宇宙双生体天体物理学与宇宙学 幽灵物质天体物理学。5： 二维数值模拟结果。 VLS。关于星系形成的一种可能方案。(p5)
...现在，处理两种物质（普通物质加上幽灵物质），如果Vthr << Vth cr，我们得到两个星系团，它们之间的距离对应于相对位置和最大距离。见图14。
** ** 图. 14 :** 联合引力不稳定性** **普通物质加上幽灵物质的示意图结果，当 **Vthr << Vth cr （初始介质为冷态）
...如果Vthr >> Vth cr，系统保持均匀，两种物质混合得非常紧密。对于Vthr » Vth cr，我们得到类似乳液的长期模式，见图15（此结果曾在以前的论文[1]中发表）。
图. 15 : Vth = Vth cr 时的乳液模式
...我们使用了两组5000个相互作用的质量点。正如我们所看到的，结果与图11 bis相似。同样的方法可以扩展到三维系统（这远超我们系统的可能性）。虽然三维系统与二维系统不同，但我们预计三维模拟会产生类似的长期三维乳液。联合不稳定性理论（耦合的杨氏方程）在第11节中介绍。
- 宇宙非常大结构的问题
...我们采用初始条件，普通物质（我们称之为普通物质）和幽灵物质的质量分布均匀。r是普通物质的质量密度，r是幽灵物质的质量分布密度，我们选择初始条件ro = 64 ro。此时，我们只需观察发生了什么。我们进行了二维数值模拟，使用两组5000个质量点，它们代表一些普通物质和幽灵物质的星系团，质量分别为M和M*，这意味着M* = 64 M。我们给这两个集合赋予二维热速度的麦克斯韦分布，<V*> = 4 < V >。我们忽略了膨胀现象（这将非常难以处理，因为我们不知道如何描述在膨胀宇宙中的引力作用）。结果如下。最重的群体，即幽灵物质，其杨氏时间比另一个群体短八倍，主导了整个过程，并通过引力不稳定性形成星系团，这些星系团排斥并限制了其他群体在剩余的位置。我们得到了二维细胞结构。整个结构的特征形成时间接近于最重群体（幽灵物质）的杨氏时间。
. 图. 16 :** F. Lansheat进行的模拟结果。** 左：幽灵物质星系团。右：普通物质结构。 . 图. 17 : 两者的叠加。 ...总体模式取决于初始条件。在以前的论文[6]中，得到了更大的幽灵物质星系团，由于选择了更高的幽灵物质初始温度，普通物质的结构更加规则。这种旨在模拟宇宙非常大尺度结构的方法，与基于暗物质的经典方法根本不同。在经典物质-暗物质系统中，稳定性存在问题：引力不稳定性通过局部增加密度，增加了热速度，使观测到的结构随时间消失。具有两种排斥性群体的系统在本质上不同，每个群体为另一个群体创造势垒。这解释了在时间和空间上的高度稳定性：普通物质的细胞将幽灵物质的星系团固定住，反之亦然。
原始版本（英文）
twin universe astrophysics and cosmology Matter ghost matter astrophysics. 5 : Results of numerical 2d simulations. VLS. About a possible schema for galaxies' formation.(p5)
...Now, dealing with two species (matter plus ghost matter), if Vthr << V th cr we get two clumps, whose distance corresponds to antipodality and maximum distance between them. See figure 14.
** ** Fig. 14 :** Schematic result of joint gravitational instability** **matter plus ghost matter, when **Vthr << Vth cr (initially cold medium)
...If Vthr >> Vth cr the system remains uniform and the two species closely mixed. For Vthr » Vth cr we get long duration emulsion-like patterns, see figure 15 (this result was presented in a former paper [1].
Fig. 15 : Emulsion pattern for Vth = Vth cr
...We have used two sets of interacting 5000 mass-points. As we can see the result is similar to the one of figure 11 bis . The same method could be extended to 3d system (which is far beyond the possibilities of our system). Although 3d systems are different from 2d systems we can expect 3d simulations would provide similar long duration 3d emulsions. The join instabilities theory (coupled Jeans equations) is presented in section 11.
- The problem of the very large structure of the Universe
...We take initial condition with uniform mass distributions for normal matter (t hat we call simply matter) and ghost matter. r being the mass density of the matter and r* the mass-distribution of the ghost matter, we choose for initial conditions ro* = 64 ro. At this level, just see what happens. We have performed 2d numerical simulations with two sets of 5000 mass-points, that are supposed to represents some clusters of matter and ghost matter, with masses M and M*, which means that M* = 64 M. We give these two sets maxwellian distributions of 2d thermal velocities with <V*> = 4 < V > . We neglect the expansion phenomena (it would be very difficult to deal with, for we do not know how to describe gravitational force in an expanding universe). The results are the following. The more massive population, the ghost matter'one, whose Jeans time is eight times shorter than the other ones runs the game and forms clumps, through gravitational instability, that repel and confines the other population in the remnant place. We get a 2d-cellular structure. The characteristic birth time of the whole structure is close to the Jeans time of the heavier population, of the ghost matter.
. Fig. 16 :** Results of simulations performed by F.Lansheat.** Left : ghost matter clumps. Right : matter structure. . Fig. 17 : Superposition of the two. ...The general pattern depends on the initial conditions. In a former paper [6] bigger clumps of ghost matter were obtained, with a more regular cellular structure for normal matter, due to the choice of a higher initial ghost matter temperature. This approach, aiming at a modelization of the very large scale structure of the Universe, is fundamentally different from the classical approaches based on the dark matter. In classical matter-dark matter systems, stability is problematic : gravitational instability, by rising up the density locally, increases the thermal velocities and makes the observed structures to disappear in time. The system with two repelling populations is qualitatively different, each population creating a potential barrier for the other one. This explains the great stability in time and space : the cells of matter keep the clumps of ghost matter in place, and vice-versa.