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Numerical Blow-up for a Nonlinear Heat Equation

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Acta Mathematica Sinica,English Series 2011年第5期27卷 845-862页

作者： Firmin k. N'GOHISSE Theodore k. BONI Universite d'Abobo-Adjame UFR-SFA Departement de Mathematiques et Informatique 01 BP 1003 Abidjan 01 Cdte d'Ivoire Institut National Polytechnique Houphouet-Boigny de Yamoussouk.o BP 1093 Yamoussoukro Cote d'Ivoire

This paper concerns the study of the numerical approximation for the following initialboundary value problem{ut-uzx=f（u）,t∈（0,1）,t∈（0,T） u（0,t）=0,t∈（0,1）,t∈（0,T） u（x,0）=u0（x）,x∈（0,1）where f（s） is a positive, increasing, C1 convex function for the nonnegative values of s, f（0）〉0, f∞ds/f（s）〈∞, u0∈C1（[0, 1]）, u0（0） = 0, u＇0（1）=0. We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiserete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertak.n for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.

关键词： Semidiscretization blow-up numerical blow-up time nonlinear heat equations

Viscosity of k.olin Slurries:Effects of Dispersant and Urea-Intercalation

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Journal of Wuhan University of Technology(Materials Science) 2017年第1期32卷 51-57页

作者：仇秀梅 LIU Yadong ALSHAMERI aref ZHU Xiaoyan 严春杰 Engineering Research Center of Nano-Geomaterials of Ministry of Education China University of GeosciencesWuhan 430074China Hubei Province Geological Experimental Testing Center Wuhan 430034China Hubei Urban Construction Vocation and Technological College Wuhan 430205China

Good fluidity（low viscosity） of highly concentrated k.olin is highly needed in paper-coating *** put forward an effective route to improve the viscosity concentration of Beihai k.olin *** effects of various factors such as solid content,pH,dispersant content,and urea-intercalation on the viscosity of k.olin slurries were *** results revealed that the viscosity of k.olin slurries significantly decreased with decreasing solid content or with increasing pH and dispersant *** was worth noting that ureaintercalation was proven to be an efficient method for promoting the dispersion of highly concentrated k.olin as compared with adding *** intercalation ratio of urea-intercalated k.olin was increased from 17.36%with 2%of urea addition to 81.30%with 6%of urea ***,the viscosity concentration of raw k.olin slurry was improved from 65.0%to 70.13%after the intercalation of urea with 6%addition,which was attributed to finer particle size,increased pH value and more negative charges of urea-intercalated ***,the route is effective to improve the dispersion of highly concentrated k.olin for paper-coating.

关键词： beihai k.olin dispersion urea-intercalation viscosity concentration

Photolysis studies on HCOOH and HCOO^- in presence of TiO_2 photocatalyst as suspension in aqueous medium

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Journal of Natural Gas Chemistry 2009年第1期18卷 50-54页

作者： G. R. Dey k. N. R. Nair k. k. Pushpa Radiation and Photochemistry Division Bhabha Atomic Research Centre Trombay Mumbai 400 085 India

Photolysis studies on formic acid （HCOOH） and formate ion （HCOO-） in presence of TiO2, a photocatalyst, as suspension in water were carried out separately using 350 nm ultraviolet light. The products, such as H2, CO, CO2 and CH4, generated during the experiments were monitored with varying the ambient, light exposure time, and the concentration of HCOOH/HCOO-. The yields of CO in all these systems increased with light exposure time. In aerated systems, CO yields were higher in contrast to the deoxygenated （Ar-purged） systems under identical conditions. It is proposed apparently that the formation of CO is tak.ng place during the chemical reduction of in-situ generated CO2, a photo-mineralized product of HCOOH/HCOO-, but not through the direct photodecomposition or photodehydration （CO＋H2O） of solute molecules. The rates of CO formation during 1.3 M HCOOH photolysis in presence of TiO2 photocatalyst were evaluated to be 0.21 and 0.13 μl/min in aerated and Ar-purged systems, respectively. As compared with HCOOH systems, the CO yields are lower when 0.2 M HCOONa was exposed to light under identical conditions. The CO growth rates were evaluated to be 0.07 and 0.046 μl/min^-1 for aerated and deoxygenated HCOONa systems, respectively; moreover, the trend is quite similar to that of the HCOOH system. Under these conditions, the emission of H2 was also observed, and its yield was significantly higher in Ar-purged system as compared with the CO yields. However, in aerated system, the yields of these products were just opposite. The formation of low yield of methane was observed during photolysis of HCOOH/HCOO ions. In CO2 ambient, the yields of CO and H2 varied drastically with time.

