Double-bracket dissipation in kinetic theory for particles with anisotropic interactions
Double-bracket dissipation in kinetic theory for particles with anisotropic interactions
复制标题
具有各向异性相互作用的粒子动力学理论中的双括号耗散
DOI：
10.1098/rspa.2010.0043
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
C. Tronci
中科院分区：
文献类型：
--
作者：
Darryl D. Holm;V. Putkaradze;C. Tronci
我们直接从耗散 Vlasov 动力学方程导出各向异性粒子动力学的运动方程，耗散由双括号方法（双括号 Vlasov 或 DBV）给出。 DBV 方程的矩导致质量密度达西定律的非局部形式。接下来，考虑具有各向异性相互作用的粒子的动力学方程，并将其转化为 DBV 形式。这些双括号动力学方程的力矩动力学表示为质量密度和方向密度的李-达西连续方程。我们还展示了如何从 DBV 的冷类等离子体矩闭合获得 Smoluchowski 模型。因此，双括号动力学框架可以作为导出不同类型动力学（从密度取向到 Smoluchowski 方程）的统一方法。还讨论了更通用的物理系统的扩展。
We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead to a non-local form of Darcy’s law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double-bracket kinetic equations is expressed as Lie–Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double-bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density-orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.