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This paper estimates from below the attractor dimension of the dynamical system determined from a chemotaxis growth model which was presented by Mimura and Tsujikawa. It is already known that the dynamical system has exponential attractors and it is also known by numerical computations that the model contains various pattern solutions. This paper is then devoted to estimating the attractor dimension from below and in fact to showing that, as the parameter of chemotaxis increases and tends to infinity, so does the attractor dimension. Such a result is in a good correlation with the numerical results.
Effects of impurity (P and B) doping on the photoluminescence (PL) properties of Si nanocrystals (nc-Si) in SiO2 thin films are studied. It is shown that with increasing P concentration, PL intensity first increases and then decreases. In the P concentration range where PL intensity increases, quenching of the defect-related PL is observed, suggesting that dangling-bond defects are passivated by P doping. On the other hand, in the range where PL intensity decreases, optical absorptiondue to the intravalley transitions of free electrons generated by P doping appears. The generation of free electrons andthe resultant three-body Auger recombination of electron-hole pairs is considered to be responsible for theobserved PL quenching. In the case of B doping, the behavior is much different. With increasing B concentration, PL intensity decreases monotonously. By combining the results obtained for P and B doped samples, theeffects of donor and acceptor impurities on the PL properties of nc-Si are discussed.
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