Preliminaries for a New Mathematical Framework for Modelling Tumour Growth Using Stress State Decomposition Technique

The main goal of the present paper is to present a mathematical framework for modelling tumour growth based on stress state decomposition technique (SSDT). This is a straightforward extension of the model for multi-phase nonsaturated soil consolidation with pollutant transport presented by the authors and may be regarded as an alternative to classical frameworks based on TCAT theory. In this preliminary work, the Representative Volume Element (RVE) for tumour is proposed along with its comparison with the corresponding one for soils modelling developed formerly by the authors. Equations standing for tumour phase are flawlessly brought into correspondence with those of gaseous phase in the soil problem showing that a similar task may be carried out for the remainders phases taking part in both RVEs. Furthermore, stresses induced by nonlinear saturation and permeability dependence on suction for soil interstitial fluids transport finds its counterpart on the contact between the cancer cell membrane and interstitial fluids rendering a higher primary variables coupling degree than what was attained in TCAT theory. From these preliminaries assessments, it may be put forward that likewise the stress state decomposition procedure stands for an alternative for modelling multi-phase nonsaturated soil consolidation with pollutant transport;it does for modelling cancer as well.

A COMBINED TECHNIQUE FOR SOLUTION OF PDE＇s VIA THE GENERALIZED DOMAIN DECOMPOSITION METHOD

The Domain Decomposition Method(DDM) is a powerful approach to solving maily types of PDE's. DDM is especially suitable for massively Parallel computers. In the past, most research on DDM has focused on the domain splitting technique. In this paper. we focus our attention on use of a combination of techniques to solve each subproblem. The central question with DDM is that of how to doal with the pseodoboundary conditions. Here, we introduce a set of operators which act on the pseudo-boundaries in the solution process, referring to this new. procedure as the 'Generalized Domain Decomposition A.Jlethod(GDDM).' We have already obtained convergence factors for GDDM with certain classes of PDE's. These ctonvergence factors show that we can derive exact solutions of the whole problem for certain types of PDE's, and can get superior speed of convergence for other types.

Destruction of VOCs by combination of corona discharge and catalysis techniques

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Study on Non-Isothermal Decomposition Kinetics of Ephedrini Hydrochloridum

The thermal decomposition processes of ephedrini hydrochloridum and its kinetics are studied by TG-DTG techniques. A combined method, which includes Achar method, Coats-Redfera method, and Ozawa method, is put forward for determining kinetic model under non-isothermal conditions. By applying the combined method, it is determined that the thermal decomposition of ephedrini hydrochloridum is subjected to cylindrical symmetric diffusion. And the reaction function isƒ(α)=2(1-α)?, apparent activation energy (115.26±3.55) kJ·mol−1, pre-exponential factor 4.62×108 s−1. Results show that the combined method is feasible and simple.

A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations

A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element （CNLSMFE） formulation and proper orthogonal decomposition （POD） technique for two-dimensional （2D） Sobolev equations is established. The error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are provided. A numerical example is used to show that the results of numerical computations are consistent with theoretical conclusions. Moreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to 2D Sobolev equations.

An efficient analytical decomposition and numerical procedure for boundary layer flow on a continuous stretching surface

An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.

A Unification of the Concepts of the Variational Iteration, Adomian Decomposition and Picard Iteration Methods;and a Local Variational Iteration Method

This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.

Strategy &Techniques for Restoration of Healthy Aquaecosystem from Toxic Super Eutrophic Water Body

