MIXED COMPATIBLE ELEMENT AND MIXED HYBRID INCOMPATIBLE ELEMENT VARIATIONAL METHODS IN DYNAMICS OF VISCOUS BAROTROPIC FLUIDS

This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.

Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea

A numerical study to a generalized Korteweg-de Vries (KdV) equation is adopted to model the propagation and disintegration of large-amplitude internal solitary waves (ISWs) in the South China Sea (SCS). Based on theoretical analysis and in situ measurements, the drag coefficient of the Chezy friction is regarded as inversely proportional to the initial amplitude of an ISW, rather than a constant as assumed in the previous studies. Numerical simulations of ISWs propagating from a deep basin to a continental shelf are performed with the generalized KdV model. It is found that the depression waves are disintegrated into several solitons on the continental shelf due to the variable topography. It turns out that the amplitude of the leading ISW reaches a maximum at the shelf break, which is consistent with the field observation in the SCS.Moreover, a dimensionless parameter defining the relative importance of the variable topography and friction is presented.

Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin（ICVEFG） method is presented for two-dimensional（2D） elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications

In this paper, an exponential inequality for the maximal partial sums of negatively superadditive-dependent （NSD, in short） random variables is established. By uSing the exponen- tial inequality, we present some general results on the complete convergence for arrays of rowwise NSD random variables, which improve or generalize the corresponding ones of Wang et al. [28] and Chen et al. [2]. In addition, some sufficient conditions to prove the complete convergence are provided. As an application of the complete convergence that we established, we further investigate the complete consistency and convergence rate of the estimator in a nonparametric regression model based on NSD errors.

GENERALIZED VARIATIONAL PRINCIPLES FOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.

On cubic Hermite coalescence hidden variable fractal interpolation functions

Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set, and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the short- coming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a gl-cubic Hermite in- terpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global G2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an al- ternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15（1） （2007）, pp. 41-53].

Possible Causes for the Persistence Barrier of SSTA in the South China Sea and the Vicinity of Indonesia

The persistence barrier refers to the lag correlation of sea surface temperature anomalies （SSTA） showing a rapid and significant decline in a specific season, regardless of the starting month. This implies that there is a decrease in forecast skill for SSTA in this specific season. This paper investigates the possible causes for the persistence barrier of SSTA in the South China Sea （SCS） and its adjacent regions from the perspective of interannuallinterdecadal time scales. The results show that the persistence barrier of SSTA exists not only in the SCS, but also in the vicinity of Indonesia south of the equator. The SCS barrier occurs around October-November, while the occurrence of the barrier in the Indonesia region is around November-December. For these two regions, the occurrence of the persistence barrier is closely associated with the interdecadal variability of SSTA, as well as the interannual variability. The persistence barriers in the SCS and the Indonesia region do not exist alone if the interdecadal variability is not considered, because SSTA have a short memory of less than 4 months, regardless of the starting month. Moreover, the influence of the interdecadal variability of SSTA on the persistence barrier of SSTA in the SCS and the Indonesia region may be associated with SSTA in the Indian Ocean and the western Pacific, but is not closely associated with the Pacific Decadal Oscillation. However, compared with the spring persistence barrier （SPB） of ENSO, the close relationship between the persistence barriers in the SCS and the Indonesia region and the interdecadal variability is unique, since the ENSO SPB is not significantly affected by such variability. In addition, although the persistence barriers in both the SCS and the Indonesia region are quite obvious in strong ENSO cases, the interdecadal variability of SSTA also plays a non-negligible role in this relationship.

Covariability of Subantarctic Mode Water and the Southern Branch of the Subtropical Indian Ocean Countercurrent in Argo Observations

The Subantarctic Mode Water(SAMW)forms in the deep mixed layer north of the Antarctic Circumpolar Current and spreads northward into the subtropical gyre.The subtropical South Indian Countercurrent(SICC)flows eastward on the north flank of the thick SAMW layer within 22°-32°S from south of Madagascar at around 25°S,50°E toward western Australia.The dynamical relation of the SAMW and the southern branch of the SICC(30°-32°S)is investigated in this work based on the monthly mean Argo data from 2004 to 2019.The physical properties of the SAMW and its pathway from the formation region are described.Most of the SAMW in the Indian Ocean sector originates from the deep mixed layers of the southeastern Indian Ocean(about 40°S,85°-105°E)and moves along the subtropical gyre.It takes around ten years to arrive east of Madagascar Island preserving its low potential vor-ticity characteristics.As a thick layer with homogeneous vertical properties,the SAMW forces the upper pycnocline to shoal,and the associated eastward shear results in the surface-intensified SICC.The SAMW forms a tongue-shaped thickness pattern,which influ-ences the southern branch of the SICC above the northern flank of the thickest SAMW layer between 24°S and 32°S.The seasonal,interannual,and decade variations of the southern branch of the SICC are closely related to the meridional gradient of the underlying SAMW thickness.The SAMW thickened and strengthened from 2005 to 2015,thereby anchoring a strengthened SICC.The interan-nual covariability of the SAMW and SICC further supports the SAMW’s role in driving SICC variability.

