Adaptive and local analysis of climate data

This paper focuses on how to extract physically meaningful information from climate data,with emphases placed on adaptive and local analysis. It is argued that many traditional statistical analysis methods with rigorous mathematical footing may not be efficient in extracting essential physical information from climate data;rather,adaptive and local analysis methods that agree well with fundamental physical principles are more capable of capturing key information of climate data. To illustrate the improved power of adaptive and local analysis of climate data,we also introduce briefly the empirical mode decomposition and its later developments.

Shear wave splitting analysis of local earthquakes from dense arrays in Shimian,Sichuan

The Shimian area of Sichuan sits at the junction of the Bayan Har block.Sichuan-Yunnan rhombic block,and Yangtze block,where several faults intersect.This region features intense tectonic activity and frequent earthquakes.In this study,we used local seismic waveform data recorded using dense arrays deployed in the Shimian area to obtain the shear wave splitting parameters at 55 seismic stations and thereby determine the crustal anisotropic characteristics of the region.We then analyzed the crustal stress pattern and tectonic setting and explored their relationship in the study area.Although some stations returned a polarization direction of NNW-SSE.a dominant polarization direction of NW-SE was obtained for the fast shear wave at most seismic stations in the study area.The polarization directions of the fast shear wave were highly consistent throughout the study-area.This orientation was in accordance with the direction of the regional principal compressive stress and parallel to the trend of the Xianshuihe and Daliangshan faults.The distribution of crustal anisotropy in this area was affected by the regional tectonic stress field and the fault structures.The mean delay time between fast and slow shear waves was 3.83 ms/km.slightly greater than the values obtained in other regions of Sichuan.This indicates that the crustal media in our study area had a high anisotropic strength and also reveals the influence of tectonic complexity resulting from the intersection of multiple faults on the strength of seismic anisotropy.

LOCAL ANALYSIS OF THE FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE TIME-DEPENDENT SINGULARLY PERTURBED PROBLEM

In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.

Local Analysis, Cardinality, and Split Trick of Quasi-biorthogonal Frame Wavelets

The notion of quasi-biorthogonal frame wavelets is a generalization of the notion of orthog- onal wavelets. A quasi-biorthogonal frame wavelet with the cardinality r consists of r pairs of functions. In this paper we first analyze the local property of the quasi-biorthogonal frame wavelet and show that its each pair of functions generates reconstruction formulas of the corresponding subspaces. Next we show that the lower bound of its cardinalities depends on a pair of dual frame multiresolution analyses deriving it. Finally, we present a split trick and show that any quasi-biorthogonal frame wavelet can be split into a new quasi-biorthogonal frame wavelet with an arbitrarily large cardinality. For generality, we work in the setting of matrix dilations.

Mesh Smoothing Method Based on Local Wave Analysis

As the mesh models usually contain noise data,it is necessary to eliminate the noises and smooth the mesh.But existed methods always lose geometric features during the smoothing process.Hence,the noise is considered as a kind of random signal with high frequency,and then the mesh model smoothing is operated with signal processing theory.Local wave analysis is used to deal with geometric signal,and then a novel mesh smoothing method based on the local wave is proposed.The proposed method includes following steps：Firstly,analyze the principle of local wave decomposition for 1D signal,and expand it to 2D signal and 3D spherical surface signal processing;Secondly,map the mesh to the spherical surface with parameterization,resample the spherical mesh and decompose the spherical signals by local wave analysis;Thirdly,propose the coordinate smoothing and radical radius smoothing methods,the former filters the mesh points＇ coordinates by local wave,and the latter filters the radical radius from their geometric center to mesh points by local wave;Finally,remove the high-frequency component of spherical signal,and obtain the smooth mesh model with inversely mapping from the spherical signal.Several mesh models with Gaussian noise are processed by local wave based method and other compared methods.The results show that local wave based method can obtain better smoothing performance,and reserve more original geometric features at the same time.

ANALYSIS OF SHEAR LOCALIZATION IN POROUS MATERIALS

A set of constitutive equations are derived based on the authors'lower bound yield loci for porous materials. By using these equations, the conditions for shear localization in porous materials are then investigated and the results are compared with those of Gurson's equations and the finite element analysis. The advantages of the present constitutive equations are fully illustrated.

Local Data Analysis for Eliminating End Restraint of Triaxial Specimen

A data processing method was proposed for eliminating the end restraint in triaxial tests of soil. A digital image processing method was used to calculate the local deformations and local stresses for any region on the surface of triaxial soil specimens. The principle and implementation of this digital image processing method were introduced as well as the calculation method for local mechanical properties of soil specimens. Comparisons were made between the test results calculated by the data from both the entire specimen and local regions, and it was found that the deformations were more uniform in the middle region compared with the entire specimen. In order to quantify the nonuniform characteristic of deformation, the non-uniformity coefficients of strain were defined and calculated. Traditional and end-lubricated triaxial tests were conducted under the same condition to investigate the effects of using local region data for deformation calculation on eliminating the end restraint of specimens. After the statistical analysis of all test results, it was concluded that for the tested soil specimen with the size of 39.1 mm × 80 ram, the utilization of the middle 35 mm region of traditional specimens in data processing had a better effect on eliminating end restraint compared with end lubrication. Furthermore, the local data analysis in this paper was validated through the comparisons with the test results from other researchers.

