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Surface Polarization Effects on Collapse Transition of Polyelectrolyte Brushes

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Chinese Journal of Polymer Science 2024年第9期42卷 1313-1320,I0006页

作者： Xiao-fei xu State Key Laboratory of Chemical Engineering and School of Chemical Engineering East China University of Science and TechnologyShanghai200237China

Polyelectrolyte brushes(PEBs)are commonly used to modify surface that have attracted great research *** dielectric permittivity of the grafted surface is typically significantly different from that of solution,which results in surface polarization(SP)effect with a jump of electric *** is thus important to study how SP alters the PEB’s structure and *** this work,the SP effects on PEB structure was studied using a statistical thermodynamic *** free energy functional to describe SP effect was constructed by using the image-charge ***,the electrostatic potential was solved from a modified Poisson-Boltzmann equation taking the ion solvation effect into *** the absence of SP,the thickness of PEB exhibited a continuous collapse transition when decreasing the solvent *** the presence of SP,the collapse became a jump-like *** energy analysis showed that the long-range Coulombic interaction dominated the transition because of the enhanced counterion condensation in the presence of *** theory provides an effective tool to study SP effect on PEBs,and the results explain the underlying physics in PEB collapse transition.

关键词： Surface polarization Polyelectrolyte brush Image charge Ion solvation Polyelectrolyte collapse transition

An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications

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Science China Mathematics 2021年第3期64卷 623-638页

作者： fei xu Qiumei Huang Beijing Institute for Scientific and Engineering Computing Faculty of ScienceBeijing University of TechnologyBeijing 100124China

In this paper, a type of accurate a posteriori error estimator is proposed for the Steklov eigenvalue problem based on the complementary approach, which provides an asymptotic exact estimate for the approximate eigenpair. Besides, we design a type of cascadic adaptive finite element method for the Steklov eigenvalue problem based on the proposed a posteriori error estimator. In this new cascadic adaptive scheme, instead of solving the Steklov eigenvalue problem in each adaptive space directly, we only need to do some smoothing steps for linearized boundary value problems on a series of adaptive spaces and solve some Steklov eigenvalue problems on a low dimensional space. Furthermore, the proposed a posteriori error estimator provides the way to refine meshes and control the number of smoothing steps for the cascadic adaptive method. Some numerical examples are presented to validate the efficiency of the algorithm in this paper.

关键词： Steklov eigenvalue problem a posteriori error estimator cascadic multigrid method adaptive finite element method complementary method

A CASCADIC MULTIGRID METHOD FOR SEMILINEAR ELLIPTIC EQUATIONS

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Journal of Computational Mathematics 2019年第1期37卷 112-129页

作者： fei xu Fusheng Luo Beijing Institute for Scientific and Engineering Computing Beijing University of Technology Beijing 100124China The Third Institute of Oceanography SOAXiamen 361005China

This paper introduce a cascadic multigrid method for solving semilinear elliptic equations based on a multilevel correction *** of the common costly way of directly solving semilinear elliptic equation on a very fine space,the new method contains some smoothing steps on a series of multilevel finite element spaces and some solving steps to semilinear elliptic equations on a very coarse *** prove the efficiency of the new method,we derive two results,one of the optimal convergence rate by choosing the appro- priate sequence of finite element spaces and the number of smoothing steps,and the other of the optimal computational work by applying the parallel computing ***,the requirement of bounded second order derivatives of nonlinear term in the existing multigrid methods is reduced to a bounded first order derivative in the new *** numerical experiments are presented to validate our theoretical analysis.

关键词： Sernilinear elliptic equation Parallel computing Cascadic multigrid Multilevel correction Finite element method

Protection zone in a diffusive predator-prey model with Ivlev-type functional response

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Applied Mathematics(A Journal of Chinese Universities) 2020年第4期35卷 437-451页

作者： ZHANG Li-na xu fei Department of Mathematics and statistics Northwest Normal UniversityLanzhou 730070China

The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is *** discuss the existence and non-existence of positive steady state solutions by using the bifurcation *** is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is ***,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.

