A partial order in the knot table II

A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.     

Measurement of an Efimov trimer binding energy in a three-component mixture of 6Li

The binding energy of an Efimov trimer state was precisely determined via radio-frequency association. It is found that the measurement results shift significantly with temperature, but that the shift becomes negligible at the lowest temperature in our experiment. The shift-free part of the trimer binding energy reveals a significant deviation from the nonuniversal theory prediction based on a three-body parameter with a monotonic binding-energy dependence.     

Evolution of groups with a hierarchical structure

The universal occurrence of a hierarchical structure and its dynamic behavior in various types of group, living or abstract, are discussed. Here the word “group” refers not only to tangible aggregation but also to invisible aggregation of social psychological and of geopolitical meaning. The evolution of these groups is simulated using a model of agents distributed on the lattices of cellular grids. It is assumed that agents, fearing isolation, interact asymmetrically with each other with regard to exchange of “power”. As an indicator of hierarchy, the Gini coefficient is introduced. Example calculations are made for the aggregation, fusion and fission of animal groups, and for the appearance of a powerful empire and the rise and fall of supremacy. It is shown that such abstract objects evolve with time in accordance with the universal rules of groups common to birds and fish.     

Effects of loading conditions and temperature on environmental stress cracking of low-density polyethylene

Fracture mechanics was used to investigate the environmental stress cracking (ESC) of low density polyethylene (LDPE). Annealed and quenched samples were prepared; a single edge notch was made and the samples were fractured under constant load in a liquid methanol environment. The relation between the stress intensity factor K and the crack speed ? has been investigated. There is a large difference between annealed and quenched samples in the variation of this relation with temperature and applied load. The cause of this difference is discussed in detail. We propose that thermally activated molecular motion is essential to ESC of the annealed LDPE while stress concentration contributes markedly to ESC of the quenched LDPE.     

Solvent effect of fluorescence on/off switching of diarylethene linked to excited-state intramolecular proton transfer fluorophore

Efficient fluorescence on/off switching of a dyad consisting of a photochromic diarylethene and a fluorescence dye based on excited state intramolecular proton transfer (ESIPT) was designed and demonstrated. Diarylethenes linked to (2-(2-methoxy-5-methylphenyl)benzothiazol-6-yl)- and (2-(2-hydroxy-5-methylphenyl)benzothiazol-6-yl)-9,9-dioctylfluorene moieties (1a and 2a, respectively) exhibited fluorescence on/off switching upon alternating irradiation with ultraviolet and visible light in various solvents. The fluorescence on/off contrast of 2a was found to be higher than that of 1a in n-hexane because the overlap integral between the absorption spectrum of the diarylethene closed-ring form and the fluorescence spectrum of 2a is larger than that of 1a. Diarylethene 2a exhibited green fluorescence with large Stokes shift in n-hexane, which is ascribed to the ESIPT process from the enol form to the keto form. In contrast, the fluorescence of 2a in N,N-dimethylsulfoxide (DMSO) was mainly observed as blue fluorescence from enol form, while diarylethene 1a exhibited blue fluorescence in n-hexane and DMSO. The fluorescence on/off contrast of 2a in n-hexane was higher than that in DMSO because of the difference in the spectral overlaps in n-hexane and DMSO.