A new method to improve validity range of Lie canonical perturbation theory: with a central focus on a concept of non-blow-up region

Validity ranges of Lie canonical perturbation theory (LCPT) are investigated in terms of non-blow-up regions. We investigate how the validity ranges depend on the perturbation order in two systems, one of which is a simple Hamiltonian system with one degree of freedom and the other is a HCN molecule. Our analysis of the former system indicates that non-blow-up regions become reduced in size as the perturbation order increases. In case of LCPT by Dragt and Finn and that by Deprit, the non-blow-up regions enclose the region inside the separatrix of the Hamiltonian, but it may not be the case for LCPT by Hori. We also analyze how well the actions constructed by these LCPTs approximate the true action of the Hamiltonian in the non-blow-up regions and find that the conventional truncated LCPT does not work over the whole region inside the separatrix, whereas LCPT by Dragt and Finn without truncation does. Our analysis of the latter system indicates that non-blow-up regions do not necessarily cover the whole regions inside the HCN well. We propose a new perturbation method to improve non-blow-up regions and validity ranges inside them. Our method is free from blowing up and retains the same normal form as the conventional LCPT. We demonstrate our method in the two systems and show that the actions constructed by our method have larger validity ranges than those by the conventional and our previous methods proposed in Teramoto and Komatsuzaki (J Chem Phys 129:094302, 2008; Phys Rev E 78:017202, 2008).     

Transient bonds and chemical reactivity of molecules

Electron delocalization between the reagent and reactant molecules is the principal driving force of chemical reactions. It brings about the formation of new bonds and the cleavage of old bonds. By taking the aromatic substitution reaction as an example, we have shown the orbitals participating in electron delocalization. The interacting orbitals obtained are localized around the reaction sites, showing the chemical bonds that should be generated and broken transiently along the reaction path. By projecting a reference orbital function that has been chosen to specify the bond being formed on to the MOs of the reactant molecules, the reactive orbitals that are very similar to the interacting orbital have been obtained. The local potential of the reaction site for electron donation estimated for substituted benzene molecules by using these projected orbitals shows a fair correlation with the experimental scale of the electron-donating and -withdrawing strength of substituent groups. The reactivity is shown to be governed by local electronegativity and local chemical hardness and also by the localizability of interaction on the reaction site. © 1996 John Wiley & Sons, Inc.     

Chemical properties of water-soluble,nonionic azo compounds as initiators for emulsion polymerization

Four kinds of water-soluble, nonionic azo compounds were studied in terms of their decomposition rate and initiator efficiency in radical polymerization, and then used for emulsion polymerization. They had relatively low initiator efficiency from 0.09 to 0.46. It was attributed to the susceptibility to a cage effect, depending on their molecular size and hydrophobicity. Four azo compounds initiated emulsion polymerization but nonionic latex particles were not obtained unexpectedly. Methanol-containing medium results in the formation of a bimodal particle size distribution as well as a bimodal molecular weight distribution. © 1996 John Wiley & Sons, Inc.     

Facile synthesis of an ambient stable pyreno[4,5-b]pyrrole monoanion and pyreno[4,5-b:9,10-b′]dipyrrole dianion: from serendipity to design

The stability of singly or multiply negatively charged π-conjugated organic compounds is greatly influenced by their electronic delocalization. Herein, we report a strategic methodology for isolation of a mysterious compound. The isolated compounds, a pyreno[4,5-b]pyrrole monoanion and pyreno[4,5-b:9,10-b′]dipyrrole dianion, were highly stable under ambient conditions due to high delocalization of the negative charge over multiple electron deficient C N groups and pyrene π-scaffolds and allowed purification by column chromatography. To our knowledge, this is the first report on TCNE type reductive condensation of malononitrile involving pyrene di- and tetraone and formation of pyrenopyrrole. All compounds were characterized by spectroscopic methods and X-ray crystallography. A UV-vis spectroscopic study shows an intense low energy absorption band with a large absorption coefficient (ε).

An ambient stable pyreno[4,5-b]pyrrole monoanion and pyreno[4,5-b:9,10-b′]dipyrrole dianion have been isolated and characterized, showing a low energy intense absorption band with the absorption coefficient reaching 7.1 × 10⁴ dm³ mol⁻¹ cm⁻¹.     

Metal-to-Oxide Charge Transfer Observed by a Kelvin Probe Force Microscope

The charge transfer from a nanometer-sized transition metal particle to a catalyst support is thought to affect reactions over the metal surface. We propose the application of Kelvin probe force microscope, which is an extension of the atomic force microscope, to observe the charge transfer particle-by-particle. Our recent results on Na adatoms, Cl adatoms, Pt adatoms and particles, and Ni particles evaporated on TiO₂(110) are reviewed.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.