Relaxation mode analysis of nonlinear birth and death processes

Nonlinear birth and death processes with one variable are considered. The general master equations describing these processes are analyzed in terms of their eigenmodes and eigenvalues using the method of a WKB approximation. Formulas for the density of eigenstates are obtained. The lower lying eigenmodes are calculated to investigate long-time relaxation, such as relaxations of metastable and unstable states. Anomalous accumulation of the lower lying eigenvalues is shown to exist when the system is infinitesimally close to a critical or marginal state. The general results obtained are applied to some instructive examples, such as the kinetic Weiss-Ising model and a stochastic model of nonlinear chemical reactions.The work at UCSD was supported in part by the National Science Foundation under Grants MPS72-04363A03 and CHE75-20624.Adapted from the author's Ph.D. dissertation at University of Tokyo, December 1974.     

Dynamic mechanical behavior of ultradrawn polyethylene films produced by gelation/crystallization from solution

This paper is concerned with the temperature dependence of mechanical properties of ultradrawn polyethylene in terms of storage modulus E' and loss factor tan by the measurement of the complex dynamic tensile modulus over ranges of temperature from 20 to 140 C. Interestingly, E' of a specimen with drawn ratio of 300 is about 120 GPa at 140 C, when the measurement is carried out at a frequency of 100 Hz. This is a very high value. In addition, the drawn specimens were irradiated to try to produce ultra-drawn polyethylene films with more excellent mechanical and thermal properties. However, the melting peak shifts to a lower temperature with increasing radiation dose. This result is probably attributed to the considerably radiation-induced scission of extended chains constructing crystals.     

A possible correlation between a Jahn-Teller coupling and a Raman scattering

It has been shown how the Raman line of a degenerate vibration can be caused by a vibronic coupling in a degenerate electronic excited state. Such a vibronic coupling is known to cause a distortion in the equilibrium conformation of the molecule (Jahn-Teller distortion) from the symmetrical conformation, and the Raman scattering tensor is found to be calculated by the use of the amount (δ) of this distortion as an empirical parameter. It has been suggested that some of the Raman lines for the degenerate stretching vibrations, which become stronger with the exciting frequency, in some molecules, are caused by such Jahn-Teller couplings. For the intensity of the Raman line at 887 cm^?1 of the degenerate stretching vibration of chromate anion, a slightly more detailed examination has been made, and the amount of the Jahn-Teller distortion in a $\text{B}\text{?}$ (T₂) electronic state has been estimated to be 0.2₀ Å amu^1/2 along the normal coordinate of this vibration.     

Numerical predictions of three-dimensional flow in a ventilated room using turbulence models

A three-dimensional recirculation flow in a ventilated room was predicted by the numerical methods in which the turbulence models are applied. The predicted results are compared with the experimental results obtained in a model room in order to estimate the practical utilities of such methods from the viewpoint of engineering. Taking account of the practicability of prediction method which the engineers regard as important, two turbulence models were selected and they were incorporated into the numerical prediction methods respectively. One is the two-equation model, in which transport equations of turbulence energy and its rate of dissipation are adopted. The other is the Deardoff's model, in which the subgrid scale eddy coefficient is utilized. The prediction was made by each numerical method. Consequently, no noticeable difference is recognized between both predicted results. Each result is compared with the experimental results. Generally speaking, each agreement is good with regard to the mean velocity. Thus we can conclude that the numerical method using the two-equation model has more practical utility than that using Deardoff's model, because it can give the solutions in a shorter computer time.