用Langevin-Gleichungen方法对Roehren颗粒层进行理论建模
Theoretische Modellierung granularer Stroeme in duennen Roehren mit Langevin-Gleichungen
摘要：
这是作者1995年在柏林洪堡大学写的毕业论文的最终版本。本文的研究对象是颗粒物料在重力作用下在竖直窄管内的流动，该流动由朗之万方程描述。忽略相互作用，我们可以求解均匀情况下的福克-普朗克方程。考虑到非弹性碰撞，导出玻尔兹曼方程。假设局部平衡，流体动力学方程导致的非均匀情况下的朗之万方程形式主义的扩展。对于某些参数范围，我们的形式主义也可以用来描述交通流。我们应用稳定性分析的流体动力学方程组，并发现临界密度的发生颗粒聚集。我们使用数值模拟的朗之万方程，以验证我们的齐次解决方案以及临界密度。
英文摘要：
This is the final version of the author's diploma thesis written at the Humboldt University of Berlin in 1995. The topic is the flow of granular material in narrow vertical pipes, driven by the gravity, that is described by Langevin equations. Neglecting the interactions, we can solve the resulting Fokker-Planck equation for the homogeneous case. The consideration of inelastic collisions leads to a Boltzmann equation. Assuming local equilibrium, the hydrodynamic equations lead to the extension of the Langevin equation formalism for the inhomogeneous case. For certain parameter ranges, our formalism can also be used to describe traffic flows. We applied stability analyses to the hydrodynamic equations and found critical densities for the occurrence of particle clustering. We used numerical simulations of the Langevin equations to verify our homogeneous solution as well as the critical densities.
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