Structural Complexity Analysis of Information Systems Based on Petri Nets

Aim To present a quantitative method for structural complexity analysis and evaluation of information systems. Methods Based on Petri net modeling and analysis techniques and with the aid of mathematical tools in general net theory(GNT), a quantitative method for structure description and analysis of information systems was introduced. Results The structural complexity index and two related factors, i.e. element complexity factor and connection complexity factor were defined, and the relations between them and the parameters of the Petri net based model of the system were derived. Application example was presented. Conclusion The proposed method provides a theoretical basis for quantitative analysis and evaluation of the structural complexity and can be applied in the general planning and design processes of the information systems.

Nonconforming finite element Stokes complexes in three dimensions

Two nonconforming finite element Stokes complexes starting from the conforming Lagrange element and ending with the nonconforming P_1-P_0 element for the Stokes equation in three dimensions are studied.Commutative diagrams are also shown by combining nonconforming finite element Stokes complexes and interpolation operators.The lower order H(gradcurl)-nonconforming finite element only has 14 degrees of freedom,whose basis functions are explicitly given in terms of the barycentric coordinates.The H(gradcurl)-nonconforming elements are applied to solve the quad-curl problem,and the optimal convergence is derived.By the nonconforming finite element Stokes complexes,the mixed finite element methods of the quad-curl problem are decoupled into two mixed methods of the Maxwell equation and the nonconforming P_1-P_0 element method for the Stokes equation,based on which a fast solver is discussed.Numerical results are provided to verify the theoretical convergence rates.

Nonconforming Finite Elements for the -curlΔcurl and Brinkman Problems on Cubical Meshes

We propose two families of nonconforming elements on cubical meshes:one for the -curlΔcurl problem and the other for the Brinkman problem.The element for the -curlΔcurl problem is the first nonconforming element on cubical meshes.The element for the Brinkman problem can yield a uniformly stable finite element method with respect to the viscosity coefficient ν.The lowest-order elements for the -curlΔcurl and the Brinkman problems have 48 and 30 DOFs on each cube,respectively.The two families of elements are subspaces of H(curl;Ω)and H(div;Ω),and they,as nonconforming approximation to H(gradcurl;Ω)and[H^(1)(Ω)]^(3),can form a discrete Stokes complex together with the serendipity finite element space and the piecewise polynomial space.

CVBEM and FVM Computational Model Comparison for Solving Ideal Fluid Flow in a 90-Degree Bend

While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.

Solvent extraction and separation of light rare earth elements (La, Pr and Nd) in the presence of lactic acid as a complexing agent by Cyanex 272 in kerosene and the effect of citric acid,acetic acid and Titriplex Ⅲ as auxiliary agents

At present, the use of rare earth elements（REEs） has become an inevitable necessity in many modern industries. In general, liquid extraction is the best commercial method for extracting REEs due to its ability to control high volumes of liquids with electrical load. With the aim of improving a separation technology that would be superior to the existing extraction systems, the extraction behaviors of La（Ⅲ）,Pr（Ⅲ）, and Nd（Ⅲ） from an HCI medium with Cyanex 272 in the presence of the complexing agent lactic acid（HLac） and auxiliary agents citric acid（H3 Cit）, acetic acid（HAc）, and Titriplex Ⅲ have been reported.The effect of pH and lactic acid concentration has been examined. The use of lactic acid as a complexing agent leading to a high extraction of REEs with Cyanex 272 at pH = 5 was compared with systems without lactic acid. The results show that the use of acetic acid along with lactic acid leads to an increase in the extraction percentage of LREEs. While use of citric acid and Titriplex Ⅲ reduces the extraction percentage of LREEs. Finally, the presence of Titriplex Ⅲ together with lactic acid could lead to an increase in the separation factor of Pr and Nd.