We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent advection velocity, diffusion coefficient, and reaction rates. We also examine a model with mass-dependent coefficients describing aggregation with sedimentation. For the simplified model, we obtain an exact solution for the stationary spatially dependent agglomerate densities. In the model describing aggregation with sedimentation, we report a new conservation law and develop a scaling theory for the densities. For numerical efficiency we exploit the low-rank approximation technique; this dramatically increases the computational speed and allows simulations of large systems. The numerical results are in excellent agreement with the predictions of our theory.
翻译:我们从分析角度和数字角度探索由平流和局部来源驱动的聚合体。 系统在一个维度上是无异的, 即沿着平流方向。 我们分析一个简化模型, 其质量独立对流速度、 扩散系数和反应率。 我们还研究一个具有质量依赖系数的模型, 描述沉积的聚合。 对于这个简化模型, 我们为固定的空间依赖群密度获得一个精确的解决方案。 在描述沉积集合的模型中, 我们报告一项新的保护法, 并为密度开发一个缩放理论。 对于数字效率, 我们利用低级近距离技术; 这极大地提高了计算速度, 并允许模拟大型系统。 数字结果与我们理论的预测非常一致 。