高石 武史

Two examples of extention of crack growth model with phase field approach are derived. A crack growth model for visco-elastic material is introduced from exctended free energy which add effect of Maxwell fluid. Another model with effect of H-embrittlement is introduced by adding some equations. Ability of phase field model which can describe crack growth phenomena of various material is shown.

2次元等方弾性体からなる平板の面外変形における亀裂進展を記述するフェーズフィールドモデルを提案する．このモデルは Francfort-Marigo の提案したエネルギーを元に、正規化されたエネルギーの勾配流として導出される．このモデルでは面の変位と亀裂領域を表すフェーズフィールドという2つのスカラー変数に対する反応拡散方程式になっており，既存の数値計算スキームでの解析が容易であるのみならず，理論解析から亀裂進展に関する多くの知見が得られることが期待される．

A complete classification of dynamics of a population of a inhibitory pulse-coupled oscillators is presented. The model is based on the work of Mirollo and Strogatz, but our model has an inhibitory coupling between oscillators which makes a sharp contrast with the dynamics of the above authors' model. The main result is that for a large class of initial conditions, the population approaches a periodic state in which all the oscillators keep finite size of phase difference (we call it "phase locking solution" here). For the remaining class of initial data except for nongeneric ones, it evolves to a periodic state with a cluster or a synchronous state depending on a size of cluster. The criterion for the classification is explicitly given and can be judged easily only by the initial condition.