Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.     

Flexible Alkylene Bridges as a Tool To Engineer Crystal Distyrylbenzene Structures Enabling Highly Fluorescent Monomeric Emission

To design ultrabright fluorescent solid dyes, a crystal engineering strategy that enables monomeric emission by blocking intermolecular electronic interactions is required. We introduced propylene moieties to distyrylbenzene (DSB) as bridges between the phenyl rings either side of its C=C bonds. The bridged DSB derivatives formed compact crystals that emit colors similar to those of the same molecules in dilute solution, with high quantum yields. The introduction of flexible seven-membered rings to the DSB core produced moderate distortion and steric hindrance in the DSB π-plane. However, owing to this strategy, it was possible to control the molecular arrangement with almost no decrease in the crystal density, and intermolecular electronic interactions were suppressed. The bridged DSB crystal structure differs from other DSB derivative structures; thus, bridging affords access to novel crystalline systems. This design strategy has important implications in many fields and is more effective than the conventional photofunctional molecular crystal design strategies.     

Oxygen vacancy promoting catalytic dehydration of formic acid on TiO2(110) by in situ scanning tunneling microscopic observation

The catalytic dehydration reaction processes of formic acid on a TiO2(110) surface at 350 K have been studied to visualize reaction intermediates and their dynamic behaviors by scanning tunneling microscopy. Three types of configurations of adsorbed formates on the surface were identified by their shapes and positions in STM images. Successive STM observations revealed transformations among the three configurations, i.e., bridge formate on a 5-fold coordinated Ti4+ row, bridge formate on an oxygen vacancy site with an oxygen atom of formate and on a 5-fold coordinated Ti4+ ion and with the other formate oxygen atom, and a monodentate formate on an oxygen vacancy site with an oxygen atom of formate. The decomposition of the monodentate formate to carbon monoxide and hydroxyl was also imaged, which is a rate-determining step in the catalytic dehydration of formic acid. Combined with first-principle DFT calculations, the overall reaction processes of the catalytic dehydration of formic acid on the surface have been elucidated. Oxygen vacancies on the surface that can be produced by dehydration of two hydroxyls in situ under the catalytic reaction conditions are essential for the reaction.     

Fullness, Connes' -groups, and ultra-products of amalgamated free products over Cartan subalgebras

Ultra-product algebras associated with amalgamated free products over Cartan subalgebras are investigated. As applications, their Connes' -groups are computed in terms of ergodic theory, and also we clarify what condition makes them full factors (i.e., their inner automorphism groups become closed).

     

On the geometry of von Neumann algebra preduals

Let \(M\) be a von Neumann algebra and let \(M_\star \) be its (unique) predual. We study when for every \(\varphi \in M_\star \) there exists \(\psi \in M_\star \) solving the equation \(\Vert \varphi \pm \psi \Vert =\Vert \varphi \Vert =\Vert \psi \Vert \) . This is the case when \(M\) does not contain type I nor type III \(_1\) factors as direct summands and it is false at least for the unique hyperfinite type III \(_1\) factor. We also characterize this property in terms of the existence of centrally symmetric curves in the unit sphere of \(M_\star \) of length \(4\) . An approximate result valid for all diffuse von Neumann algebras allows to show that the equation has solution for every element in the ultraproduct of preduals of diffuse von Neumann algebras and, in particular, the dual von Neumann algebra of such ultraproduct is diffuse. This shows that the Daugavet property and the uniform Daugavet property are equivalent for preduals of von Neumann algebras.     

Effects of sub-millimeter-bubble injection on transition to turbulence in natural convection boundary layer along a vertical plate in water

Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section.