Parallel ocean general circulation modeling

We have developed a global ocean model on the massively parallel CM-2 Connection Machine based on the Bryan-Cox-Semtner ocean general circulation model. This paper discusses the Connection Machine implementation of the model and its performance, as well as major changes that were made in the algorithms and numerical methods. In order to increase the parallel efficiency, we reformulated the barotropic equations to solve for the surface-pressure field rather than the volume-transport streamfunction. In addition to being more efficient, this method has several other advantages over the streamfunction formulation: (1) any number of islands can be included in the computational grid at no extra cost; (2) the model can handle steep gradients in the bottom topography; and (3) the free-surface height is a prognostic variable, which simplifies assimilation of altimetric data into the model. We have also developed a new parallelizable preconditioning method for the solution of the elliptic equation for the surface-pressure field. In order to use a standard conjugate gradient algorithm, an approximate-factorization technique is used to split off the Coriolis terms and obtain a symmetric operator. We then apply a symmetric local approximate-inverse operator as a preconditioning matrix, which is very effective in accelerating convergence to a solution.     

Causes and cures for the infinities in slow-motion expansions in general relativity

The causes of the divergent integrals arising in slow-motion expansions of the general relativistic field equations are studied and a remedy for them is suggested. This is done within the context of a model problem involving a coupled nonlinear scalar field and isotropic oscillator. The model is shown to give rise to divergent integrals directly attributable to the nonlinearity when the field is assumed to be analytic in a slowness parameter. Application of a nonregular perturbation approach which includes the method of matched asymptotic expansions is shown to eliminate the infinite contributions.Supported in part by The National Science Foundation under grant no. PH 79-15.     

Operator product expansions and composite field operators in the general framework of quantum field theory

The short distance behavior of field operator products is analyzed. It is shown that under certain conditions operator product expansions can be derived which give complete information on the short distance behavior and lead to the construction of composite field operators.Suported in parts by funds from the National Science Foundation Grant No. GP-25609.     

A tree formula for use in cluster expansions with general multibody interactions

In applications of statistical mechanics and quantum field theory one requires a formula for the activitiesA(P) that are determined by partition functions of a polymer system of the formZ(X)=expE(X). A simple general formula is given which generalizes the tree formula of Glimm, Jaffe, Spencer, Brydges and Federbush.     

Temperature-dependent third cumulant of tunneling noise

Poisson statistics predicts that the shot noise in a tunnel junction has a temperature independent third cumulant e(2)I, determined solely by the mean current I. Experimental data, however, show a puzzling temperature dependence. We demonstrate theoretically that the third cumulant becomes strongly temperature dependent and may even change sign as a result of feedback from the electromagnetic environment. In the limit of a noninvasive (zero-impedance) measurement circuit in thermal equilibrium with the junction, we find that the third cumulant crosses over from e(2)I at low temperatures to -e(2)I at high temperatures.     

Test for the cumulant approximation in the critical region

A cumulant approximation in wide use is tested, in the critical region, against a straightforward product-average decomposition approximation previously used in conjunction with a new integral representation for the Ising model. It is found that for the calculation of the transition temperature, the cumulant approximation is significantly inferior to the product-average approximation.     

Critical Binder cumulant of two-dimensional Ising models

The fourth-order cumulant of the magnetization, the Binder cumulant, is determined at the phase transition of Ising models on square and triangular lattices, using Monte Carlo techniques. Its value at criticality depends sensitively on boundary conditions, details of the clusters used in calculating the cumulant, and symmetry of the interactions or, here, lattice structure. Possibilities to identify generic critical cumulants are discussed.     

