往复活塞式制冷压缩机性能系数的曲面回归方程

采用非线性二乘法对国产１２．５系列往复活塞式制冷压缩机的实测性能数据进行拟合，得出描述该系列制冷压缩机性能系数与运行工况之间相关关系的曲面回归方程，为制冷系统的数值计算、动态特性模拟和优化设计提供数学模型。     

Low correlation between redshift and intrinsic brightness for quasars and galaxies in a de sitter universe

Since the discovery of quasars, it has been recognized that these objects must have either an extraordinary intrinsic brightness or a nonlinear redshift. The most widely accepted current belief incorporates a linear (Hubble) redshift- distance relation and time evolution within a Big Bang model. We reconsider the possibility of a nonlinear (de Sitter) redshift-distance relation and find quasar intrinsic brightness to be not at all extraordinary. Given a de Sitter law, intrinsic brightness is found to be independent of redshift over five orders of magnitude.     

地形作用下有限振幅Rossby波的稳定性分析

本文用微分方程定性理论方法分析了地形对有限振幅Rossby波的稳定性影响。结果表明:地形北坡有利于波动出现不稳定,南坡使波动稳定;西坡使导式波动不稳定但使曳式波动稳定,东坡使导式波动稳定但使曳式波动不稳定。     

Stochastic analysis of spatial variability in unconfined groundwater flow

In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhars work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio.     

Mapping nonlinear shallow-water tides: a look at the past and future

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost’s complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions. While M can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems. In memory of Christian Le Provost     

Effect of perturbations on the non linear stability of triangular points in the restricted three-body problem with variable mass

The effect of small perturbations ε and ε ^′ in the Coriolis and the centrifugal forces, respectively on the nonlinear stability of the triangular points in the restricted three-body problem with variable mass has been studied. It is found that, in the nonlinear sense, the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios, which depend upon ε, ε ^′ and β, the constant due to the variation in mass governed by Jeans’ law.     

Linear and nonlinear vibration of non-uniform beams on two-parameter foundations using p-elements

A hierarchical finite element is presented for the geometrically nonlinear free and forced vibration of a non-uniform Timoshenko beam resting on a two-parameter foundation. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. With the enriching degrees of freedom, the accuracy of the computed results and the computational efficiency are greatly improved. The arc-length iterative method is used to solve the nonlinear eigenvalue equation. The computed results of linear and nonlinear vibration analyses show that the convergence of the proposed element is very fast with respect to the number of Legendre orthogonal polynomials used. Since the elastic foundation and the axial load applied at both ends of the beam affect the ratios of linear frequencies associated with the internal resonance, they influence the nonlinear vibration characteristics of the beam. The axial tensile stress of the beam in nonlinear vibration is investigated in this paper, and attention should be paid to the geometrically nonlinear vibration resulting in considerably large axial tensile stress in the beam.     

Experimental investigation of the harmonic generation by waves over a submerged plate

Experiments in a wave flume have been performed to analyse the nonlinear interaction between regular gravity waves and a submerged horizontal plate used as breakwater. A new method, based on the Doppler shift generated by a moving probes, has been used to discriminate the incident fundamental mode and the reflected fundamental mode. The relationships of the reflection and transmission coefficients to the wave number at different submergence depth ratios are presented. The accurate discrimination, by this method, of the phase-locked and free modes allows the quantification of the higher harmonics generated by the breakwater and the analysis of the nonlinear interaction between the waves and the submerged plate. The transfer of energy from the fundamental mode to higher harmonics is very large in the cases of small submergence depth ratios. The vortices produced at the edges take part in the production of higher harmonics by interaction with the free surface but involve, at the same time, a dissipation process that increases the efficiency of the breakwater.     

Forecast of the Decadal Average Sunspot Number

The forecast of the decadal average sunspot number (SN) becomes possible with an extension of telescopic observations based on proxy reconstructions using the tree ring radiocarbon data during the Holocene. These decadal numbers (SN_RC) provide a powerful statistic to verify the forecasting methods. Complicated dynamics of long-term solar activity and noise of proxy-based reconstruction make the one-step-ahead forecast challenging for any forecasting method. Here we construct a continuous data set of SN_RC which extends the group sunspot number and the international sunspot number. The known technique of nonlinear forecast, the local linear approximation, is adapted to estimate the coming SN. Both the method and the continuous data set were tested and tuned to obtain the minimum of a normalized average prediction error (E) during the last millennium using several past millennia as a training data set. E=0.58σ _D is achieved to forecast the SN successive differences whose standard deviation is σ _D=7.39 for the period of training. This corresponds to the correlation (r=0.97) between true and forecasted SN. This error is significantly smaller than the prediction error when the surrogate data were used for the training data set, and proves the nonlinearity in the decadal SN. The estimated coming SN is smaller than the previous one.     

Nonlinear Force-Free Modeling of Coronal Magnetic Fields. II. Modeling a Filament Arcade and Simulated Chromospheric and Photospheric Vector Fields

We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional, and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model. When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though, like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various codes will not necessarily converge to the correct, or even the same, solution. On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many steps described above.