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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

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

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

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.

Multi-agent communication-based train control system for Indian railways： the behavioural analysis

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Journal of Modern Transportation 2015年第4期23卷 272-286页

作者： Anshul Verma k. k. Pattanaik Information and Communication Technology Atal BihariVajpayee - Indian Institute of Information Technology andManagement Gwalior 474015 India

Multi-agent technology has been used in many complex distributed and concurrent systems. A railway system is such a safety critical system and careful inves- tigation of the functional components is very important. Study of the various functional components in communi- cation-based train control （CBTC） system necessitates a good structural design followed by its validation and ver- ification through a formal modelling technique. The work.presented here is the follow up of our multi-agent-based CBTC system for Indian railway designed using the methodology for engineering system of software agents. Behavioural analysis of the designed system involves several operating scenarios that arise during train run, and helps in understanding the reaction of the system to such situations. This validation and verification are very important as it allows the system designer to critically evaluate the desired function of the system and to correct the design errors, if any, before its actual implementation. Modelling, validation and verification of the structural design through Coloured petri net （CPN） are central to this paper. Analysis of simulation results validates the efficacy of the design.

关键词： CBTC Multi-agent Fault resolution Modelling Validation and verification CPN

LR-normal orthogroups

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Science China Mathematics 2006年第3期49卷 330-341页

作者： SHUM k. P. SEN M. k. Faculty of Science Department of Pure Mathematics

A new k.nd of regular orthogroups, namely, the LR-normal orthogroups is introduced and investigated. In particular, we will introduce the gearing techniques for fitting semigroup components on a semilattice in the con... 详细信息

关键词： LR-regular orthogroups, LR-normal orthogroups, gearing of semigroups.

Prediction of the position of coal particles in an air dense medium fluidized bed system

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International Journal of Mining Science and Technology 2015年第3期25卷 421-427页

作者： Prusti Pallishree Sahu Ashok.k. Biswal Surendra k. Council of Scientific & Industrial Research-Institute of Minerals and Materials Technology

An air dense medium fluidized bed separator(ADMFBS) is used for dry beneficiation of coal using ultrafine magnetite particles as a pseudo-fluid medium. In this process, the coal particle gains additional weight due to coating on its surface and deposition at dead zone area by fine magnetite ***, the effective density of coal particle increases and the position of coal particle changes accordingly. In this work. an attempt was made to predict the position of coal particle in non-bubbling condition dense medium fluidized bed system. Coal particles of different shape such as cubical, rectangular prism,spherical and triangular prism with different projected area and density were used. The results show that the position of coal particle in air dense medium fluidized bed follows descending order with respect to the increase of density, projected area of coal particle and different shapes(i.e., triangular prism, cubical,rectangular prism and spherical). Empirical mathematical correlations were developed to predict the position of coal particle.

关键词： Coal beneficiation Pseudo-fluid medium Dead zone area Effective density

Melt film formation and disintegration during novel atomization process

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中国有色金属学会会刊：英文版 2007年第6期17卷 1276-1281页

作者：刘允中 k. Min agawa H. k.k.sawa k. Halada School of Mechanical Engineering South China University of Technology Ecomaterials Research Center National Institute for Materials Science 1-2-1 Sengen Tsukuba Cit y Ibaraki 305-0047 Japan

Hybrid atomization is a new powder-mak.ng method and can produce economically very fine, clean, spherical tin alloy powders with average particle size about 10μm and narrow size distributions. The k.y concept of hybrid atomization is to control the liquid film formation on disk.for fine powder production. Low-pressure gas atomization was utilized to promote the formation of a very thin stable liquid film before centrifugal break.p and give a better preparation for the final disintegration of melts. Besides the break.p ability of the rotating atomizer, the characteristics of liquid film on rotating disk.affect the atomization mechanism and results remark.bly. The main disintegration mode of melt is the break.p type of liquid film, which depends on the film instability and the atomization ability of the rotating disk. On the other hand, the mean powder size relates closely to the film thick.ess. The powder size distribution is mainly controlled by the atomization mode and the stability, flow type of liquid film on the rotating disk. A very thin, stable liquid film with long ligaments and a small pitch in LF mode results in very fine uniform tin alloy powders.

关键词：混合雾化薄膜雾化模式合金