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## Large Scale Numerical Simulation Project |
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Research group photo |
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## Analysis of solitons in protoplanetary disc with MVS-1000M## Participants:V. A. Vshivkov (supervisor),
where is
is the time-dependent one-particle distribution function along coordinates
and velocities,
is the acceleration of unit mass particle, is
the friction force between gas and dust components of the medium. Gravitational
potential,, could
be divided
where 1 presents either the potential of immobile central mass (either galactic black hole or protostar) or the potential of a rigid system which is out of disc plane (either the stars of galactic halo or molecular cloud). The second part of potential 2 is determined by the additive distribution of the moving particles and gas. 2 satisfies the Poisson equation:
In the case of infinitesimally thin disc the bulk density
of the mobile media
is equal to zero
(
The equations of gas dynamics take the following form: where is
the density of gas full energy, is
the internal energy, where k
– distance from the Sun to the Earth Corresponding characteristic values of the particle velocity V_{0},
time t_{0}, potential 0,
density 0(0)
and pressure p_{0} are written as:
In the following text all the parameters are given in
sizeless units. Here here
The physical parameters that are set as initial data for the computational experiment are given in the table 2. The most important among them are the masses: mass of central body, mass of gas component and mass of dust component
In the course of computational experiments it was found out that the
solitons definitely arise when the mass ratio is M
The difference between the computational experiments
is shown in the table 3. The computations are conducted with the grid
in cylindrical coordinate system. Nevertheless, to draw a 2D spatial
distribution of some function
The size of the exposed domain is 2.0*2.0, coordinates
of the centre are (0.0, 0.0), moment of time is 4.0. A – 120*128*128
nodes (computational experiment I), B - 200*256*128 nodes (computational
experiment II), C - 300*256*128 nodes(computational experiment V).
On the contrary, on finer grids density waves have small size (fig. 3) and they remain stable during a large period of time, ?T = 4.0, figure 3, A, B and C. In fig. 3C it is seen that upper and lower solitons are shifted from initial position. But the most important result is that these density waves remain stable and keep small size.
The following fact proves that these structures are density waves and
not clumps of dust. The matter of the disc rotates around the disc centre,
but the solitons remain in its position. It should be noticed that in
fact the soliton moves as a density wave, but its velocity could be oriented
either along the flow or in the opposite direction.
Let us consider the soliton scaled-up. With the same physical parameters the soliton either remained nearly immobile (computational experiment III, fig. 5) or oscillated around some point (computational experiment IV, fig. 6). Let us remind that these are two different solitons from the same computational experiment.
In the computational experiment VI the absorption of a density wave by soliton occured, fig. 7. First the density wave arises (fig. 7A), then it approaches the soliton (fig. 7B). After absorption the soliton deviates from the initial position (fig. 7C) but then returns back (fig. 7D). It should be noticed that such a phenomenon is impossible for clumps. Thus figure 7 proves wave nature of the structures observed in our computational experiments - the solitons.
## Literature:1. Snytnikov V.N., Dudnikova G.I., Gleaves J.T., Nikitin S.A., Parmon
V.N., Stoyanovsky V.O., Vshivkov V.A., Yablonsky G.S.,Zakharenko V.S..
Space chemical reactor of protoplanetary disk. // Adv. Space Res. Vol.
30, No. 6, pp. 1461-1467, 2002 |
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