关键词： Ivlev-type functional response protection zone bifurcation

Optimal production lot size with process deterioration under an extended inspection policy

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Journal of Systems Engineering and Electronics 2009年第4期20卷 768-776页

作者： Hu fei xu Genqi Ma Lixia Dept. of Mathematics Tianjin Univ. Tianjin 300072 P. R. China

A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.

关键词： production lot size product inspection policy deteriorating production system economic manufacturing quantity.

Some topics on the smooth particle hydrodynamics method

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Acta Mechanica Sinica 2023年第2期39卷 1-2页

作者： fei xu Renato Vacondio School of Aeronautics Northwestern Polytechnical UniversityXi'an 710072China Department of Engineering and Architecture University of ParmaParmaItaly

The smooth particle hydrodynamics(SPH)method is one of the earliest meshfree methods,first proposed in 1977[1,2],to solve astrophysical *** the past years,as a Lagrangian,particle method,the SPH method has been widely applied in computational engineering *** provides novel insights for solving complex problems in fluid dynamics and solid mechanics involving large deformations.

关键词： problems. particle hydrodynamics

Realization of Numbers As the Degrees of Maps between Manifolds

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1413-1424页

作者： Young Min LEE fei xu Department of Mathematics Seoul National University Seoul 151747 Republic of Korea School of Mathematics Capital Normal University Beijing 100048 P. R. China

We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms.

关键词： Oriented closed manifold degree of a map integral quadratic form

Variation of Out-of-Plane Constraint and Its Effects on Fracture

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上海交通大学学报 2004年第Z2期38卷 212-216页

作者： fei xu Yulong Li Wanlin Guo Department of Mechanical Engineering Tokyo University of Science Noda2788510 Japan School of Aeronautics Northwestern Polytechnical University Xi''an710072 P. R. China School of Aeronautics Northwestern Polytechnical University Xi''an710072 P. R. China School of Aeronautics and Astronauts Nanjing University of Aeronautics and AstronautsNaniing210016 P.R.China

The limitations of using one-parameter to describe the crack-tip fields have prompted investigators to consider better descriptions of the crack tip fields. The two-parameter descriptions, such as J-Q theory, have been an important development in this field. But under the consideration of plane strain and three-dimensional problem, the effects of the out-of-plane stress can not be neglected In this paper, effects of the in-plane constraint as well as the out-of-plane constraint are studied by aid of the finite element method on the plane strain condition. It is obvious that both the in-plane constraint (Q factor) and the out-of-plane constraint (Tz = σzz/(σxx + σyy) ) affect the crack tip *** important features of the out-of-plane constraint are described out based on the simulation results. At the end of this paper, a three-parameter formulation is proposed, in which both the in-plane constraint and the out-of-plane constraint are considered. Comparing with the results of the FEM numerical simulation, the three-parameter description can provide a better prediction near the crack tip.

关键词： in-plane constraint out-of-plane constraint three-parameter formulation crack tip field elastic-plastic

Cure of a New Type Composite on Noise Control and Effect of Filler Modification

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Journal of Materials Science & Technology 2003年第Z1期19卷 135-136页

作者： Jun CAI fei xu Weimin CAI School of Municipal and Environment Englineering Harbin Institute of Technology Harbin150001china School of Environment Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China School of Environment Science and Engineering Shanghai Jiao Tong University Shanghai 200240 China

A new type composite of high efficiency sound attenuation was cured. The superfine tungsten powder, plasticizerand stabilizer are added into the PVC resin and blended in the mixing chamber of a HAAKE rheometer. The effect ofthe filler modification is considered in the composite cure. The properties of modified composite and unmodified oneare studied by SEM morphology viewing, acoustic and mechanical measurement. The test results indicate that thereason of the better soundproof and mechanical properties is the particle uniform dispersion and stronger adhesion.

关键词： Composite, Filler modification, Soundproof property, Mechanical property