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Journal of Computational Mathematics 2008年第1期26卷 1-22页

作者： Xin Wen shi jin LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China Department of Mathematics University of Wisconsin Madison WI 53706 USAand Department of Mathematical Sciences Tsinghua University Beijing 100084 China

We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].

关键词： Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients Error estimate Half order error bound

Chloride resistance of Cr-bearing alloy steels in carbonated concrete pore solutions

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International Journal of Minerals,Metallurgy and Materials 2020年第4期27卷 494-504页

作者： jing Ming jin-jie shi Jiangsu Key Laboratory of Construction Materials School of Materials Science and EngineeringSoutheast UniversityNanjing 211189China

The effect of carbonation on the chloride resistance of low-carbon steel and two Cr-bearing alloy steels in simulated concrete pore solutions was *** chloride threshold values of steels were determined on the basis of corrosion potential(Ecorr)and polarization resistance(Rp).Moreover,the chloride-induced corrosion behavior of steels was evaluated using electrochemical impedance spectroscopy,cyclic voltammetry,cathodic potentiodynamic polarization,and scanning electron microscopy/energy dispersive X-ray spectroscopy *** steels have higher chloride resistance than low-carbon steel in carbonated and non-carbonated concrete pore *** chloride resistance of alloy steels improves with increasing Cr *** addition,the chloride resistance of all steels is negatively affected by the carbonation of concrete pore solution,especially for alloy steel with high Cr content in the presence of high chloride content.

关键词： alloy steel concrete pore solution carbonation chloride resistance electrochemical measurements

Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

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Communications in Theoretical Physics 2006年第1X期46卷 175-182页

作者： shi jin ZHU shi-Qun School of Physical Science and Technology Suzhou University Suzhou 215006 China

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.

关键词： logistic growth model first-order-like phase transition re-entrance-like phase transition colored noise

On a Sharp Volume Estimate for Gradient Ricci Solitons with Scalar Curvature Bounded Below

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Acta Mathematica Sinica,English Series 2011年第5期27卷 871-882页

作者： shi jin ZHANG Beijing International Center for Mathematical Research Peking University Beijing 100871 P. R. China

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota＇s argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of the scalar curvature for expanding Ricci solitons; we also provide a direct （elliptic） proof of this sharp estimate. Moreover, if the scalar curvature attains its minimum value at some point, then the manifold is Einstein.

关键词： Ricci solitons Einstein manifold scalar curvature

Analysis of Microstructure of Silicon Carbide Fiber by Raman Spectroscopy

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Journal of Materials Science & Technology 2008年第2期24卷 261-264页

作者： Baohong jin Nanlin shi Institute of Metal Research Chinese Academy of Sciences Shenyang 110016 China

The SiC fiber was prepared by chemical vapour depostion, which consists of tungsten core, SiC layer and carbon coating. The microstructure of the fiber was investigated using Raman spectroscopy, illustrating SiC variation in different region of the fiber. The result shows that the SiC layer can be subdivided into two parts in the morphologies of SiC grains; their sizes increase and their orientations become order with increasing distance from the fiber center. It is demonstrated that the mount of free carbon in the fiber is responsible for the variation of SiC grains in sizes and morphologies. The analysis of Raman spectra shows that the predominant β-SiC has extensive stacking faults within the crystallites and mixes other polytypes and amorphous SiC into the structure in the fiber.

关键词： Raman spectra Optical phonon SiC fiber Carbon content

On the mean field limit of the Random Batch Method for interacting particle systems

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Science China Mathematics 2022年第1期65卷 169-202页

作者： shi jin Lei Li School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai 200240China

The Random Batch Method proposed in our previous work(jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of *** this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete *** this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.

关键词： Random Batch Method mean field limit chaos Wasserstein distance nonlinear Fokker-Planck equation

Influence of mill scale and rust layer on the corrosion resistance of low-alloy steel in simulated concrete pore solution

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International Journal of Minerals,Metallurgy and Materials 2017年第1期24卷 64-74页

作者： jin-jie shi jing Ming Jiangsu Key Laboratory of Construction Materials School of Materials Science and EngineeringSoutheast UniversityNanjing 211189China

Electrochemical impedance spectroscopy, cyclic potentiodynamic polarization measurements, and scanning electron microscopy in conjunction with energy-dispersive X-ray spectroscopy were used to investigate the influence of mill scale and rust layer on the passivation capability and chloride-induced corrosion behaviors of conventional low-carbon（LC） steel and low-alloy（LA） steel in simulated concrete pore solution. The results show that mill scale exerts different influences on the corrosion resistance of both steels at various electrochemical stages. We propose that the high long-term corrosion resistance of LA steel is mainly achieved through the synergistic effect of a gradually formed compact, adherent and well-distributed Cr-enriched inner rust layer and the physical barrier protection effect of mill scale.

