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(meteorobs) Excerpts from "CCNet DIGEST, 29 April 1999"
But just the one for today... -Lew
------- Forwarded Message
From: Benny J Peiser <b.j.peiser@livjm.acdot uk>
To: cambridge-conference@livjm.acdot uk
Subject: CCNet DIGEST, 29 April 1999
Date: Thu, 29 Apr 1999 11:21:26 -0400 (EDT)
CCNet DIGEST, 29 April 1999
---------------------------
[...]
(8) HIGH-ACCURACY STATISTICAL SIMULATION OF PLANETARY ACCRETION
S. Inaba et al., TOKYO INSTITUTE OF TECHNOLOGY
=========================================
(8) HIGH-ACCURACY STATISTICAL SIMULATION OF PLANETARY ACCRETION
S. Inaba, H. Tanaka, K. Ohtsuki, K. Nakazawa: High-accuracy statistical =
simulation of planetary accretion: I. Test of the accuracy by=20
comparison with the solution to the stochastic coagulation equation.=20
EARTH PLANETS AND SPACE, 1999, Vol.51, No.3, pp.205-217
=20
*) TOKYO INSTITUTE OF TECHNOLOGY, FAC SCI,DEPT EARTH & PLANETARY=20
SCIENCE, TOKYO 1528551,JAPAN
=20
The object of this series of studies is to develop a highly accurate=20
statistical code for describing the planetary accumulation process. In=20
the present paper, as a first step, we check the validity of the method =
proposed by Wetherill and Stewart (1989) by comparing the results=20
obtained by their method with the analytical solution to the stochastic =
coagulation equation (or to a well-evaluated numerical solution). As=20
the collisional probability Aii between bodies with masses of im(1) and =
jm(1) (m(1) being the unit mass), we consider the two cases: one is=20
A(ij) proportional to i x j and another is A(ij) proportional to min(i, =
j)(i(1/3) + j(1/3))(i + j). In both cases, it is known that runaway=20
growth occurs. The latter case corresponds to a simplified model of the =
planetesimal accumulation. We assumed that a collision of two bodies=20
leads to their coalescence. Wetherill and Stewart's method contains=20
some parameters controlling the practical numerical computation. Among=20
these, two parameters are important: the mass division parameter delta, =
which determines the mass ratio of the adjacent mass batches, and the=20
time division parameter epsilon, which controls the size of a time step =
in numerical integration. Through a number of numerical simulations for =
the case of A(ij) =3D i x j, we find that when delta less than or equal =
to 1.6 and epsilon less than or equal to 0.03 the numerical simulation=20
can reproduce the analytical solution within a certain level of=20
accuracy independently of the size of the body system. For the case of=20
the planetesimal accumulation, it is shown that the simulation with=20
delta less than or equal to 1.3 and epsilon less than or equal to 0.04=20
can describe precisely runaway growth. Because the accumulation process =
is stochastic, in order to obtain reliable mean values it is necessary=20
to take the ensemble mean of the numerical results obtained with=20
different random number generators. It is also found that the number of =
simulations, N-c, demanded to obtain the reliable mean value is about=20
500 and does not strongly depend on the functional form of A(ij). From=20
the viewpoint of the numerical handling, the above value of delta (less =
than or equal to 1.3) and N-c(similar to 500) are reasonable and,=20
hence, we conclude that the numerical method proposed by Wetherill and=20
Stewart is a valid and useful method for describing the planetary=20
accumulation process. The real planetary accumulation process is more=20
complex since it is coupled with the velocity evolution of the=20
planetesimals. In the subsequent paper, we will complete the=20
high-accuracy statistical code which simulate the accumulation process=20
coupled with the velocity evolution and test the accuracy of the code=20
by comparing with the results of N-body simulation. Copyright 1999,=20
Institute for Scientific Information Inc.
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