No abstract

No abstract

Dynamic phase transition in the Ginzburg-Landau model of the anisotropic XY spin system in a rotating external field is studied. We observe several types of oscillations, limit cycles, quasiperiodic oscillations and chaotic motions. It is found that limit cycle oscillations can have the periodicity of multiple times of the period of the applied field and that the system shows two kinds of scenarios leading to the onset of quasiperiodic oscillations, i.e., the saddle-node and Hopf bifurcations. Furthermore, this paper reports the findings of chaotic behaviors in the context of dynamic phase transition and that there exist two types of chaos with and without a certain kind of symmetry.

In a previous paper, we reported that the reaction of cerium metal in 2‐methoxyethanol yielded a transparent colloidal solution of ultrafine (2 nm) ceria particles [M. Inoue, M. Kimura, T. Inui, Chem. Commun., 957 (1999)]. In this paper, the solvothermal reaction of other rare‐earth metals in 2‐methoxyethanol has been examined. Reactions of Sm and Yb metals in 2‐methoxyethanol at 300°C yielded transparent colloidal solutions of Sm2O3 and Yb2O3 particles. However, the reaction of rare‐earth metals of Y, Eu, Gd, and Tb in 2‐methoxyethanol at 300°C resulted in recovery of the starting materials. Transparent colloidal solutions of the oxides of these elements were obtained by reaction in the presence of a small amount of acetic acid. The solvothermal reaction of rare‐earth metals in 2‐aminoethanol was also examined.

We study pattern dynamics in a one-dimensional anisotropic XY model driven by a rotating external field. We find that the dynamical properties change qualitatively through a dynamic phase transition, which is a bifurcation of the spatially uniform states under a periodic external field. When two stable uniform limit cycles coexist, we observe a domain wall structure. Furthermore, there is a domain wall connecting domains of different phases of one limit cycle attractor. We find a periodic structure which is caused by the collapse of the domain wall. We derive approximate equations that describe the long time behavior of the domain walls and find that some results based on this approximation are qualitatively in agreement with those of numerical simulations. The properties of the interaction between the two domain walls depend on the symmetry of the wall. We observe a propagation of the phase wave in the quasi-periodic phase. This result implies the possibility of a phase description in non-autonomous systems. We find two chaotic patterns with different statistical properties in the symmetry-broken chaos region. * )