There are complex river-lake systems in the Taihu Lake catchment with total water surface area of 6174.7 km2, and population density of 1079/km2, including Taihu Lake water surface area of 2338 km2. The water systems in this catchment have healthy aquaecosystems during long history. However, in some riverlets in this catchment the water quality was estimated as “acute toxicity for higher organisms” and over standards for many heavy metal elements content;there were no any living plants and macro organisms in the water body, because there were developed a series of industry with abundant release of heavy metals and difficult decomposition organic chemical components along the riverlets during last decades. The even more serious situation was observed in sediments of the riverlets. How to restore such riverlet into a healthy aquaeosystem with abound plants and higher organisms? The main strategy and techniques are described in this paper as summarizing a report of engineering in a riverlet in Wuxi New District during last years, which leads to restore the aquaecosystem into a healthy one with abundant surface plant cultured on floating islands and observed living fish, lobster, frog, toad, mollusk and others in the riverlet. The main techniques are: 1) softwall buffer technic;2) floating eco-island technic by using which can culture any plant which can be cultured in solution;3) immobilized nitrogen cycle bacteria (INCB) technic;4) tattering esters and other big-molecule organic chemicals by using electronic pulse technic and photosensitization technic;5) mist spray facility technic for improving dissolved oxygen in deep water layers;6) technic for buffering and suppressing H2S release from water;7) the appropriate portion of surface with cultured plant to the total water surface area is about 1/3;8) Cress [Oenanthe Ljavanica (Bl.) DC.] and Myriophyllum verticilatum L. may be cultured in Taihu Lake catchment during the whole year as main plants with mosaic combination of other supplement plants in different seasons.

A High-order Coupled Compact Integrated RBF Approximation Based Domain Decomposition Algorithm for Second-order Differential Problems

This paper presents a high-order coupled compact integrated RBF(CC IRBF)approximation based domain decomposition(DD)algorithm for the discretisation of second-order differential problems.Several Schwarz DD algorithms,including one-level additive/multiplicative and two-level additive/multiplicative/hybrid,are employed.The CCIRBF based DD algorithms are analysed with different mesh sizes,numbers of subdomains and overlap sizes for Poisson problems.Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here.Especially,the present CCIRBF two-level method converges quite rapidly even when the domain is divided into many subdomains,which shows great promise for either serial or parallel computing.For practical tests,we then incorporate the CCIRBF into serial and parallel two-level multiplicative Schwarz.Several numerical examples,including those governed by Poisson and Navier-Stokes equations are analysed to demonstrate the accuracy and efficiency of the serial and parallel algorithms implemented with the CCIRBF.Numerical results show:(i)the CCIRBF-Serial and-Parallel algorithms have the capability to reach almost the same solution accuracy level of the CCIRBF-Single domain,which is ideal in terms of computational calculations;(ii)the CCIRBF-Serial and-Parallel algorithms are highly accurate in comparison with standard finite difference,compact finite difference and some other schemes;(iii)the proposed CCIRBF-Serial and-Parallel algorithms may be used as alternatives to solve large-size problems which the CCIRBF-Single domain may not be able to deal with.The ability of producing stable and highly accurate results of the proposed serial and parallel schemes is believed to be the contribution of the coarse mesh of the two-level domain decomposition and the CCIRBF approximation.It is noted that the focus of this paper is on the derivation of highly accurate serial and parallel algorithms for second-order differential problems.The scope of this work does not cover a thorough analysis of computational time.

Economical and Technical Indices of Decomposition Processes of Typical Rare Earth Minerals in China

The typical treatment processes we of main rare earth resources in China, especially the economical and technical indices of the minerals decomposition of such as ionic adsorptive rare earth deposit ore, bastnasite and mixed with monazite in Baotou, was presented. The dispersive ionic adsorptive rare earth deposit ore, which is enriched on valuable middle and heavy elements, concentrated by bicarbonate precipitation after exchanging with ammonium sulphate solution. Planting and waste liquid should be focused. Bastnasite and/or monazite, which is enriched light rare earth, centralized with high content and capacity,concentrated by gravimetric, magnetic, floating, then decomposed by calcinations and leaching. Waste liquid, gases and dregs should be treated properly. Investors interested in RE industry can find out the technical and economic characters and history of various RE minerals. Engineers and workers in RE industry can also find the differences of the plants, so as to make more efforts on improving management. However, solving environment protection problems for each process should be committed extraordinarily in order to make a sustainable development of RE industry.

