Rhodium-Catalyzed Enantioselective Synthesis,Structures, and Properties of Single and Double Azahelicene-Like Molecules

The enantioselective synthesis of aza[6] and [7]helicene-like molecules have been achieved by the cationic rhodium(I)/axially chiral biaryl bisphosphine complex-catalyzed intramolecular [2+2+2] cycloaddition of cyanodiynes. This protocol was successfully applied to the diastereo- and enantioselective synthesis of an S-shaped double aza[6]helicene-like molecule with a high ee value of 89 %. Although no epimerization and racemization were observed in the double carbo[6]helicene-like molecule at 80 °C, epimerization and racemization of the double aza[6]helicene-like molecule proceeded at 80 °C. This double aza[6]helicene-like molecule showed good fluorescent quantum yields and chiroptical responses under both neutral and acidic conditions.     

Morphological change of crystalline polymer films by annealing: substrate‐ and heating/cooling‐rate‐dependent surface roughness

We study the morphological change of crystalline polymer films by annealing using atomic force microscope, X‐ray diffraction, and Fourier transform infrared spectroscopy techniques. As typical samples, we employ high‐density and low‐density polyethylene films prepared by the cast method. After annealing at 135 °C for 4 h, the surface roughness of polyethylene films by the atomic force microscope significantly increases, and the crystallite size by the X‐ray diffraction also shows some increase, while the Fourier transform infrared spectroscopy spectrum hardly exhibits any change. This can be well explained as a result of the growth of crystal structure by recrystallization during annealing. More interestingly, we find that the choice of the substrate and also the heating/cooling rates for annealing significantly influences the surface roughness of the films. Copyright © 2017 John Wiley & Sons, Ltd.     

Photodimerization of benzene -photochromism of layered dithiacyclophane-

A novel cage compound was obtained by irradiation of a quadruple-layered dithiacyclophane and showed thermally reverse reaction.     

Rank of 3-tensors with 2 slices and Kronecker canonical forms

Tensor type data are becoming important recently in various application fields. We determine the rank of a 3-tensor with 2 slices in comparison with its Kronecker canonical form over the complex and real number field.     

Twist decompositions of gluing homeomorphisms of planar Heegaard diagrams of genus two

We will give a very simple algorithm to decompose a gluing homeomorphism of a planar Heegaard diagram of genus two into Dehn twists associated with the canonical base.

     

Hydrodynamic limit for a spin system on a multidimensional lattice

Summary The hydrodynamic limit for a Markov process of [0, )-valued spin fields on a periodic multidimensional lattice is studied. In the process a positive real number, called energy, is attached to each site of the lattice and each couple of adjacent sites exchange thier energy by random amounts at random times. The law of the exchange is such that the sum of the total energy is conserved, and that the process is reversible and of gradient type for the energy distribution. We show that under diffusion type scaling of space and time, the macroscopic energy distribution converges to a deterministic limit which is characterized by a non-linear diffusion equation /t=2^–1P(), whereP is an increasing function which in a typical case equals const·².     

Crystal structures of calcium IV and V under high pressure

High-pressure phases IV and V of calcium discovered in 2005 have the highest superconducting transition temperature of 25 K among all the elements; however, their crystal structures have not been determined. From the x-ray powder diffraction data, both Ca IV and V have been found to form unique and complex structures with a coordination number of 7. They were confirmed to be identical to the theoretical models that were recently predicted [Ishikawa, Phys. Rev. B 77 020101(R) (2008)].     

Z(2) gauge neural network and its phase structure

We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable _Si=±1$S_i=\pm 1$ on the i$i$-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable _Jij=±1$J_{ij}=\pm 1$ describes a state of the synaptic connection between j$j$-th and i$i$-th neurons. The gauge symmetry allows for a self-coupling energy among _Jij$J_{ij}$’s such as _JijJjkJki$J_{ij}{J}_{jk}{J}_{ki}$, which describes reverberation of signals. Explicitly, we consider the three models; (I) an annealed model with full and partial connections of _Jij$J_{ij}$, (II) a quenched model with full connections where _Jij$J_{ij}$ is treated as a slow quenched variable, and (III) a quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of the reverberation term, and compare them with each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched models (II) and (III).     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.