Burgers动力学中的合并与分裂
Merging and fragmentation in the Burgers dynamics
摘要：
我们探讨了无粘极限，所谓的“粘附模型”在宇宙学中，在一个政权，（几乎）所有的流体粒子嵌入点一样的大规模晕的无噪声的伯格斯动力学。根据以前的工作，我们把我们的调查集中在一个“几何”模型，在激波流形内的物质演化是从几何结构定义的。这一假设与通常的连续性方程成立的假设不同，但在无粘极限下，两种模型在规则区域一致。利用该"几何模型“的动力学的Legendre变换和凸包的制定，我们研究了随时间的演化的物质分布和相关的分区的拉格朗日和欧拉空间。我们描述了如何晕质量分布来自拉格朗日空间中的三角剖分，而欧拉空间中的对偶Voronoi样镶嵌给出了空区域的边界，激波节点位于其顶点。然后，我们强调，这种动力学实际上导致晕碎裂的空间维度大于或等于2（在本文中研究的无粘限制）。这是最容易看到的拉格朗日空间三角形的属性，我们说明了这个过程中的二维（2D）的情况。特别是，我们解释了点状晕如何只通过三体碰撞合并，而两体碰撞总是会产生两个新的大规模激波节点（在2D）。这推广到更高的维度，我们简要说明了三维（3D）的情况。这导致了一个特定的图像，通过连续的晕碎裂和合并的连续形成的巨大的晕。
英文摘要：
We explore the noiseless Burgers dynamics in the inviscid limit, the so-called ``adhesion model'' in cosmology, in a regime where (almost) all the fluid particles are embedded within point-like massive halos. Following previous works, we focus our investigations on a ``geometrical'' model, where the matter evolution within the shock manifold is defined from a geometrical construction. This hypothesis is at variance with the assumption that the usual continuity equation holds but, in the inviscid limit, both models agree in the regular regions. Taking advantage of the formulation of the dynamics of this ``geometrical model'' in terms of Legendre transforms and convex hulls, we study the evolution with time of the distribution of matter and the associated partitions of the Lagrangian and Eulerian spaces. We describe how the halo mass distribution derives from a triangulation in Lagrangian space, while the dual Voronoi-like tessellation in Eulerian space gives the boundaries of empty regions with shock nodes at their vertices. We then emphasize that this dynamics actually leads to halo fragmentations for space dimensions greater or equal to 2 (for the inviscid limit studied in this article). This is most easily seen from the properties of the Lagrangian-space triangulation and we illustrate this process in the two-dimensional (2D) case. In particular, we explain how point-like halos only merge through three-body collisions while two-body collisions always give rise to two new massive shock nodes (in 2D). This generalizes to higher dimensions and we briefly illustrate the three-dimensional (3D) case. This leads to a specific picture for the continuous formation of massive halos through successive halo fragmentations and mergings.
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