论文标题
从扩散通量到狭窄的窗户在三个维度上重建点源
Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions
论文作者
论文摘要
我们开发了一种计算方法，以定位从通量扩散颗粒的稳态梯度的来源，这是通过狭窄的窗户分布在三维半空间或球体上的边界上的狭窄窗户。这种方法基于使用neumann-green的功能求解混合边界固定扩散方程并匹配渐近。我们计算概率通量，并开发出高度有效的分析 - 布朗尼数值方案。该方案通过避免了无限域中的布朗轨迹的明确计算来加速模拟时间。我们得出的分析公式与从快速数值仿真方案获得的结果一致。使用粒子通量的分析表示，我们展示了如何重建点源的位置。此外，我们研究了由于通量中存在的加性波动而引起的源重建的不确定性。我们还研究了各种窗口配置（群集与统一分布）对恢复源位置的影响。
We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three dimensional half-space or on a sphere. This approach is based on solving the mixed boundary stationary diffusion equation with the Neumann-Green's function and matched asymptotic. We compute the probability fluxes and develop a highly efficient analytical-Brownian numerical scheme. This scheme accelerates the simulation time by avoiding the explicit computation of Brownian trajectories in the infinite domain. Our derived analytical formulas agree with the results obtained from the fast numerical simulation scheme. Using the analytical representation of the particle fluxes, we show how to reconstruct the location of the point source. Furthermore, we investigate the uncertainty in the source reconstruction due to additive fluctuations present in the fluxes. We also study the influence of various window configurations (cluster vs uniform distributions) on recovering the source position.
