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.     

A variant of Shelah's characterization of Strong Chang's Conjecture

Shelah considered a certain version of Strong Chang's Conjecture which we denote , and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an apparently weaker version, denoted , and prove an analogous characterization of it. In particular, is equivalent to the assertion that the the Friedman‐Krueger poset is semiproper. This strengthens and sharpens results by Cox and sheds some light on problems posed by Usuba, Torres‐Perez and Wu.     

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).     

Mechanosensitive membrane probes: push-pull papillons

ABSTRACT

Design, synthesis and evaluation of push-pull N,N′-diphenyl-dihydrodibenzo[a,c]phenazines are reported. Consistent with theoretical predictions, donors and acceptors attached to the bent mechanophore are shown to shift absorption maxima to either red or blue, depending on their positioning in the chromophore. Redshifted excitation of push-pull fluorophores is reflected in redshifted emission of both bent and planar excited states. The intensity ratios of the dual emission in more and less polar solvents imply that excited-state (ES) planarization decelerates with increasing fluorophore macrodipole, presumably due to attraction between the wings of closed papillons. ES planarization of highly polarisable papillons is not observed in lipid bilayer membranes. All push-pull papillon amphiphiles excel with aggregation-induced emission (AIE) from bent ES as micelles in water and mechanosensitivity in viscous solvents. They are not solvatochromic and only weakly fluorescent (QY < 4%).     

Controllable Electronic Structures and Photoinduced Processes of Bay‐Linked Perylenediimide Dimers and a Ferrocene‐Linked Triad

A series of perylene‐3,4,9,10‐bis(dicarboximide) (PDI) dimers linked through the bay regions was systematically synthesized to examine the electronic structures and photophysical properties in dependence on the distance and orientation between the two PDI units. The spectroscopic and electrochemical measurements suggested that the coupling value of a directly linked PDI dimer (PDI)₂ is much larger than those of para‐ and meta‐phenylene‐bridged PDI dimers p‐(PDI)₂ and m‐(PDI)₂. The width of Davydov splitting was quantitatively evaluated to compare the coupling values between the two PDI units in these dimers by absorption spectroscopy in frozen 2‐methyl‐THF. Excimer formation of PDI dimers induced the strong fluorescence quenching and large red‐shifts. Femtosecond transient absorption revealed a broad absorption derived from an excimer in the range from about 600 nm to the near‐IR region. The rate constants of formation and decay of the excimer are strongly dependent on the coupling values. Time‐resolved measurements on ferrocene‐linked p‐(PDI)₂ revealed a competition between the photoinduced processes of electron transfer and excimer formation in PhCN, which is in sharp contrast with the sole electron‐transfer process in toluene.     

Coumarin synthesis on π-acidic surfaces

Catalysis with anion–π interactions is emerging as an important topic in supramolecular chemistry. Among the reactions explored so far on π-acidic surfaces, coumarin synthesis stands out as a cascade process with several coupled anionic transition states. Increasing π-acidity has been shown in a different context to increase transition-state stabilisation and thus catalytic activity. In this report, we explore the possible use of macrocycles to accelerate coumarin synthesis between two π-acidic surfaces. To our disappointment, we found that compared to monomeric π-acids, coumarin synthesis within divalent macrocycles is clearly slower. Hindered access to an overly confined active site within the macrocycles could possibly account for this loss in activity, but several other explanations are certainly possible. However, operational coumarin synthesis on monomeric π-acidic surfaces is shown to tolerate structural modifications. Best results are obtained with structures that aim for proximity without obstructing transition-state stabilisation on the π-acidic surface.     

Synthesis,Properties, and Redox Behavior of 1,1,4,4‐Tetracyano‐2‐ferrocenyl‐1,3‐butadienes Connected by Aryl,Biaryl, and Teraryl Spacers

Aryl‐substituted 1,1,4,4‐tetracyano‐1,3‐butadienes (FcTCBDs) and bis(1,1,4,4‐tetracyanobutadiene)s (bis‐FcTCBDs), possessing a ferrocenyl group on each terminal, were prepared by the reaction of a variety of alkynes with tetracyanoethylene (TCNE) in a [2+2] cycloaddition reaction, followed by retro‐electrocyclization of the initially formed [2+2] cycloadducts (i.e., cyclobutene derivatives). The characteristic intramolecular charge transfer (ICT) between the donor (ferrocene) and acceptor (TCBD) moieties were investigated by using UV/Vis spectroscopy. The redox behaviors of FcTCBDs and bis‐FcTCBDs were examined by cyclic voltammetry (CV) and differential pulse voltammetry (DPV), which revealed their properties of multi‐electron transfer depending on the number of ferrocene and TCBD moieties. Moreover, significant color changes were observed by visible spectroscopy under the electrochemical reduction conditions.     

Planarized Phenyldithienylboranes: Effects of the Bridging Moieties and π-Extension on the Photophysical Properties and Lewis Acidity

Two kinds of planarized phenyldithienylboranes, which contain (CH₃)₂C- or CH₂-bridging moieties, were synthesized. The difference of the bridging moieties affects their packing structures and photophysical properties. In particular, the (CH₃)₂C-bridged derivative exhibits a large Stokes shift, unusual for such planarized compounds, that results from a large structural relaxation in the excited state. A series of π-extended derivatives was synthesized, among which a p-(diphenylamino)phenyl-substituted derivative shows large solvatochromism in the fluorescence spectra, while maintaining high quantum yields even in polar solvents. The Lewis acidity of the phenyldithienylborane derivatives was also assessed by titration with pyridine. The Lewis acidity of the boron center is affected not only by the difference in the steric bulk of the bridging moieties, but also by the electronic effect of the substituents introduced at remote positions relative to the boron atom. These results demonstrate the characteristic features of planarized phenyldithienylboranes as building blocks for boron-based π-electron materials.