first oxidation state of TPA, the results of molecular orbital calculations indicate that the electrons of the HOMO level are distributed in the triphenylamine group, which induces a resonance‐stabilized TPA^.+. Based on these results, TPA/TPA^.+ is suggested to have a sufficient stability for further application in organic semiconductor devices.     

A remark on boundary level admissible representations

We point out that it is immediate by our character formula that in the case of a boundary level the characters of admissible representations of affine Kac–Moody algebras and the corresponding W-algebras decompose in products in terms of the Jacobi form ${?}_{11}(\tau ,z)$.     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Proton Order–Disorder Phenomena in a Hydrogen‐Bonded Rhodium–η5‐Semiquinone Complex: A Possible Dielectric Response Mechanism

A newly synthesized one‐dimensional (1D) hydrogen‐bonded (H‐bonded) rhodium(II)–η⁵‐semiquinone complex, [Cp*Rh(η⁵‐p‐HSQ‐Me₄)]PF₆ ([ 1 ]PF₆; Cp*=1,2,3,4,5‐pentamethylcyclopentadienyl; HSQ=semiquinone) exhibits a paraelectric–antiferroelectric second‐order phase transition at 237.1 K. Neutron and X‐ray crystal structure analyses reveal that the H‐bonded proton is disordered over two sites in the room‐temperature (RT) phase. The phase transition would arise from this proton disorder together with rotation or libration of the Cp* ring and PF₆^? ion. The relative permittivity ε_b′ along the H‐bonded chains reaches relatively high values (ca., 130) in the RT phase. The temperature dependence of ¹³C CP/MAS NMR spectra demonstrates that the proton is dynamically disordered in the RT phase and that the proton exchange has already occurred in the low‐temperature (LT) phase. Rate constants for the proton exchange are estimated to be 10^?4–10^?6 s in the temperature range of 240–270 K. DFT calculations predict that the protonation/deprotonation of [ 1 ]⁺ leads to interesting hapticity changes of the semiquinone ligand accompanied by reduction/oxidation by the π‐bonded rhodium fragment, producing the stable η⁶‐hydroquinone complex, [Cp*Rh³⁺(η⁶‐p‐H₂Q‐Me₄)]²⁺ ([ 2 ]²⁺), and η⁴‐benzoquinone complex, [Cp*Rh⁺(η⁴‐p‐BQ‐Me₄)] ([ 3 ]), respectively. Possible mechanisms leading to the dielectric response are discussed on the basis of the migration of the protonic solitons comprising of [ 2 ]²⁺ and [ 3 ], which would be generated in the H‐bonded chain.     

Skeleton transformation of α-pyrone induced by 5-aryl substituent into ring-fused dihydrofuran

A skeleton transformation of 5-aryl-α-pyrones into dihydrofurans was developed. In the course of our study of the skeleton transformation reaction of α-pyrones by using dimethylsulfoxonium methylide, α-pyrones having an aryl group at the 5-position were converted into corresponding dihydrofurans as major products and bicyclo[3.1.0]hexanes as minor products. Selectivity for dihydrofurans was improved by optimizing the reaction conditions and investigating the substituent effect.     

Synthesis of All Stereoisomers of Monomeric Spectomycin A1/A2 and Evaluation of Their Protein SUMOylation-Inhibitory Activity

A synthetic methodology to access all possible stereoisomers of spectomycin A1 (SMA1) and A2 (SMA2) has been established through late-stage diversification. The key reaction for the construction of all four diastereomers is an intramolecular cyclization based on the umpolung of π-allyl palladium species with bis(pinacolato)diborane (B₂(pin)₂). Silyl group assisted direct benzylic oxidation of each isomer enabled construction of the fragile β-hydroxytetralone skeleton to provide the SMAs. The relative and absolute stereochemistry of SMA2 was also determined, and the absolute stereochemistry of SMA1 was extrapolated based on the optical rotation of SMA2. The axial chirality of SMAs is discussed based on circular dichroism spectra and DFT calculations, and it is concluded that the M isomer is predominant in solution. Biochemical assessment of all isomers in vitro revealed that the C9 hydroxyl group and dimeric structure were both important for protein SUMOylation-inhibitory activity.