Instability of Turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (Turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.Comment: This is a new version of the paper. Presentation of results was essentially revised according to referee suggestion

伊勢地域における中央構造線の地表トレースの決定と周辺地域におけるジオツーリズムへの利活用

早大学位記番号:新7814早稲田大

A Comparative Study of the Formation of Contracts in Japanese, English, and German Law

The basic elements of a contract, namely, offer and acceptance, the intention to be bound, and consideration, and requirements of form found in English, German, and Japanese law are compared against the background of their historical development, the legal consciousness and practices existing in these countries. In this way, awareness is built both of the theoretical or practical differences and the underlying socio-cultural reasons. This in turn aids in the comprehension of why certain variations exist, which, although sometimes deceptively small, may have great importance for contracting in practice.PublishedThe basic elements of a contract, namely, offer and acceptance, the intention to be bound, and consideration, and requirements of form found in English, German, and Japanese law are compared against the background of their historical development, the legal consciousness and practices existing in these countries. In this way, awareness is built both of the theoretical or practical differences and the underlying socio-cultural reasons. This in turn aids in the comprehension of why certain variations exist, which, although sometimes deceptively small, may have great importance for contracting in practice

Sub-6 optical-cycle Kerr-lens mode-locked Tm:Lu2O3 and Tm:Sc2O3 combined gain media laser at 2.1 μm

We present a combined gain media Kerr-lens mode-locked laser based on a Tm:Lu2O3 ceramic and a Tm:Sc2O3 single crystal. Pulses as short as 41 fs, corresponding to less than 6 optical cycles, were obtained with an average output power of 42 mW at a wavelength of 2.1 μm and a repetition rate of 93.3 MHz. Furthermore, a maximum average power of 316 mW with a pulse duration of 73 fs was achieved