Gradients of potential fields on rough surfaces: Perturbative calculation of the singularity distribution function f( alpha ) for small surface dimension.
Gradients of potential fields on rough surfaces: Perturbative calculation of the singularity distribution function f( alpha ) for small surface dimension.
复制标题
粗糙表面上势场的梯度：小表面尺寸的奇点分布函数 f( alpha ) 的微扰计算。
DOI：
10.1103/physreve.47.957
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
Meneveau
中科院分区：
文献类型：
--
作者：
Sarkar;Meneveau
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An exact solution to the Laplace equation with Dirichlet boundary conditions on a simple boundary is used in an iterative fashion to study the case of a stochastic rough surface with fractal dimension D=2+\ensuremath{\epsilon}. For small \ensuremath{\epsilon}, an analytic expression is derived for the spectrum of singularities f(\ensuremath{\alpha}) of the gradient of the potential normal to the boundary, using the random multiplier approach. A binomial approximation to the multiplicative process is shown to severely underestimate f(\ensuremath{\alpha}) for low values of \ensuremath{\alpha}.