数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2012年
5期
839-843
,共5页
扩散问题%质量守恒定律%浓度时间函数%傅里叶分析
擴散問題%質量守恆定律%濃度時間函數%傅裏葉分析
확산문제%질량수항정률%농도시간함수%부리협분석
diffusion equation%law of Mass conservation%density-time function%Fourier analysis
本文针对核污染扩散问题,建立了对放射性粉尘在空气中传播方向和浓度变化的模型.首先根据质量守恒定律导出无风条件下放射性物质的扩散,然后在扩散模型中应用风速方向上的浓度时间函数,得到改进的扩散模型.模型中考虑到风场影响下的放射性物质扩散规律,采用对流扩散模型,引入时间分数阶偏微分方程,进而通过已知数据分析放射性尘埃对其扩散趋势做出预测.
本文針對覈汙染擴散問題,建立瞭對放射性粉塵在空氣中傳播方嚮和濃度變化的模型.首先根據質量守恆定律導齣無風條件下放射性物質的擴散,然後在擴散模型中應用風速方嚮上的濃度時間函數,得到改進的擴散模型.模型中攷慮到風場影響下的放射性物質擴散規律,採用對流擴散模型,引入時間分數階偏微分方程,進而通過已知數據分析放射性塵埃對其擴散趨勢做齣預測.
본문침대핵오염확산문제,건립료대방사성분진재공기중전파방향화농도변화적모형.수선근거질량수항정률도출무풍조건하방사성물질적확산,연후재확산모형중응용풍속방향상적농도시간함수,득도개진적확산모형.모형중고필도풍장영향하적방사성물질확산규률,채용대류확산모형,인입시간분수계편미분방정,진이통과이지수거분석방사성진애대기확산추세주출예측.
In this paper,we construct a differential model to describe the variation of density and propagation of radioactive dusts released from a nuclear power plant.We derived a diffusion equation which models the propagation of the radioactive dusts in accordance with the law of mass conservation. Taking account of the wind force and the decay of radionuclide,we improve the model to establish a fractional order differential equation.With the known data,we determine the coefficients in the equation and use it to predict the influence of the radioactive dusts to different regions in China.
