Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process an...Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.展开更多
We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is c...We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.展开更多
By the inversion method of uneven slippage of faults in the depths(Liu et al ., 1995) and using the crustal deformation data of six phases, the movement states of seismic fault of the Tangshan earthquake in five ti...By the inversion method of uneven slippage of faults in the depths(Liu et al ., 1995) and using the crustal deformation data of six phases, the movement states of seismic fault of the Tangshan earthquake in five time periods before, during and after that earthquake are computed. The result of computation has revealed the movement process of seismic fault, during which the fault moved at an increasing rate before the quake, slipped suddenly during the quake, and became relaxed, adjusted and stabilized gradually after the quake. Moreover, the recurrence period of earthquakes in Tangshan is computed using the relation that the slippage of seismic fault bears with strain energy.展开更多
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
For the two main recurrence behaviors of segment-rupturing earthquakes on active faults of the Chinese mainland,this paper establishes corresponding empirical distributions forearthquake recurrence interval. The resul...For the two main recurrence behaviors of segment-rupturing earthquakes on active faults of the Chinese mainland,this paper establishes corresponding empirical distributions forearthquake recurrence interval. The results show that, for the time-predictable recurrence, the normalized recurrence interval, T/Tt, obeys very well the lognormal distributions: LN (μ1=0.00, σ21 =0. 152), where, T is an observed recurrence interval, and Tt is the average recurrence interval that is correlative with the size of the preceding event. For the quasi-periodic recurrence, the normalized recurrence interval, T/T, follows the lognormal distribution : LN(μq=0.00, σ2q=0.242), where, T is the median of recurrence intervals for various cycles. A statistical test suggests that, there is no significant difference between the latter distribution, built by this paper, and the recurrence interval distribution for the characteristic earthquakes of the Circum-Pacific Plate boundaries (NB model). Accordingly, this paper combines these two distributions into one and obtains a more stable lognormal distribution :LN (μ = 0.00, σ2 = 0.222), for the quasi-periodic recurrence interval.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41106001)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100094110016)+1 种基金the Special Research Funding of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2009585812)the Priority Academic Program Development of Jiangsu Higher Education Institutions (Coastal Development and Conservancy)
文摘Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.
基金supported by the Ministry of Science and Technology of Taiwan,China(Grant Nos.NSC-99-2112-M-032-002-MY3 and NSC 102-2112-M-032-003-MY3)the National Center for Theoretical Sciences(North)(NCTS-n)of China
文摘We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.
文摘By the inversion method of uneven slippage of faults in the depths(Liu et al ., 1995) and using the crustal deformation data of six phases, the movement states of seismic fault of the Tangshan earthquake in five time periods before, during and after that earthquake are computed. The result of computation has revealed the movement process of seismic fault, during which the fault moved at an increasing rate before the quake, slipped suddenly during the quake, and became relaxed, adjusted and stabilized gradually after the quake. Moreover, the recurrence period of earthquakes in Tangshan is computed using the relation that the slippage of seismic fault bears with strain energy.
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
文摘For the two main recurrence behaviors of segment-rupturing earthquakes on active faults of the Chinese mainland,this paper establishes corresponding empirical distributions forearthquake recurrence interval. The results show that, for the time-predictable recurrence, the normalized recurrence interval, T/Tt, obeys very well the lognormal distributions: LN (μ1=0.00, σ21 =0. 152), where, T is an observed recurrence interval, and Tt is the average recurrence interval that is correlative with the size of the preceding event. For the quasi-periodic recurrence, the normalized recurrence interval, T/T, follows the lognormal distribution : LN(μq=0.00, σ2q=0.242), where, T is the median of recurrence intervals for various cycles. A statistical test suggests that, there is no significant difference between the latter distribution, built by this paper, and the recurrence interval distribution for the characteristic earthquakes of the Circum-Pacific Plate boundaries (NB model). Accordingly, this paper combines these two distributions into one and obtains a more stable lognormal distribution :LN (μ = 0.00, σ2 = 0.222), for the quasi-periodic recurrence interval.