关键词： formic acid formate ion photolysis TiO2

Catalytic ignition of light hydrocarbons

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Journal of Natural Gas Chemistry 2009年第2期18卷 115-123页

作者： k. L. Hohn Department of Chemical Engineering Kansas State UniversityManhattan KS 66506-5102 USA

Catalytic ignition refers to phenomenon where sufficient energy is released from a catalytic reaction to maintain further reaction without additional external heating. This phenomenon is important in the development of catalytic combustion and catalytic partial oxidation processes, both of which have received extensive attention in recent years. In addition, catalytic ignition studies provide experimental data which can be used to test theoretical hydrocarbon oxidation models. For these reasons, catalytic ignition has been frequently studied. This review summarizes the experimental methods used to study catalytic ignition of light hydrocarbons and describes the experimental and theoretical results obtained related to catalytic ignition. The role of catalyst metal, fuel and fuel concentration, and catalyst state in catalytic ignition are examined, and some conclusions are drawn on the mechanism of catalytic ignition.

关键词： catalytic ignition hydrocarbon oxidation

Special Properties of Morita Contexts

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Algebra Colloquium 2024年第2期31卷 309-322页

作者： kamal Payk.n L.A.Bok.t Department of Mathematics Tafresh UniversityTafreshIran 不详

In this paper we continue the study of various ring theoretic properties of Morita *** and sufficient conditions are obtained for a general Morita context or a trivial Morita context or a formal triangular matrix ring to satisfy a certain ring property which is among being k.sch,completely primary,quasi-duo,2-primal,NI,semiprimitive,projective-free,*** also characterize when a general Morita context is weak.y principally quasi-Baer or strongly right mininjective.

关键词： Morita context formal triangular matrix ring k.sch quasi-duo k.the's conjecture weak.y principally quasi-Baer

Analysis Scheme for Density Modulation Experiments to Study Particle Confinements

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Plasma Science and Technology 2006年第1期8卷 65-71页

作者： k. TANAk. C. MICHAEL k. k.WANATA T. TOk.ZAWAI M. SHOJI k. TOI 高翔揭银先 National Institute for Fusion Science Toki 509-5292 Japan Institute of Plasma Physics Chinese Academy of Science Hefei 230031 China

Density modulation experiments are powerful experimental schemes for the study of particle transport. The diffusion coefficients （D） and convection velocity （V）, which cannot be evaluated from the particle balance in the equilibrium state, can be obtained separately. Further, the estimated values of D and V are determined independent of the absolute value of the particle source rate, which is difficult to obtain experimentally. However, the sensitivities and interpretation of D and V from the modulation experiments need to be considered. This paper describes numerical techniques for solving the particle balance equation of the modulation components. Examples of the analysis are shown regarding the data of LHD experiments, and the results of the modulation experiments are discussed.

关键词： density modulation, particle confinements, diffusion coefficient convection velocity

The mathematical weighting of GNSS observations based on different types of receivers/antennas and environmental conditions

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Geodesy and Geodynamics 2023年第5期14卷 521-540页

作者： kamal Parvazi Saeed Farzaneh Abdolreza Safari School of Surveying and Geospatial Engineering College of EngineeringUniversity of TehranNorth Kargar Street***TehranIran