关键词： steel reinforced concrete low alloy steel low carbon steel steel corrosion corrosion resistance

Electrochemical and analytical characterization of three corrosion inhibitors of steel in simulated concrete pore solutions

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International Journal of Minerals,Metallurgy and Materials 2012年第1期19卷 38-47页

作者： jin-jie shi Wei Sun School of Materials Science end Engineering Southeast University Nanjing 211189 China Jiangsu Key Laboratory of Construction Materials Southeast University Nanjing 211189 China

Corrosion inhibitors for steel, such as sodium phosphate （Na3PO4）, sodium nitrite （NaNO2）, and benzotriazole （BTA）, in simulated concrete pore solutions （saturated Ca（OH）2） were investigated. Corrosion behaviors of steel in different solutions were studied by means of corrosion potential （Ecorr）, linear polarization resistance （LPR）, electrochemical impedance spectroscopy （EIS）, and potentiodynamic polarization （PDP）. A field emission scanning electron microscope （FESEM） equipped with energy dispersive X-ray analysis （EDXA） was used for observing the microstructures and morphology of corrosion products of steel. The results indicate that, compared with the commonly used nitrite-based inhibitors, Na3PO4 is not a good inhibitor, while BTA may be a potentially effective inhibitor to prevent steel from corrosion in simulated concrete pore solutions.

关键词： steel corrosion inhibitors electrochemical analysis concrete solutions

AN ASYMPTOTIC PRESERVING SCHEME FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN THE HIGH FIELD REGIME

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Acta Mathematica Scientia 2011年第6期31卷 2219-2232页

作者： shi jin Li Wang Department of Mathematics and Institute of Natural Sciences Shanghai Jiao Tong University Shanghai 20040 China Department of Mathematics University of Wisconsin-Madison 480 Lincoln Drive Madison WI 53706 USA

The Vlasov-Poisson-Fokker-Planck system under the high field scaling describes the Brownian motion of a large system of particles in a surrounding bath where both collision and field effects （electrical or gravitational） are dominant. Numerically solving this system becomes challenging due to the stiff collision term and stiff nonlinear transport term with respect to the high field. We present a class of Asymptotic-Preserving scheme which is efficient in the high field regime, namely, large time steps and coarse meshes can be used, yet the high field limit is still captured. The idea is to combine the two stiff terms and treat them implicitly. Thanks to the linearity of the collision term, using the discretization described in [jin S, Yah B. J. Comp. Phys., 2011, 230： 6420-6437] we only need to invert a symmetric matrix. This method can be easily extended to higher dimensions. The method is shown to be positive, stable, mass and asymptotic preserving. Numerical experiments validate its efficiency in both kinetic and high field regimes including mixing regimes.

关键词： Vlasov-Poisson-Fokker-Planck equation high field limit asymptoticpreserving schemes

ON THE QUASI-RANDOM CHOICE METHOD FOR THE LIOUVILLE EQUATION OF GEOMETRICAL OPTICS WITH DISCONTINUOUS WAVE SPEED

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Journal of Computational Mathematics 2013年第6期31卷 573-591页

作者： jingwei Hu shi jin Institute for Computational Engineering and Sciences (ICES) The University of Texas at Austin 201 East 24th St Stop C0200 Austin TX 78712 USA Department of Mathematics University of Wisconsin-Madison 480 Lincoln Drive Madison WI 53706 USA Department of Mathematics Institute of Natural Sciences and MOE Key Lab in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China

We study the quasi-random choice method （QRCM） for the Liouville equation of ge- ometrical optics with discontinuous locM wave speed. This equation arises in the phase space computation of high frequency waves through interfaces, where waves undergo partial transmissions and reflections. The numerical challenges include interface, contact discon- tinuities, and measure-valued solutions. The so-called QRCM is a random choice method based on quasi-random sampling （a deterministic alternative to random sampling）. The method not only is viscosity-free but also provides faster convergence rate. Therefore, it is appealing for the prob!em under study which is indeed a Hamiltonian flow. Our analy- sis and computational results show that the QRCM 1） is almost first-order accurate even with the aforementioned discontinuities; 2） gives sharp resolutions for all discontinuities encountered in the problem; and 3） for measure-valued solutions, does not need the level set decomposition for finite difference/volume methods with numerical viscosities.

关键词： Liouville equation High frequency wave Interface Measure-valued solution,Random choice method Quasi-random sequence.