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Pole-Based Approximation of the Fermi-Dirac Function

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 729-742页

作者： Lin LIN Jianfeng LU Lexing YING Weinan E dedicated to professor andrew majda on the Occasion of his 60th birthday

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. they are of great interest for electronic structure calculations.

关键词： Contour integral Fermi-Dirac function Rational approximation

Ocean-Atmosphere Interaction in the Lifecycle of ENSO:the Coupled Wave Oscillator

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 715-728页

作者： Jialin LIN dedicated to professor andrew majda on the Occasion of his 60th birthday

To explain the oscillatory nature of E1 Nino/Southern Oscillation （ENSO）, many ENSO theories emphasize the free oceanic equatorial waves propagating/reflecting within the Pacific Ocean, or the discharge/recharge of Pacific-basin-averaged ocean heat content. ENSO signals in the Indian and Atlantic oceans are often considered as remote response to the Pacific SST anomaly through atmospheric teleconnections. This study investigates the ENSO life cycle near the equator using long-term observational datasets. Space-time spectral analysis is used to identify and isolate the dominant interannual oceanic and atmospheric wave modes associated with ENSO. Nino3 SST anomaly is utilized as the ENSO index, and lag-correlation/regression are used to construct the composite ENSO life cycle. the propagation, structure and feedback mechanisms of the dominant wave modes are studied in detail. the results show that the dominant oceanic equatorial wave modes associated with ENSO are not free waves, but are two ocean-atmosphere coupled waves including a coupled Kelvin wave and waves are not confined only to the Pacific a coupled equatorial Rossby （ER） wave. these Ocean, but are of planetary scale with zonal wavenumbers 1-2, and propagate all the way around the equator in more than three years, leading to the longer than 3-year period of ENSO. When passing the continents, they become uncoupled atmospheric waves. the coupled Kelvin wave has larger variance than the coupled ER wave, making the total signals dominated by eastward propagation. Surface zonal wind stress （x） acts to slow down the waves. the two coupled waves interact with each other through boundary reflection and superposition, and they also interact with an off-equatorial Rossby wave in north Pacific along 15N through boundary reflection and wind stress forcing. the precipitation anomalies of the two coupled waves meet in the eastern Pacific shortly after the SST maximum of ENSO and excite a dry atmospheric Kelvin wave which

关键词： ENSO Ocean-atmosphere interaction Equatorial waves

Approximating Stationary Statistical Properties

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Chinese Annals of Mathematics,Series B 2009年第6期30卷 831-844页

作者： Xiaoming WANG dedicated to professor andrew majda on the Occasion of his 60th birthday with Admiration and Friendship）

It is well-known that physical laws for large chaotic dynamical systems are revealed *** times these statistical properties of the system must be approximated *** main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems *** result on temporal approximation is a recent finding of the author,and the result on spatial approximation is a new *** to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are also discussed.

关键词： Stationary statistical property Invariant measure Global attractor Dissipative system Time discretization Spatial discretisation Uniformly dissipative scheme Infinite Prandtl number model for convection Barotropic quasi-geostrophic equations