Signal difference-based deadband H_∞ control approach for networked control systems with limited resources

This paper investigates a signal difference-based dead- band H∞ control approach for networked control systems （NCSs） with limited resources. The effects of variable network-induced de- lays, sampling intervals and data transmitting deadbands are con- sidered simultaneously and the model of the NCS is presented. A Lyapunov functional is adopted, which makes full use of the network characteristic information including the bounds of net- work delay （BND）, the bounds of sampling interval （BSI） and the bounds of transmission deadband （BTD）. In the meanwhile, the new H∞ performance analysis and controller design conditions for the NCSs are proposed, which describe the relationship of BND, BSI, BTD and the system＇s performance. Three examples are used to illustrate the advantages of the proposed methods. The results have shown that the proposed method not only effectively reduces the data traffic, but also guarantees the system asymptotically sta- ble and achieves the prescribed H∞ disturbance attenuation level.

Application of Conditional Nonlinear Optimal Perturbation to Targeted Observation Studies of the Atmosphere and Ocean

This paper reviews progress in the application of conditional nonlinear optimal perturbation to targeted observation studies of the atmosphere and ocean in recent years, with a focus on the E1 Nifio-Southern Oscillation （ENSO）, Kuroshio path variations, and blocking events. Through studying the optimal precursor （OPR） and optimally growing initial error （OGE） of the occurrence of the above events, the similarity and localization features of OPR and OGE spatial structures have been found for each event. Ideal hindcasting experiments have shown that, if initial errors are reduced in the areas with the largest amplitude for the OPR and OGE for ENSO and Kuroshio path variations, the forecast skill of the model for these events is significantly improved. Due to the similarity between patterns of the OPR and OGE, additional observations implemented in the same sensitive region would help to not only capture the precursors, but also reduce the initial errors in the predictions, greatly increasing the forecast abilities. The similarity and localization of the spatial structures of the OPR and OGE during the onset of blocking events have also been investigated, but their application to targeted observation requires further study.

Comparison of winter wheat yield sensitivity to climate variables under irrigated and rain-fed conditions

Crop simulation models provide alternative, less time-consuming, and cost-effective means of deter- mining the sensitivity of crop yield to climate change. In this study, two dynamic mechanistic models, CERES （Crop Environment Resource Synthesis） and APSIM （Agricultural Production Systems Simulator）, were used to simulate the yield of wheat （Triticum aestivum L.） under well irrigated （CFG） and rain-fed （YY） conditions in relation to different climate variables in the North China Plain （NCP）. The study tested winter wheat yield sensitivity to different levels of temperature, radiation, precipitation, and atmospheric carbon dioxide （COa） concentration under CFG and YY conditions at Luancheng Agro-ecosystem Experimental Stations in the NCR The results from the CERES and APSIM wheat crop models were largely consistent and suggested that changes in climate variables influenced wheat grain yield in the NCR There was also significant variation in the sensitivity of winter wheat yield to climate variables under different water （CFG and YY） conditions. While a temperature increase of 2℃ was the threshold beyond which temperature negatively influenced wheat yield under CFG, a temperature rise exceeding 1℃ decreased winter wheat grain yield under YY. A decrease in solar radiation decreased wheat grain yield under both CFG and YY conditions. Although the sensitivity of winter wheat yield to precipitation was small under the CFG, yield decreased significantly with decreasing precipitation under the rain- fed YY treatment. The results also suggest that wheat yield under CFG linearly increased by ≈ 3.5% per 60 ppm （parts per million） increase in CO2 concentration from 380 to560ppm, and yield under YY increased linearly by ≈ 7.0% for the same increase in CO2 concentration.

Semi-stable distributions in free probability theory

Semi-stable distributions, in classical probability theory, are characterized as limiting distributions of subsequences of normalized partial sums of independent and identically distributed random variables. We establish the noncommutative counterpart of semi-stable distributions. We study the characterization of noncommutative semi-stability through free cumulant transform and develop the free semi-stability and domain of semi-stable attraction in free probability theory.