An idealized radiative transfer scheme for use in a mechanistic general circulation model from the surface up to the mesopause region

A new and numerically efficient method to compute radiative flux densities and heating rates in a general atmospheric circulation model is presented. Our method accommodates the fundamental differences between the troposphere and middle atmosphere in the long-wave regime within a single parameterization that extends continuously from the surface up to the mesopause region and takes the deviations from the gray limit and from the local thermodynamic equilibrium into account. For this purpose, frequency-averaged Eddington-type transfer equations are derived for four broad absorber bands. The frequency variation inside each band is parameterized by application of the Elsasser band model extended by a slowly varying envelope function. This yields additional transfer equations for the perturbation amplitudes that are solved numerically along with the mean transfer equations. Deviations from local thermodynamic equilibrium are included in terms of isotropic scattering, calculating the single scattering albedo from the two-level model for each band. Solar radiative flux densities are computed for four energetically defined bands using the simple Beer-Bougert-Lambert relation for absorption within the atmosphere. The new scheme is implemented in a mechanistic general circulation model from the surface up to the mesopause region. A test simulation with prescribed concentrations of the radiatively active constituents shows quite reasonable results. In particular, since we take the full surface energy budget into account by means of a swamp ocean, and since the internal dynamics and turbulent diffusion of the model are formulated in accordance with the conservation laws, an equilibrated climatological radiation budget is obtained both at the top of the atmosphere and at the surface.     

Electron scattering from nonlinear molecules using multicentre wavefunction expansions

Summary The scattering of slow electrons by polyatomic molecules is studied within a full quantum formulation of the problem, and the wavefunctions of the target molecular bound electrons are obtained from a multicentre expansion (MCE) of Gaussian-type orbitals (GTOs) within the single-determinant Hartree-Fock (HF)-SCF scheme. It is shown that the scattering calculations require the solution of radial coupled equations where the interaction is obtained as a further multipolar expansion at the target centre of mass (c.o.m.), while the relevant numerical procedures are discussed for systems like SiH₄, GeH₄ and CF₄. The ensuing interaction coefficients are used to carry out convergence studies of the scattering cross-sections, over a broad range of energies, in the case of silane targets. The results are found to be rapidly converging for such a system, while the different behaviour expected for other targets is also analysed and explained.     

A remark on truncation schemes of cumulant hierarchies

We discuss some problems obtained by truncating a cumulant hierarchy at ordern > 2. We show that such a truncation scheme is not consistent witha in its whole range of definition nonnegative probability function.     

Resonant state expansions of the continuum

It is shown that the set of bound states and single-pa tide esonances consisting of the outgoing solutions of the Schödinge equation can be used as a ep esentation to describe p ocesses taking place in the continuum part of nuclear spectra. This is the first thoough investigation of completeness properties using realistic nuclear wave functions.This work was supported in part by the OTKA Foundation Hungary (contract number 3010) and by the Swedish Natural Science Research Council.     

Plane-wave expansions of the optical field

Plane-wave expansions of the type introduced by Whittaker are compared with plane-wave expansions of the type introduced by Weyl for wave fields radiated by sources confined to finite space-time domains. The domains of validity and the plane-wave amplitudes are determined for both types of expansions.     

Determination of critical behaviour in lattice statistics from series expansions

A simple method is proposed for determining the critical point (μ) and given the critical exponent (γ) from terms of a series expansion for a restricted class of functions. The advantage of the method is that under certain reasonable assumptions it provides precise estimates for errors.     

国家气候中心大气环流模式冬季模式误差特征分析

本文利用1982—2010年国家气候中心第二代月动力延伸预测系统中大气环流模式(BCC_AGCM)的回报资料和美国国家环境预测中心和美国国家大气研究中心(NCEP/NCAR)再分析资料,分析了该模式对冬季气温预测的误差特征及其与外强迫的联系.结果表明模式能够在整体上较好地反映出欧亚区域冬季气温的变化趋势,能抓住东亚冬季风区气温年际变化的主要空间模态,对东亚冬季风区冬季气温具有一定的预报能力.预报误差的空间分布和时间演变特征的结果表明,误差在陆地大于海洋,高纬地区大于低纬地区,同时与海拔高度也有密切关系.预报误差的主要模态与一些关键区域的海温和海冰存在显著的相关性,表明模式对外强迫异常的响应能力存在缺陷.这为结合模式对关键区海温和海冰异常的响应能力,有针对性地改进模式对东亚冬季风区冬季气温的预测能力提供了依据.     

Application of the Monte Carlo method for evaluating the Niemeijer-van Leeuwen cumulant expansion

We show that the large cell size problem of the real space renormalization can be handled effectively by Monte Carlo methods. As a demonstration, the second-order cumulant expansion is calculated for the three-dimensional simple cubic Ising model, using a 3 × 3 × 3 cell.