الكونيات الكونية التوأمية

cosmology of the twin universe Matter ghost matter astrophysics. 4 :

Joint gravitational instabilities.(p2)

2. Didactic image of the phenomenon.

There is a classical image of the Jeans instability. Consider the following "machine :

**Fig.**2 : A foam mattress with vibrating plates covered with small buck-shots.

...We could fabricate something of this type with certain flat loud-speakers. We could also put a plate of glass on top, to prevent the shot from jumping overboard. Having done this we could regulate at will the "temperature" of this kind of two-dimensional gas. It would simply be proportional to the square of the shot's average agitation speed.

...Agitating the shot in every direction would have the effect of opposing their tendency to assemble themselves in the basins. Heating this "gas" would make the basins disappear. But reducing the shot's state of agitation would make them reappear.

...A certain amount of time is needed for basins to be formed, for shot to assemble there and then to attract their little comrades. The heavier the shot, or the more numerous, the faster will basins appear (2d simulation of the accretion phenomenon). It does not depend on the size of the depressions which tend to form.

...We cover the mattress with shot corresponding to a certain density of matter r in grams per square inch. The basins will form in a time t which depends on this density. (In astrophysics this accretion time is proportional to the inverse of the root squared of the density of matter r. See annex)

Let us take a depression having a diameter D. The shot has a speed of agitation V. Therefore it crosses the basin in a time:

t = D/V.

...This is also the time which the shot takes to leave this type of basin, or, if we prefer, the time all accidental condensation of matter takes to disperse naturally by simple thermal agitation.

...If this time is less than the time t of basin formation, the depression cannot be formed. Even before it had begun to be formed, the shot which would have served to create it would be gone to set up the same housekeeping elsewhere. Therefore, for a given density of shot r on the mattress, and for their equally fixed agitation speed V, the basins which can form will be those such that:
t < D/V.

This is to say that only those basins will form having a diameter superior to:

V t.

Fig.3 :** 2d simulation of Jeans gravitational instability.**

...The diameter of such a condensation of matter depends on the equilibrium if the force of gravity, tending to contract it, is balanced by the force of pressure, tending to dilate it. Calculation shows that this happens when the diameter is very close to the Jeans distance.

...We now show to simulate joint gravitational instabilities. We have to shift to another model. Consider a swiming pool, filled by water. Put an horizontal plane linen, at mid depth. Upon : some balls, denser than water. Below : ping-pong balls. The first objets tend to weight on the linen, the second to lift it. Initially the two forces balance eah other. We must add some turbulence of the water, sustained by fans, that simulate de thermal agitation state in both sides. We take it equal (but they could be different).
. **Fig.**4 : 2d simulation of joint gravitational instability. 1 : a clump of weighting balls forms. ** **
...On the figure 4 the formation of a weighting balls clump. But the problem is symmetrical. In some places the ping-pong balls may form their own clump, and repel the weighting balls. See figure 5

** ** . Fig.5 : 2d simulation of joint gravitational instability. 2 : a clump of ping-pong balls forms. ** **