On the rate of convergence of solutions in free boundary problems via penalization

The rate of convergence of approximate solutions via penalization for free boundary problems are concerned. A key observation is to obtain global bounds of penalized terms which give necessary estimates on integrations by the nonlinear adjoint method by L.C. Evans.     

Trifluorosulfonylation Cascade in Allenols: Stereocontrolled Synthesis of Bis(triflyl)enones

Herein, we report investigations embodying the first example of reversal of the native regioselectivity in the reaction of allenols with electrophiles. The effortlessness of C−C bond formation, mild reaction conditions, neither catalysts nor light irradiation, and exquisite selectivity, both in terms of functional-group tolerance and chemo-, site-, and stereo-selectivity, converts this trifluorosulfonylation-rearrangement sequence into an appealing protocol for the preparation of novel functionalized enones. The synthetic utility of this method has been validated by the conversion of the initially prepared bis(triflyl)enones into a variety of bis(triflyl)-functionalized molecules such as 1,3-dienes, allylic alcohols, pyrroles, pyrazoles, and chromenes. Besides, DFT calculations have provided a reliable understanding of observed selectivity.     

Multidynamic Crystalline Molecular Rotors Comprising an N-Heterocyclic Carbene Binuclear Au(I) Complex Bearing Multiple Rotators

We report multidynamic molecular rotations in crystals using a concave-shape N-heterocyclic carbene (NHC) binuclear Au(I) complex rotor bearing pyrazine and tetrahydrofuran (THF) molecules as multicomponent rotators. Single-crystal X-ray diffraction (XRD) measurements revealed that two THF molecules are located near the central pyrazine encapsulated by two bulky NHC ligands. From ²H solid-state NMR analysis, it was observed that the pyrazine rotated in a 2-fold site exchange with a 180° rotational angle and a 31 kJ mol⁻¹ energy barrier, while the THF molecules showed a 23°-38° libration with a lower energy barrier (14 kJ mol⁻¹). Interestingly, the pyrazine rotation was accelerated when the THF molecules rotated in fast site exchange with a large angle of libration, suggesting that the rotators exhibit multidynamics in a correlated manner.     

Cover Feature: Fluoroalkyl Sulfoximines for Versatile Photocatalytic Radical Fluoroalkylations (Chem. Rec. 9/2023)

Fluoroalkyl sulfoximines, which serve as electron-accepting fluoroalkyl radical sources, are easy-to-handle, solid, and bench-stable chemicals. Fluoroalkyl radicals can be generated from sulfoximine reagents using strong one-electron injectors, such as a highly reducing photoredox catalyst in the excited state. Our group has developed photocatalytic radical di- and mono-fluoromethylation and α-monofluoroalkylation of olefins with the corresponding fluoroalkyl sulfoximines. In this personal account, appropriate combinations of fluoroalkyl sulfoximines and photoredox catalysts, leading to successful radical fluoroalkylation, have been discussed.     

Prediction of soil reaction forces on a moldboard plow surface

Using mathematical models, approximate trajectories of soil furrow subslices were determined and the forces occurring on the moldboard surface were calculated. The various components of the normal force along the trajectory line of the middle section of the furrow slice were analysed in relation to the velocity of plowing operation and the curvature of the path. The soil reaction forces encountered by the share portion of the plow were also determined by a model which used the method of trial wedges to determine the angle of the failure surface with the horizontal. The sum of the calculated forces was compared with that obtained by actual plowing experiments performed in the laboratory.     

Several contributions to soil compactibility induced by cyclic loading test

To investigate the soil compactibility during the cyclic loading, three different kinds of paddy field soils were prepared so as to clarify interrelationships among stress amplitude ratio, bulk density, soil water content and pore water pressure. The presetting values of specimen include the soil water content(percent dry basis) and bulk density of 25% d.b. and 1.1 Mg/m³ respectively. The relation between the number of cyclic loading and axial strain exhibited an asymptotically increasing trend, converging toward a specific value for each experimental condition. Possible effect caused by elastic–plastic characteristics could be recognized, when axial strain for 0.5 Hz excitation becomes greater than the one of 1.0 Hz under same stress amplitude ratio. When the stress amplitude ratio took 0.1, the absolute value of axial strain of 0.5 Hz was greater than the one of 1.0 Hz, whereas its decreasing trend was recognized in the sequence of silt, clay and silty sand. The qualitative relations between pore water pressure and number of cyclic loading were also examined to scrutinize the effect of effective water pressure to the soil compactibility.     

Triaxial force measurement at specific positions on a soil-cutting blade

In order to create a mathematical model of a soil-cutting blade, it is necessary to understand thoroughly the behavior of a soil slice and its interaction with the blade surface. The triaxial force transducer was developed to serve as one of the various tools to verify the proposed mathematical model. The prototype model transducer was fabricated, calibrated and tested with a soil slice on a flat cutting blade. The calibration results have indicated high sensitivity and the capability of simultaneous measurement in three directions. As a technological refinement, the detecting part of this triaxial force transducer was tapered to solve the problem of soil clogging in the opening clearance. Furthermore, the effects of the clearance configurations between the bore on the soil-cutting blade and the detecting part which is embedded in this bore were investigated to determine the most desirable configuration. The comparative results indicated that by tapering both the detecting part and the bore, the tangential stress measurement gained the highest value, and provided the most satisfactory condition for three-dimensional stress management.     

Thermal and optical properties of highly fluorinated copolymers of methacrylates

Copolymers of pentafluorophenylhexafluoroisopropyl methacrylate (FPPMA) with trifluoroethyl methacrylate (TFEMA) were prepared in THF solution and in bulk using azobisisobutyronitrile as a free radical initiator. The monomer reactivity ratios of TFEMA (M₁) and FPPMA (M₂) were calculated as r₁ = 0.55 and r₂ = 0.07. The refractive indices of poly(TFEMA) and poly(FPPMA) are very similar as 1.435 and 1.430, respectively, at 532 nm, and the copolymer films were transparent. The glass transition temperatures (T_g) of the copolymers were in the range of 80–90°C and showed a negative deviation from the Gordon–Taylor equation. The thermal decomposition temperature (T_d) was increased with the content of FPPMA in copolymers. Low water absorption for 1:1 FPPMA/TFEMA copolymer was detected. Copolymers of FPPMA with hexafluoroisopropyl methacrylate (HFPMA) were also prepared. The monomer reactivity ratios of HFPMA (M₁) and FPPMA (M₂) were calculated as r₁ = 0.43 and r₂ = 0.10. The T_gs of the copolymers were in the range of 88–95°C and showed also a negative deviation from the Gordon–Taylor equation. T_g and T_d of the copolymers were increased with the content of FPPMA. The refractive index of poly(HFPMA) (1.384 at 532 nm) is much lower than that of FPPMA homopolymer, but copolymer films obtained were clear and transparent. Copyright © 2013 John Wiley & Sons, Ltd.