Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem

Overlapping balancing domain decomposition methods and their combination with restricted additive Schwarz methods are proposed for the Helmholtz equation. These new methods also extend previous work on non-overlapping balancing domain decomposition methods toward simplifying their coarse problems and local solvers. They also extend restricted Schwarz methods, originally designed to overlapping domain decomposition and Dirichlet local solvers, to the case of non-overlapping domain decomposition and/or Neumann and Sommerfeld local solvers. Finally, we introduce coarse spaces based on partitions of unity and planes waves, and show how oblique projection coarse problems can be designed from restricted additive Schwarz methods. Numerical tests are presented.     

A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.     

FEM model of the ohmic resistance of IP-SOFCs

In the present work, the ohmic resistance of an integrated planar-SOFC (IP-SOFC) has been evaluated by developing a model whose equations have been solved numerically through an FEM method. The model allows to estimate the distribution of voltage and current density in the cell. A comparison between simulated and experimental data of area specific resistance is reported, which shows satisfactory agreement. The mathematical model has also been used to carry out some parametric studies for optimisation purposes. Indeed, a reduction in cell pitch length and an increase in electrode thickness are predicted to lead to a reduction in ohmic losses in IP-SOFCs.     

Time-dependent modelling and asymptotic analysis of electrochemical cells

A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler–Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented.     

Mathematical models of the VEGF receptor and its role in cancer therapy

We present an analysis of a stochastic model of the vascular endothelial growth factor (VEGF) receptor. This analysis addresses the contribution of ligand-binding-induced oligomerization, activation of src-homology 2 domain-carrying kinases and receptor internalization in the overall behaviour of the VEGF/VEGF receptor (VEGFR) system. The analysis is based upon a generalization of a Wentzel-Kramers-Brillouin (WKB) approximation of the solution of the corresponding master equation. We predict that tumour-mediated overexpression of VEGFRs in the endothelial cells (ECs) of tumour-engulfed vessels leads to an increased sensitivity of the ECs to low concentrations of VEGF, thus endowing the tumour with increased resistance to anti-angiogenic treatment.     

Nodally exact Ritz discretizations of 1D diffusion–absorption and Helmholtz equations by variational FIC and modified equation methods

This article presents the first application of the Finite Calculus (FIC) in a Ritz-FEM variational framework. FIC provides a steplength parametrization of mesh dimensions, which is used to modify the shape functions. This approach is applied to the FEM discretization of the steady-state, one-dimensional, diffusion–absorption and Helmholtz equations. Parametrized linear shape functions are directly inserted into a FIC functional. The resulting Ritz-FIC equations are symmetric and carry a element-level free parameter coming from the function modification process. Both constant- and variable-coefficient cases are studied. It is shown that the parameter can be used to produce nodally exact solutions for the constant coefficient case. The optimal value is found by matching the finite-order modified differential equation (FOMoDE) of the Ritz-FIC equations with the original field equation. The inclusion of the Ritz-FIC models in the context of templates is examined. This inclusion shows that there is an infinite number of nodally exact models for the constant coefficient case. The ingredients of these methods (FIC, Ritz, MoDE and templates) can be extended to multiple dimensions     

企业材料耗用的统计分析与评价

本文利用回归分析导出材料耗用的回归方程 ,并对方程进行拟合优度检测和显著性检验 ,以及对材料耗用情况进行综合评价。     

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Effect of 3D lip deformations on elastohydrodynamic lip seals behaviour

The numerical simulation of comparative elastohydrodynamic lubrication between axisymmetrical and 3D elastic approaches on the radial lip seals is presented in order to determine the 3D effect of the elastic aspect of the seal lip. Indeed, the consideration of 3D model in other words the circumferential variation of the lip elastic deformation indicated a difference in the deformation distribution of the lip compared to the axisymmetrical approach. Consequently, the results show that the presence of the circumferential variation of the seal lip deformation has a significant effect on the pumping rate values.     

高压下CO在甲醇-碳酸二甲酯中的溶解度测定

利用自行建立的高压下测定气体在液体中溶解度的装置,在温度25~75℃、压力2.00~10.00MPa条件下,首次测定了CO在甲醇、碳酸二甲酯及甲醇-碳酸二甲酯混合体系中的溶解度,并用PR方程计算了CO的气相逸度,溶解度数据符合方程f=Hx。揭示了CO在甲醇、碳酸二甲酯及甲醇-碳酸二甲酯混合体系中的溶解度规律。将亨利系数和温度进行关联,关联误差很小。这表明用此关联式可预测和推算CO在这些溶剂中的溶解度。