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

The catalytic effect of alumina on the destruction of toluene, benzene, acetone and methanol, in DC pulsed corona discharge reactor was studied. In the presence of alumina the inlet concentration of the VOCs was varied from ~5×10-6 mol/L to ~80×10-6 mol/L, and their decomposition efficiency (conversion %) was found to be 99%-80% for toluene, 99%-97% for benzene, 95%-92% for acetone, and 72%-85% for methanol. Corresponding decomposition in the absence of alumina was 90%-38% for toluene, 89%-57% for benzene, 42%-30% for acetone, and 47%-19% for methanol. Feed gas flow rate was 400 cm 3/min and power reading from DC source was 74 W in all of the experiments. Alumina also shifted the CO/CO 2 ratio in the by products in favor of CO 2. Ozone concentration at the reactor outlet was higher in the presence of alumina. Enhancement in VOCs decomposition by alumina was explained on the basis of higher concentration of ozone and its precursor atomic oxygen O . Decomposition efficiency (conversion %) for individual compounds was found to be inversely proportional to the ionization potential of the compound, under identical conditions. Double DC high voltage sources pulse generator was tested and found to improve VOCs decomposition compared with the conventional single DC high voltage source.

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 process-level hierarchical structural decomposition analysis (SDA) of energy consumption in an integrated steel plant

A hierarchical structural decomposition analysis(SDA) model has been developed based on process-level input-output(I-O) tables to analyze the drivers of energy consumption changes in an integrated steel plant during 2011-2013. By combining the principle of hierarchical decomposition into D&L method, a hierarchical decomposition model for multilevel SDA is obtained. The developed hierarchical IO-SDA model would provide consistent results and need less computation effort compared with the traditional SDA model. The decomposition results of the steel plant suggest that the technology improvement and reduced steel final demand are two major reasons for declined total energy consumption. The technical improvements of blast furnaces, basic oxygen furnaces, the power plant and the by-products utilization level have contributed mostly in reducing energy consumption. A major retrofit of ancillary process units and solving fuel substitution problem in the sinter plant and blast furnace are important for further energy saving. Besides the empirical results, this work also discussed that why and how hierarchical SDA can be applied in a process-level decomposition analysis of aggregated indicators.

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.

Structural Decomposition Analysis on Energy Intensity Changes at Regional Level

As China's energy intensity fluctuated in recent years, it is necessary to examine whether this fluctuation happened at a regional level. This paper establishes a decomposition model by using the structural decomposition analysis (SDA) method at a regional level. Then this model is employed to empirically analyze the changes of Beijing's energy intensity. The conclusions are as follows: during 2002-2010, except petroleum, the energy intensity decreased and the changes were mostly attributed to the technology changes, while the final use variation actually increased the energy intensity; comparing different periods of 2002-2010, the decline rates of energy intensity for coal and hydropower were decreasing, resulting from the production technology being more energy-intensive than before; the energy intensity changes of petroleum firstly increased substantially and then decreased moderately.

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.

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.

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.

Evolution trends and structural decomposition of China's green value-added over 40 years of reform and opening-up

China's 40-year history of reform and opening-up includes rapid economic development as well as pollution and environmental governance.Using a four-stage division,this study explores the evolution trend and structural decomposition of China's green value-added by constructing a non-competitive input-output table for environmental pollution from 1978 to 2017.The results indicate that pollution production coefficients increased continuously,and the green value-added index decreased.Additionally,the structural decomposition showed that investment and export were critical for economic growth during the period,though they were accompanied by serious pollution problems.The pollution generated by the raw material(represented by coal mining)and processing industries(represented by the textiles)were not controlled effectively.Pollution treatment for these industries should be strengthened in the future.The study has implications for government officials,policy makers,and academics.First,China should make green development a core concept for economic development,increase environmental pollution governance,develop a“green GDP,”incorporate the external costs of environmental pollution into the national economic accounting system.Second,it must change the investment and export structure as well as the traditional economic development pattern that exacerbates pollution.Specifically,the country should develop industries with low pollution and promote the export of industries producing high value-added products and increase green GDP per capita.Third,it should closely monitor the development of highly polluting industries.Upgrading technology to reduce pollution and strengthening pollution treatment will reduce the number of polluting industries and improve environmental governance efficiency.

Quantum Mechanical Image of Matrices' LDU Decomposition

For classical transformation （q1,q2） → （Aq1 ＋ Bq2, Cq1 ＋ Dq2）, where AD - CB ≠ 1, we find its quantum mechanical image by using LDU decomposition of the matrix （A B C D ）. The explicit operators L, D, and U axe derived and their physical meaning is revealed, this also provides a new way for disentangling some exponential operators.

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.

Decomposition Method for Complex 3D Problems in Electron Optics

The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM （Finite Difference Method） and FEM （Finite Element Method） mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM （Boundary Element Method） based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU （Central Processor Unit） desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz＇s algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code ＂POISSON-3＂.

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.