The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutatio...The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.展开更多
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
Resonance may occur when the periods of incoming waves are close to the eigen-periods of harbor basin.The amplified waves by resonance in harbor will induce serious wave hazards to harbor structures and vehicles in it...Resonance may occur when the periods of incoming waves are close to the eigen-periods of harbor basin.The amplified waves by resonance in harbor will induce serious wave hazards to harbor structures and vehicles in it.Through traditional theoretical approaches,the eigen-periods of harbor basin with regular shapes can be obtained.In our study,we proposed a numerical model to simulate the behavior characteristics of the harbor waves.A finite difference numerical model based on the shallow water equations(SWE) is developed to simulate incoming tsunami and tidal waves.By analyzing the time series data of water surface wave amplitude variations at selected synthetic observation locations,we estimate the wave height and arrival time in coastal area.Furthermore,we use frequency spectrum analysis to investigate the natural frequencies from the data recorded at the synthetic observation stations.展开更多
基金Supported in part by the National natural Science Foundation of China under Grant No.10675170Major State Basic Research Developing Program under Gant No.2007CB815003
文摘The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
基金supported by the National Natural Science Foundation of China (Grant Nos.40574012 and 40676039)National Basic Research Program of China(Grant No. 2008CB425701)+1 种基金National High-tech R& D Program of China(Grant No. 2010AA012402)K. C. Wong Magna Fund in Ningbo University
文摘Resonance may occur when the periods of incoming waves are close to the eigen-periods of harbor basin.The amplified waves by resonance in harbor will induce serious wave hazards to harbor structures and vehicles in it.Through traditional theoretical approaches,the eigen-periods of harbor basin with regular shapes can be obtained.In our study,we proposed a numerical model to simulate the behavior characteristics of the harbor waves.A finite difference numerical model based on the shallow water equations(SWE) is developed to simulate incoming tsunami and tidal waves.By analyzing the time series data of water surface wave amplitude variations at selected synthetic observation locations,we estimate the wave height and arrival time in coastal area.Furthermore,we use frequency spectrum analysis to investigate the natural frequencies from the data recorded at the synthetic observation stations.