Multivariate time delay analysis based local KPCA fault prognosis approach for nonlinear processes

Currently, some fault prognosis technology occasionally has relatively unsatisfied performance especially for in- cipient faults in nonlinear processes duo to their large time delay and complex internal connection. To overcome this deficiency, multivariate time delay analysis is incorporated into the high sensitive local kernel principal component analysis. In this approach, mutual information estimation and Bayesian information criterion （BIC） are separately used to acquire the correlation degree and time delay of the process variables. Moreover, in order to achieve prediction, time series prediction by back propagation （BP） network is applied whose input is multivar- iate correlated time series other than the original time series. Then the multivariate time delayed series and future values obtained by time series prediction are combined to construct the input of local kernel principal component analysis （LKPCA） model for incipient fault prognosis. The new method has been exemplified in a sim- ple nonlinear process and the complicated Tennessee Eastman （TE） benchmark process. The results indicate that the new method has suoerioritv in the fault prognosis sensitivity over other traditional fault prognosis methods.

LOCALIZED ANALYSIS OF THIN-WALLED STRUCTURE’S BUCKLING/INITIAL POST-BUCKLING AND ITS ACCURACY

A method of localization is proposed to lower the high order of equations in FEM calcula- tion for the stability of a complex thin-walled structure.The localized analysis enables us to obtain both the upper and lower limits for the bifurcating point in a whole linear elastic structural system,as well as an ap- proximate solution to asymptotic post-buckling problem.Some numerical examples are included.

Local Structure Analysis of Lead Zinc Niobate-Barium Titanate Ceramic by X-Ray Absorption Spectroscopy and Density Functional Calculation

The local structure of an alternative Pb（Zn1/3Nb2/3）O3-based perovskite ceramic is investigated. The 0.07BaTiO33-0.93Pb（Zn1/3Nb2/3）O3 ceramic is synthesized using a combination of Zn3Nb2O8 B-site precursor and BaTiO33 perovskite phase stabilizer. Then, x-ray absorption spectroscopy and density functional theory are employed to calculate the local structure configuration and formation energy of the prepared samples. Ba2＋ is found to replace Pb2＋ in AA-site with Zn2＋ occupying BB-site in Pb（Zn1/3Nb2/3）O3, while in the neighboring structure, Ti4＋4＋ replaces Nb5＋5＋ in BB-site with Pb2＋2＋ occupying AA-site. With the substitution of BaTiO33 in Pb（Zn1/3Nb2/3）O3, the bond length between Zn2＋ and Pb2＋ is longer than that of the typical perovskite phase of Pb（Zn1/3Nb2/3）O3. This indicates the key role of BaTiO33 in decreasing the steric hindrance of Pb2＋ lone pair, and the mutual interactions between Pb2＋ lone pair and Zn2＋ and the formation energy is seen to decrease. This finding of the formation energy and local structure configuration relationship can further extend a fundamental understanding of the role of BaTiO33 in stabilizing the perovskite phase in PbZn13Nb23O3-based materials, which in turn will lead to an improved preparation technique for desired electrical properties.

A New Method of Color Edge Detection Based on Local Structure Analysis

Human's real life is within a colorful world. Compared to the gray images, color images contain more information and have better visual effects. In today's digital image processing, image segmentation is an important section for computers to "understand" images and edge detection is always one of the most important methods in the field of image segmentation. Edges in color images are considered as local discontinuities both in color and spatial domains. Despite the intensive study based on integration of single-channel edge detection results, and on vector space analysis, edge detection in color images remains as a challenging issue.

Groups Analysis and Localized Solutions of the(2+1)-Dimensional Ito Equation

By means of the modified Clarkson and Kruskal （CK） direct method and the variable separation approach, we investigate the （24-1）-dimensional Ito equation which was constructed by Ito in 1980. The full symmetry group with the Kac-Moody-Virasoro algebra structure and the variable separation solutions are obtained. By selecting appropriate arbitrary functions, some special soliton excitations are shown graphically. The results presented here would be beneficial for understanding the （2-t-1）-dimensional Ito equation better.

INTEGRATION OF A ZONAL FUNCTION RELATED TO THE LOCAL HARMONIC ANALYSIS ON SPHERES

In studying Local harmonic analysis on the sphere S',R.S.Strichartz introduced certain zonab functionsid(x,y))which satisfy the equation

Composite grid method for analysis of electromagnetic field

In this paper, a composite grid method (CGM) for finite element (FE) analysisof an electromagnetic field with strong local interest is proposed. The method is based on theregular finite element method in conjunction with three basic steps, i.e. global analysis, localanalysis, and modified global analysis. In the first two steps, a coarse finite element mesh is usedto analyze the global model to obtain the nodal potentials which are subsequently used asartificial boundary conditions for local regions of interest. These local regions with theprescribed boundary conditions are then analyzed with refined meshes to obtain more accuratepotential and density distribution In the third step, a modified global analysis is performed toobtain more improved solution for potential and density distribution. And iteratively, successivelyimproved solutions can be obtained until the desired accuracy is achieved. Various numericalexperiments show that CCM yields accurate solutions with significant savings in computing timecompared with the regular finite element method.