Correction of failure in antenna array using matrix pencil technique

In this paper a non-iterative technique is developed for the correction of faulty antenna array based on matrix pencil technique（MPT）. The failure of a sensor in antenna array can damage the radiation power pattern in terms of sidelobes level and nulls. In the developed technique, the radiation pattern of the array is sampled to form discrete power pattern information set. Then this information set can be arranged in the form of Hankel matrix（HM） and execute the singular value decomposition（SVD）. By removing nonprincipal values, we obtain an optimum lower rank estimation of HM. This lower rank matrix corresponds to the corrected pattern. Then the proposed technique is employed to recover the weight excitation and position allocations from the estimated matrix. Numerical simulations confirm the efficiency of the proposed technique, which is compared with the available techniques in terms of sidelobes level and nulls.

Direct spectral domain decomposition method for 2D incompressible Navier-Stokes equations

An efficient direct spectral domain decomposition method is developed coupled with Chebyshev spectral approximation for the solution of 2D, unsteady and in- compressible Navier-Stokes equations in complex geometries. In this numerical approach, the spatial domains of interest are decomposed into several non-overlapping rectangu- lar sub-domains. In each sub-domain, an improved projection scheme with second-order accuracy is used to deal with the coupling of velocity and pressure, and the Chebyshev collocation spectral method （CSM） is adopted to execute the spatial discretization. The influence matrix technique is employed to enforce the continuities of both variables and their normal derivatives between the adjacent sub-domains. The imposing of the Neu- mann boundary conditions to the Poisson equations of pressure and intermediate variable will result in the indeterminate solution. A new strategy of assuming the Dirichlet bound- ary conditions on interface and using the first-order normal derivatives as transmission conditions to keep the continuities of variables is proposed to overcome this trouble. Three test cases are used to verify the accuracy and efficiency, and the detailed comparison be- tween the numerical results and the available solutions is done. The results indicate that the present method is efficiency, stability, and accuracy.

Soliton Solutions and Numerical Treatment of the Nonlinear Schrodinger’s Equation Using Modified Adomian Decomposition Method

In this paper, the improved Adomian decomposition method (ADM) is applied to the nonlinear Schr&oumldinger’s equation (NLSE), one of the most important partial differential equations in quantum mechanics that governs the propagation of solitons through optical fibers. The performance and the accuracy of our improved method are supported by investigating several numerical examples that include initial conditions. The obtained results are compared with the exact solutions. It is shown that the method does not need linearization, weak or perturbation theory to obtain the solutions.

A study on coupling technique and implementation of the wave-circulation coupled model

The coupler is fundamental for a coupled model to realize complex interactions among component models.This paper focuses on the coupling process of Wave-Circulation(W-C) coupled model which consists of MASNUM(key laboratory of marine science and numerical modeling wave model)and POM(Princeton Ocean Model).The current coupling module of this coupled model is based on the inefficient I/O file,which has already become a performance bottleneck especially when the coupled model utilizes a large number of processes.To improve the performance of the W-C model,a flexible coupling module based on the model coupling toolkit(MCT) is designed and implemented to replace the current I/O file coupling module in the coupled model.Empirical studies that we have carried out demonstrate that our online coupling module can dramatically improve the parallel performance of the coupled model.The online coupling module outperforms the I/O file coupling module.When processes increase to 96,the whole process of EXP-C takes only 695.8 seconds,which is only 58.8%of the execution time of EXP-F.Based on our experiments under 2D Parallel Decomposition(2DPD),we suggest setting parallel decomposition strategies automatically to component models in order to achieve high parallel efficiency.

Quantum Mechanical Image of Matrices' LDU Decomposition

为古典转变(q1， q2 )(Aq1 + Bq2， Cq1 + Dq2 ) 广告 CB 1，我们由使用矩阵的 LDU 分解发现它的量机械图象。明确的操作员，，并且？被导出，他们的物理意思被揭示，这也为解开一些指数的操作员提供一个新方法。

Recent Advances in the Analytical Techniques for PFASs and Corresponding Intermediates During Their Chemical Decomposition

Per-and polyfluoroalkyl substances(PFASs)have been restricted from production and consumption in many countries due to their persistence and biological toxicity.With the development of removal technologies,the requirement on the detection of different kinds of PFASs and their derivates is increasing.A suitable analytical method is the prerequisite and basis for the study of the degradation of PFASs.As various analytical methods have been reported,questions about which one is more suitable have arisen.It is a right time to summarize the past and suggest the future.In this paper,we summarized and discussed the analytical methods applied in the chemical degradation of PFASs.We also proposed the current problems and discussed the future directions in this field.

