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Multistable Spatiotemporal Dynamics in the Driven Frenkel-Kontorova Lattice

Communications in Theoretical Physics 2001年第7期36卷 37-43页

作者： ZHENG Zhi-Gang Department of Physics Beijing Normal University Beijing 100875 China

Spatiotemporal dynamics of the damped dc-driven Frenkel-Kontorova lattice is studied. Multistable topologies are shown. Intermittency of the dynamical contraction factor is found, and this behavior is a consequence of the collisions of kinks and antikinks. Fast kinks and antikinks are unstable. The transition from the localized kink to the whirling mode is found to be a temporal bifurcation cascade of generations of kink-antikink pairs and the collision-induced avalanche dynamics. Noise-induced topology transition is observed and discussed.

关键词： Frenkel-Kontorova model, kink-antikink pair, dynamical contraction factor

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Dirac structures on protobialgebroids

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Science China Mathematics 2006年第10期49卷 1341-1352页

作者： YIN Yanbin HE Longguang LMAM Capital Normal University Beijing 100037 China LMAM Capital Normal University Beijing 100037 China

Protobialgebroids include several kinds of algebroid structures such as Lie algebroid,Lie bialgebroid, Lie quasi-bialgebroid, etc. In this paper, the Dirac theories are generalized from Lie bialgebroid to protobialgebroid. We give the integrable conditions for a maximally isotropic subbundle being a Dirac structure for a protobialgebroid by the notion of a characteristic pair. From the integrable conditions, we found out that the Dirac structure has closed relations with the twisting of a protobialgebroid. At last, some special cases of the Dirac structures for protobialgebroids are discussed.

关键词： Lie bialgebroid, protobialgebroid, characteristic pair, Courant algebroid,twisted Poisson manifold, supermanifold.

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Global behavior of gear system using mixed cell mapping

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Science China(Physics,Mechanics & Astronomy) 2004年第Z1期47卷 113-119页

作者： SHEN Yunwen LIU Mengjun DONG Haijun Northwestern Polytechnical University Xi'an 710072 China Northwestern Polytechnical University Xi'an 710072 China Northwestern Polytechnical University Xi'an 710072 China

In some mechanical nonlinear systems, the transient motion will be undergoing a very long process and the attractor-basin boundaries are so complicated that some difficulties occur in analyzing the system global behavior. To solve this problem a mixed cell mapping method based on the point mapping and the principle of simple cell mapping is developed. The algorithm of the mixed cell mapping is studied. A dynamic model of a gear pair is established with the backlash, damping, transmission error and the time-varying stiffness taken into consideration. The global behaviors of this system are analyzed. The coexistence of the system attractors and the respective attractor-basin of each attractor with different parameters are obtained, thus laying a theoretical basis for improvement of the dynamic behaviors of gear system.

关键词： mixed cell mapping, global analysis, attractor-basin, gear pair, nonlinear dynamic system.

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The structure of blocks

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Science China Mathematics 2002年第12期45卷 1578-1581页

作者：王立中 Department of Mathematics Beijing University Beijing China

In this paper, we focus on the structure of p-blocks with defect group satisfying some specialcondition. These special conditions include: two elements of the defect group are conjugate to each other indefect D if and only if they are conjugate to each other in G; the number of conjugacy classes whose p-partis contained in P by conjugacy is not larger than |P|.

关键词： block, b-Brauer pair, defect group, conjugation.

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