The stochastic Boltzmann equation and hydrodynamic fluctuations

Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation.     

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.     

Energy loss of 1000 keV electrons in thin silicon crystals as measured by high voltage electron microscopy

Abstract

Energy loss spectra of 1000 keV electrons transmitted by [111]-: riented thin silicon crystals were observed by an energy analyzer attached to the HVEM. The crystals were set to the systematic 220 Bragg reflection. Measurements were made for crystal thickness ranging from 1000 to 10,000 Å, which were determined by observations of pendellösung fringes.

Results were analyzed with Landau's transport equation, giving the : onclusion that the loss probability, which is the reciprocal of the mean free path, is 0.52 ± 0.02 × 10^?3 A^?1 for plasmon excitation and 1.50 ± 0.02 × 10^?3 A^?1 for L-electron excitation.     

Resistivity control of sputtered amorphous-silicon by ion-implantation

The resistivity of a hydrogenated sputtered amorphous-silicon is controlled by using room temperature implantation of P⁺. It is found that the defects produced by implantation can be minimized by annealing at 300°C in an H₂ atmosphere, and also found that there is a threshold implanted dose, beyond which the resistivity begins to be controlled by changing the dose.     

The resonant secondary emission of the F center in alkali halides

The secondary radiation after resonant excitation of F center and its linear polarization P correlated to the polarization of resonant light have been measured for five alkali halides at low temperatures. In KC1, the spectrum of P over the whole Stokes region is divided into three successive regions, the depolarization range at the one-phonon Raman scattering, the near plateau range, and the depolarization range down to vanishing. The former two have common relevance to resonant energy and symmetries of coupled phonons. These relevances are interpreted adopting a configuration coordinate model for 2s- and 2p-like excited states.     

High pressure Raman study on the local structure of 1-ethyl-3-methylimidazolium tetrafluoroborate

We have investigated the pressure-induced Raman spectral changes of 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF₄]). We found that [emim][BF₄] did not crystallize up to 1.2 GPa. The Raman CH stretching spectra arising from the CH₃ groups of the ethyl-chain and the CH₃ group adjacent to the imidazolium-ring in [emim]⁺ cation largely changed against pressure. Moreover, the Raman intensity of the CH₂ (N) bending band arising from the alkyl-chain drastically changes with increasing pressure, but that of the imidazolium-ring in-plane bending band arising from the imidazolium-ring is independent of pressure. Our results show that the environment around the alkyl-chain of [emim][BF₄] is largely perturbed rather than that around the imidazolium-ring upon compression.     

McMullen's conditions and some lower bounds for general convex polytopes

We give a lower bound for the number of vertices of a generald-dimensional polytope with a given numberm ofi-faces for eachi = 0,..., d/2 – 1. The tightness of those bounds is proved using McMullen's conditions. Form greater than a small constant, those lower bounds are attained by simpliciali-neighbourly polytopes.     

Properties of holomorphic Wiener functions —skeleton,contraction, and local Taylor expansion

Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education     

Heat capacities of copper(II) formate tetrahydrate and tetradeuterate: A comparative study of phase transitions in layer hydrate crystals

The heat capacities of copper(II) formate tetrahydrate and tetradeuterate have been measured from 12 to 300 K with an adiabatic calorimeter. They have sigmoidal temperature dependence except near the antiferroelectric-paraelectric transition temperatures, 235.78 ± 0.05 K and 245.64 ± 0.05 K, respectively. The corresponding enthalpy changes are 836.0 ± 1.0 J mol^?1 and 936.9 ± 0.5 J mor^?1. The entropy changes are 3.546 ± 0.005 JK^?1mol^?1 and 3.814 ± 0.002 JK^?1 mol^?1. The heat capacities are larger in the high temperature phase than in the low temperature phase, the difference amounting to 5.74 JK^?1 mol^?1 and 7.15 JK^?1 mol^?1 for the hydrate and the deuterate, respectively. The heat capacity anomaly is compared with those in tin(II) chloride dihydrate and potassium hexacyanoferrate trihydrate and discussed in relation to the structure of the hydrogen bond networks in these substances. The discussion is extended to include possible properties of the hydrogen bond frameworks in ices I_h and II.     

Waveguide holograms: A new approach to hologram integration

A new class of holography is proposed, in which (1) the evanescent part of a guided wave, or (2) the guided wave in a thin-film hologram is utilized as the reference wave and/or the illuminating one. The hologram was designated as “wave-guide hologram” and has advantages in the possibility of integration, wide field of view, and compactness and high reliability of the reconstructing system. The possibility of the waveguide hologram has been proved through reconstruction experiments with a guided wave of a waveguide hologram recorded with a plane reference wave.