Statistics – Computation
Scientific paper
Mar 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999ep%26s...51..205i&link_type=abstract
Earth, Planets and Space, Volume 51, p. 205-217.
Statistics
Computation
15
Scientific paper
The object of this series of studies is to develop a highly accurate statistical code for describing the planetary accumulation process. In the present paper, as a first step, we check the validity of the method proposed by Wetherill and Stewart (1989) by comparing the results obtained by their method with the analytical solution to the stochastic coagulation equation (or to a well-evaluated numerical solution). As the collisional probability Aij between bodies with masses of i m1 and j m1 (m1 being the unit mass), we consider the two cases: one is Aij i × j and another is Aij min (i, j)(i1/3+ j1/3)(i + j). In both cases, it is known that runaway growth occurs. The latter case corresponds to a simplified model of the planetesimal accumulation. We assumed that a collision of two bodies leads to their coalescence. Wetherill and Stewart's method contains some parameters controlling the practical numerical computation. Among these, two parameters are important: the mass division parameter d, which determines the mass ratio of the adjacent mass batches, and the time division parameter e, which controls the size of a time step in numerical integration. Through a number of numerical simulations for the case of Aij= i × j, we find that when d≤ 1.6 and e<= 0.03 the numerical simulation can reproduce the analytical solution within a certain level of accuracy independently of the size of the body system. For the case of the planetesimal accumulation, it is shown that the simulation with d<1.3 and e<= 0.04 can describe precisely runaway growth. Because the accumulation process is stochastic, in order to obtain reliable mean values it is necessary to take the ensemble mean of the numerical results obtained with different random number generators. It is also found that the number of simulations, Nc, demanded to obtain the reliable mean value is about 500 and does not strongly depend on the functional form of Aij. From the viewpoint of the numerical handling, the above value of d(<= 1.3) and Nc(~ 500) are reasonable and, hence, we conclude that the numerical method proposed by Wetherill and Stewart is a valid and useful method for describing the planetary accumulation process. The real planetary accumulation process is more complex since it is coupled with the velocity evolution of the planetesimals. In the subsequent paper, we will complete the high-accuracy statistical code which simulate the accumulation process coupled with the velocity evolution and test the accuracy of the code by comparing with the results of N-body simulation.
Inaba Satoshi
Nakazawa Kazuhiro
Ohtsuki Keiji
Tanaka Hajime
No associations
LandOfFree
High-accuracy statistical simulation of planetary accretion: I. Test of the accuracy by comparison with the solution to the stochastic coagulation equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with High-accuracy statistical simulation of planetary accretion: I. Test of the accuracy by comparison with the solution to the stochastic coagulation equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and High-accuracy statistical simulation of planetary accretion: I. Test of the accuracy by comparison with the solution to the stochastic coagulation equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1445840