本文選題：隨機(jī)擴(kuò)散方程 + 擴(kuò)散輸運(yùn)方程　； 參考：《強(qiáng)激光與粒子束》2017年12期

【摘要】：引入核函數(shù)法對(duì)隨機(jī)擴(kuò)散方程(SDE)樣本的密度分布進(jìn)行統(tǒng)計(jì),希望用核函數(shù)來減少統(tǒng)計(jì)漲落。由于SDE樣本的密度隨時(shí)間發(fā)展,越來越稀疏,所以核函數(shù)也應(yīng)該越來越大,也就是說核函數(shù)應(yīng)該隨時(shí)間在變化。通過一個(gè)瞬時(shí)釋放的二維擴(kuò)散問題(具有解析解),從定性和定量?jī)蓚�(gè)角度比較了變帶寬核函數(shù)法和傳統(tǒng)統(tǒng)計(jì)方法在密度分布統(tǒng)計(jì)中的性能差別,論述了變帶寬核函數(shù)法的優(yōu)缺點(diǎn),變帶寬核函數(shù)法在犧牲部分峰值的前提下可以很好地解決SDE樣本密度分布統(tǒng)計(jì)漲落問題,在工程應(yīng)用中值得推廣。
[Abstract]:The kernel function method is introduced to calculate the density distribution of the random diffusion equation (SDE) samples, and it is hoped that the kernel function can be used to reduce the statistical fluctuation. Because the density of SDE samples is more and more sparse with time, so the kernel function should be bigger and larger, that is to say, the kernel function should change with time. Through a two-dimensional diffusion problem with instantaneous release (with analytical solution), the performance differences between the variable bandwidth kernel function method and the traditional statistical method in density distribution statistics are compared qualitatively and quantitatively. The advantages and disadvantages of the variable bandwidth kernel function method are discussed. The variable bandwidth kernel function method can solve the statistical fluctuation problem of SDE sample density distribution at the premise of sacrificing partial peak value, and it is worth popularizing in engineering application.
【作者單位】： 杭州電子科技大學(xué)信息工程學(xué)院;
【基金】：國家自然科學(xué)基金項(xiàng)目(11475050,61503109,11705041) 浙江省科技廳公益性項(xiàng)目(2015C33035)
【分類號(hào)】：O211.63
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本文編號(hào)：2030071