英语翻译The paper deals with a diffusing particle that escapes f

英语翻译
The paper deals with a diffusing particle that escapes from a cavity to the outer world through a narrow cylindrical tunnel.We derive expressions for the Laplace transforms of the particle survival probability,its lifetime probability density,and the mean lifetime.These results show how the quantities of interest depend on the geometric parameters （the cavity volume and the tunnel length and radius） and the particle diffusion coefficients in the cavity and in the tunnel.Earlier suggested expressions for the mean lifetime,which correspond to different escape scenarios,are contained in our result as special cases.In contrast to these expressions,our formula predicts correct asymptotic behavior of the mean lifetime in the absence of the cavity or tunnel.To test the accuracy of our approximate theory we compare the mean lifetime,the lifetime probability density,and the survival probability the latter two are obtained by inverting their Laplace transforms numerically with corresponding quantities found by solving numerically the three-dimensional diffusion equation,assuming that the cavity is a sphere and that the particle has the same diffusion coefficient in the cavity and in the tunnel.Comparison shows excellent agreement between the analytical and numerical results over a broad range of the geometric parameters of the problem.

文章论述了一种扩散的粒子逃离了腔向外的世界通过一条狭窄的圆柱隧道.我们得到的拉氏变换表达式的生存概率,其生命周期中粒子的概率密度,平均寿命.这些结果显示兴趣取决于数量的几何参数(腔体积和隧道长度、半径和粒子扩散系数腔和在隧道里.早些时候的平均一生建议表达式,它对应于不同的逃避场景,都被包含在我们的结果作为特殊情况.这些表达方式相比,我们的公式预测正确的意思是一生的渐近性态无腔或隧道.我们测试的准确性,我们比较了近似理论意味着一生,一辈子概率密度,后两种生存概率的递推关系式来得到他们的拉普拉斯转换数值与相应数量的三维数值模拟发现通过求解扩散方程,假如该腔球体和粒子具有相同的扩散系数在腔内,在隧道里.比较显示出非凡的之间的协议解析及数值结果而广泛的几何参数的问题.