Stochastic models play an important role in achieving high accuracy in positioning,the ideal estimator in the least-squares(LS)can be obtained only by using the suitable stochastic *** study investigates the role of variance component estimation(VCE)in the LS method for Precise Point Positioning(PPP).This estimation is performed by considering the ionospheric-free(IF)functional model for code and the phase observation of Global Positioning System(GPS).The strategy for estimating the accuracy of these observations was evaluated to check.the effect of the stochastic model in four modes:a)antenna type,b)receiver type,c)the tropospheric effect,and d)the ionosphere *** results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unk.own components in the PPP *** is because a constant empirical variance may not be suitable for various receivers and antennas under different *** were compared in two cases using the stochastic model of nominal weight and weight estimated by *** position error difference for the east-west,north-south,and height components was 1.5 cm,4 mm,and 1.8 cm,***,weight estimation with LS-VCE can provide more appropriate ***,the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE *** to the results,the LS-VCE has a higher convergence rate than the nominal *** weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11,13,12,and 9 min,respectively.

关键词： Stochastic model Global positioning system Variance component estimation Least-squares Precise point positioning Elevation-dependent model

Structural and Dielectric Properties of ZnO Added (Na_(1/2)Bi_(1/2))TiO_3 Ceramics

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Journal of Materials Science & Technology 2011年第3期27卷 213-217页

作者： k.mini k.mari Ashutosh Prasad kamal Prasad University Department of Physics T.M.Bhagalpur University

Structural and dielectric properties of polycrystalline samples of lead-free （l-x）（Nal/2Bil/2）TiO3-xZnO, prepared using a high-temperature solid-state reaction method, were investigated in the composition range of 0≤x≤0.10. Rietveld analyses of X-ray diffraction data indicated the formation of a single-phase hexagonal structure with R3c symmetry. Williamson-Hall approach was applied to estimate the apparent particle size and lattice strain of the compounds. Temperature dependence of dielectric constant showed that the addition of ZnO to （Na1/2Bi1/2）TiO3 shifted the phase transition temperature towards higher side, a property favourable for practical applications of these ceramics. Further, temperature dependent permittivity data provided low temperature coefficient of capacitance （TCC〈8%） up to 100℃. Furthermore, a decrease in the value of dielectric loss with an increase in ZnO content was observed.

关键词： Lead-free Perovsk.tei Sodium bismuth titanate Ceramic Crystal structure Dielectric properties

A discrete model for prediction of radon flux from fractured rock.

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Journal of Rock.Mechanics and Geotechnical Engineering 2018年第5期10卷 879-892页

作者： k.M. Ajayi k. Shahbazi R Tuk.araja k. k.tzenstein Department of Mechanical Engineering South Dakota School of Mines and Technology Rapid City SD 57701 USA b Department of Mining Engineering and Management South Dakota School of Mines and Technology Rapid City SD 57701 USA Department of Geology and Geological Engineering South Dakota School of Mines and Technology Rapid City SD 57701 USA

Prediction of radon flux from the fractured zone of a propagating cave mine is basically associated with uncertainty and complexity. For instance, there is restricted access to these zones for field measure- ments, and it is quite difficult to replicate the complex nature of both natural and induced fractures in these zones in laboratory studies. Hence, a technique for predicting radon flux from a fractured rock.using a discrete fracture network.（DFN） model is developed to address these difficulties. This model quantifies the contribution of fractures to the total radon flux, and estimates the fracture density from a measured radon flux considering the effects of advection, diffusion, as well as radon generation and decay. Radon generation and decay are classified as reaction processes. Therefore, the equation solved is termed as the advection-diffusion-reaction equation （ADRE）. Peclet number （Pe）, a conventional dimensionless parameter that indicates the ratio of mass transport by advection to diffusion, is used to classify the transport regimes. The results show that the proposed model effectively predicts radon flux from a fractured rock. An increase in fracture density for a rock.sample with uniformly distributed radon generation rate can elevate radon flux significantly compared with another rock.sample with an equivalent increase in radon generation rate. In addition to Pe, two other independent dimensionless parameters （derived for radon transport through fractures） significantly affect radon dimensionless flux. Findings provide insight into radon transport through fractured rock. and can be used to improve radon control measures for proactive mitigation.

关键词： Radon mass flux Radon dimensionless flux Stochastic model Discrete fracture network.(DFN) Caving mining method Fractured rock.