There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
Tidal rivers are intrinsically complex because tidal propagation is influenced by river discharge. This study aims to examine the seasonal variation of tidal prism and energy variance in the tidal river of the Changji...Tidal rivers are intrinsically complex because tidal propagation is influenced by river discharge. This study aims to examine the seasonal variation of tidal prism and energy variance in the tidal river of the Changjiang(Yangtze) River estuary in China. In order to quantify the behaviour of river and tide,we use numerical modelling that has been validated using measured data. We conduct our analysis by quantifying the discharge and energy variance in separate components for both the river and the tide,during wet and dry seasons. We note various definitions of tidal prism and explore the difference between tidal discharge on the flood and ebb and tidal storage volume. The results show that the river discharge attenuates the tidal motion and reduces the tidal flood discharge but the tidal storage volume is approximately constant with different riverine discharge since part of the fresh water discharge is intercepted and captured in the estuary due to the backwater effect. It appears that the tidal discharge adjusts according to the variation of river discharge to keep a constant tidal storage volume. An analysis of the hydraulics shows that the transition from tidal dominance(at the mouth) to river dominance(upstream) depends on the location of tidal current reversal which varies from wet season to dry season. Duringthe wet season,the Changjiang River estuary is totally dominated by energy from fresh water discharge.展开更多
Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscilla...Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.展开更多
We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's appro...We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities(large ball probabilities) for general Gaussian random variables in Banach spaces. As applications,explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.展开更多
文摘There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
基金Supported by the National Basic Research Program of China(973 Program)(No.2010CB951204)the National Natural Science Foundation of China(No.44107180)the 111 Project(No.B08022)
文摘Tidal rivers are intrinsically complex because tidal propagation is influenced by river discharge. This study aims to examine the seasonal variation of tidal prism and energy variance in the tidal river of the Changjiang(Yangtze) River estuary in China. In order to quantify the behaviour of river and tide,we use numerical modelling that has been validated using measured data. We conduct our analysis by quantifying the discharge and energy variance in separate components for both the river and the tide,during wet and dry seasons. We note various definitions of tidal prism and explore the difference between tidal discharge on the flood and ebb and tidal storage volume. The results show that the river discharge attenuates the tidal motion and reduces the tidal flood discharge but the tidal storage volume is approximately constant with different riverine discharge since part of the fresh water discharge is intercepted and captured in the estuary due to the backwater effect. It appears that the tidal discharge adjusts according to the variation of river discharge to keep a constant tidal storage volume. An analysis of the hydraulics shows that the transition from tidal dominance(at the mouth) to river dominance(upstream) depends on the location of tidal current reversal which varies from wet season to dry season. Duringthe wet season,the Changjiang River estuary is totally dominated by energy from fresh water discharge.
文摘A new dispersive relation is found and a half-pow tormulas for the generalize Miodek equation under the deeaying conditions at infinity are obtained.
基金supported by the National Natural Science Foundation of China (Grant No. 50595412)the National Basic Research Program of China ("973" Program) (Grant No. 2009CB219700)
文摘Sensitivities of eigen-solutions to control variables play an important role in microgrid studies,such as coordinated optimal design of controllers and parameters,robust stability analysis on control variables,oscillation modes analysis on a system,etc.Considering the importance of sensitivities and the complexity of state matrix in a microgrid,parameter perturbations are utilized in this paper to analyze the construction characteristics of state matrix.Then,the sensitivities of eigenvalues and eigenvectors to control variables are obtained based on the first-order matrix perturbation theory,which makes the complex derivations of sensitivity formulas and repeated solutions of eigenvalue problem unnecessary.Finally,the effectiveness of the matrix perturbation based approach for sensitivity calculation in a microgrid is verified by a numerical example on a low-voltage microgrid prototype.
基金supported by the Simons Foundation(Grant No.246211)
文摘We obtain new upper tail probabilities of m-times integrated Brownian motions under the uniform norm and the Lp norm. For the uniform norm, Talagrand's approach is used, while for the Lp norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities(large ball probabilities) for general Gaussian random variables in Banach spaces. As applications,explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of m-times integrated Brownian motions are presented as well.