Numerical analysis on the influence of vortex motion in a reverse Stairmand cyclone separator by using LES model

This study aims to analyze the influence of vortex motion in a reverse Stairmand cyclone separator by using LES model.The mathematical analysis indicated that the energy dissipation and the flow characteristics of incompressible fluid are directly related to on the vortex motion.The results of the Q criterion-based iso-vortex surface could well reflect the tendency of the vortex structure,in which the iso-vortex surface exhibited a distorted distribution rather than around the center axis.At the turning point of velocity vector,vortices were formed and developed,and the point was the center of the local vortex core.In addition,the vortex formed an irregular annular region around the wall at the bottom of vortex finder.The vortex structure near the dust hopper presented a strong distortion.Moreover,there were two rotating flow in the opposite direction within the dust hopper.These phenomena would affect the separation performance,which was significance to cyclone separator.

Geochemical Anomalies Identified by Multifractal Modeling: Implications for Mineral Exploration in the Ziyoutun Cu-Au District, Jilin Province, China

The Ziyoutun Cu-Au district is located in the Jizhong–Yanbian Metallogenic Belt and possesses excellent prospects. However, the thick regolith and complex tectonic settings present challenges in terms of detecting and decomposition of weak geochemical anomalies. To address this challenge, we initially conducted a comprehensive analysis of 1:10,000-scale soil geochemical data. This analysis included multivariate statistical techniques, such as correlation analysis, R-mode cluster analysis, Q–Q plots and factor analysis. Subsequently, we decomposed the geochemical anomalies, identifying weak anomalies using spectrum-area modeling and local singularity analysis. The results indicate that the assemblage of Au-Cu-Bi-As-Sb represents the mineralization at Ziyoutun. In comparison to conventional methods, spectrumarea modeling and local singularity analysis outperform in terms of identification of anomalies. Ultimately, we considered four specific target areas(AP01, AP02, AP03 and AP04) for future exploration, based on geochemical anomalies and favorable geological factors. Within AP01 and AP02, the geochemical anomalies suggest potential mineralization at depth, whereas in AP03 and AP04 the surface anomalies require additional geological investigation. Consequently, we recommend conducting drilling, following more extensive surface fieldwork, at the first two targets and verifying surface anomalies in the last two targets. We anticipate these findings will significantly enhance future exploration in Ziyoutun.

ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM

A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.

PROBABILISTIC METHODOLOGY OF LOW CYCLE FATIGUE ANALYSIS

The cyclic stress-strain responses (CSSR), Neuber's rule (NR) and cyclic strain-life relation (CSLR) are treated as probabilistic curves in local stress and strain method of low cycle fatigue analysis. The randomness of loading and the theory of fatigue damage accumulation (TOFDA) are considered. The probabilistic analysis of local stress, local strain and fatigue life are constructed based on the first-order Taylor's series expansions. Through this method proposed fatigue reliability analysis can be accomplished.

Finite Element Analysis of the Material’s Area Affected during a Micro Thermal Analysis Applied to Homogeneous Materials

Micro-thermal analysis (μ-TA), with a miniaturized thermo-resistive probe, allows topographic and thermal imaging of surfaces to be carried out and permits localized thermal analysis of materials. In order to estimate the effective volume of material thermally affected during this localized measurement, simulations, using finite element method were used. Several parameters and conditions were considered. So, thermal conductivity was found to be the driving physical parameter in thermal exchanges. Indeed, the evolution of the heat affected zone (HAZ) versus thermal conductivity can well be described by a linear interpolation. Therefore it is possible to estimate the HAZ before experimental measurements. This result is an important progress especially for accurate interphase characterization in heterogeneous materials.

Real-Time and Spatial Electroanalysis of Biomolecules in One Living Cell Using Liquid-Phase Modified Nanopipette

The well-developed solid-phase modified strategy at the electrode has enabled the preparation of biosensors for the detection of multiple analytes,even in single living cells.However,limited assay elements can be modified at the solid surface,restricting the types of molecules that can be analyzed and the sensitivity of detection.Here,a novel liquid-phase modified strategy at the tip of a nanopipette is designed to realize real-time and local analysis of biomolecules inside the cell that are barely detectable using solid-phase modified nanoelectrodes.This design utilizes the nanotip structure at a platinized carbon open nanopipette to stably retain a nanodroplet that contains the required reagents with high reactivity for the assay of the target analyte.The generated hydrogen peroxide is electrochemically quantified at the Pt layer to carry out the real-time measurement in a living cell with a spatial resolution of 70 nm.Taking advantage of highly spatial and real-time detection,uneven distribution of sphingomyelinase(SMase)in the living CT26 cell is unprecedentedly shown to exhibit the significance in the establishment of liquid-phase modified nanopipette.This new modification strategy opens up a new direction for sensor design and consequently advances the development of biosensors in the chemical and biological research.