基于EMD-SVD的矿山微震信号降噪方法及其应用

为了提高微震监测技术对微震信号分析处理的准确性,充分提取微震信号波形中的有效信息,针对矿山微震信号非平稳、非线性的特点,提出了一种基于经验模态分解(EMD)和奇异值分解(SVD)的联合降噪方法。该方法首先通过EMD分解获得信号的IMF分量,利用相关系数、方差贡献率和相似度对IMF分量进行了优选;然后使用优选后的IMF分量重构一维微震信号时间序列的相空间数据,经过SVD分解后,利用奇异值能量百分比确立了SVD重构阶数,并根据SVD恢复原理得到了降噪后的一维微震时间序列;最后以山东某矿现场矿山爆破为例,采用不同降噪方法对3类典型微震信号进行了降噪处理,并对其降噪效果进行了对比分析。结果表明,EMD-SVD降噪方法与传统降噪方法相比,其平均信噪比提高了35%,平均均方根误差降低了50%,有效剔除了微震信号的噪声分量,保留了信号的特征信息。该研究对分析矿山微震信号、微震事件定位及煤矿动力灾害监测具有重要意义。

基于改进的辛周期模态分解的滚动轴承复合故障诊断方法

辛周期模态分解(symplectic period mode decomposition, SPMD)方法可以准确地提取周期脉冲分量,是一种有效的滚动轴承单一故障诊断方法。但在滚动轴承出现复合故障时,尤其是强背景噪声下,周期脉冲信号往往较微弱,使得SPMD难以提取出不同周期的脉冲分量,进而限制了其在复合故障诊断中的应用。对此,提出了改进的辛周期模态分解(improved symplectic period mode decomposition, ISPMD)方法。该方法首先采用求差增强技术和最小噪声幅值反卷积相结合的方法对信号进行降噪,增强周期脉冲,以准确估计故障周期;然后构造对应的周期截断矩阵,并通过辛几何相似变换和周期冲击强度获得辛几何周期分量;最后对残差信号采用迭代分解,进而得到不同周期的辛几何周期分量。试验结果表明,ISPMD能准确提取出周期脉冲分量,是一种有效的滚动轴承复合故障诊断方法。

基于鲁棒M估计协方差矩阵相位优化的DSInSAR矿区形变监测研究

针对时序干涉合成孔径雷达(Interferometric Synthetic Aperture Radar,InSAR)技术在矿区所处区域内耕地、裸地等自然地表地物上无法识别有效监测点信息,致使矿区地表形变信息不足及形变解译困难等问题,提出一种基于鲁棒M估计协方差矩阵特征值分解相位优化的DSInSAR技术,并基于34景Sentinel-1A影像获取了霄云煤矿2022年的地表时序形变。推导基于鲁棒M估计协方差矩阵估计公式,提高对样本异常值及异质像素的鲁棒性,开展基于鲁棒M估计协方差矩阵特征值分解的相位优化处理,分析了上述优化模型与通用相位优化模型的相似性,最终通过对优化估计相位开展相位信息解译处理来获取最终的形变信息。实验结果表明:基于鲁棒M估计协方差矩阵特征值分解相位优化的DSInSAR技术较常规SBAS技术及基于最大似然估计协方差矩阵的DSInSAR技术在监测点密度上分别提高了约11.4倍、0.2倍,且与水准数据对比具有最小的均方根误差,约22 mm;此外,霄云煤矿共包含三个主要形变场,其地表沉降的时序变化呈现出较显著的非线性趋势,煤矿内地表的视线向最大沉降量约418 mm。研究成果为矿区地表形变规律反演及矿区灾害防控提供重要数据支撑。