双粒子系统中的非定域相互作用
Nonlocal interactions in coagulating particle systems
摘要：
我们考虑一个三维系统，由大量的小球形粒子，移动由于重力或层流剪切和合并时，他们交叉。可以应用尺寸比标准以将合并限制到尺寸相似的颗粒（相互作用的局部性）或尺寸不同的颗粒（非局部性）。我们进行直接数值模拟（DNS）的粒子系统，并研究由此产生的质谱。在平均场近似下，这些系统可以用Smoluchowski凝聚方程（SCE）描述。DNS的粒子系统与本地化强制显示SCE的标度解或Kolmogorov-Zakharov谱，表示一个恒定的质量通量。没有尺寸比标准的DNS显示-4/3标度的大颗粒在重力系统中，这意味着一个恒定的流量的粒子数，我们也发现分析假设非局域性的相互作用在SCE。对于层流剪切，这种非局部性只是边缘的，我们的DNS表明，需要对标度解进行校正。
英文摘要：
We consider a three dimensional system consisting of a large number of small spherical particles, which move due to gravity or with laminar shear and which merge when they cross. A size ratio criterion may be applied to restrict merging to similar sized particles (locality of interactions) or particles dissimilar in size (nonlocality). We perform direct numerical simulations (DNS) of this particle system and study the resulting mass spectra. In mean field approximation, these systems can be described by the Smoluchowski coagulation equation (SCE). DNS of the particle system with locality enforced show the scaling solutions or Kolmogorov-Zakharov spectra for the SCE, signifying a constant mass flux. DNS without a size ratio criterion show -4/3 scaling for large particles in a system with gravity, signifying a constant flux in number of particles, which we also find analytically by assuming nonlocality of interactions in the SCE. For laminar shear, this nonlocality is only marginal, and our DNS show that a correction to the scaling solution is required.
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