title: Stochastic and deterministic methods for simulating the evolution of solid bodies in protoplanetary disks
creator: Beutel, Karl Moritz
subject: ddc-000
subject: 000 Generalities, Science
subject: ddc-004
subject: 004 Data processing Computer science
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-520
subject: 520 Astronomy and allied sciences
subject: ddc-530
subject: 530 Physics
description: Planets emerge from the rotating disk of gas and dust surrounding young stars. Although the process of planet formation has been subject to theoretical and numerical studies for several decades, it has only very recently become possible to not only detect protoplanetary disks but also resolve their substructures. The annular accumulations of dust observed in many protoplanetary disks are suspected to provide favourable conditions for the formation of planetary cores through runaway growth.    To simulate the growth of rocky planets from agglomeration of dust grains, many orders of magnitude in particle number and mass have to be spanned, necessitating the use of statistical methods for abundant particles. However, the gravitational influence of the heaviest bodies must be accounted for with an N-body simulation in order to correctly describe features such as radial redistribution through gravitational scattering. A comprehensive simulation of planet formation thus needs to combine statistical and deterministic methods. Unlike grid-based statistical methods, representative particle methods allow for a natural combination with an N-body simulation, but they are often hampered by their high computational cost.    This work is geared towards simulation methods for planet formation processes as may occur in the dust rings observed in many protoplanetary disks. To this end, we develop an extension of the Representative Particle Monte Carlo method, overcoming some conceptual restrictions that heretofore impeded its use in simulating runaway growth processes. To address the problem of computational cost, we go on to devise a novel computational scheme for stochastic processes, herein referred to as the bucketing scheme, that enjoys linear scaling characteristics with regard to the number of representative particles, as opposed to the quadratic scaling characteristics of the traditional scheme. The bucketing scheme is built upon interval-valued calculations of the mutual interaction rates between representative particles, which are often non-trivial to implement. We therefore propose an ‘interval-aware’ programming paradigm to allow for a simpler implementation of interval-valued numerical routines. We test the simulation method, the computational scheme, and the programming paradigm by implementing a radially resolved statistical model of collisions and dynamical heating designed for studying runaway growth among planetesimals.    Our work lays the foundation for an efficient yet accurate hybrid simulation of protoplanetary growth processes with a combination of statistical and deterministic particle-based methods.
date: 2024
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/34794/1/thesis-final.pdf
identifier: DOI:10.11588/heidok.00034794
identifier: urn:nbn:de:bsz:16-heidok-347946
identifier:   Beutel, Karl Moritz  (2024) Stochastic and deterministic methods for simulating the evolution of solid bodies in protoplanetary disks.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/34794/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng