Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation
Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recen...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Associação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol)
2009-06-01
|
| Series: | Materials Research |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392009000200017 |
| _version_ | 1811307962111623168 |
|---|---|
| author | Paulo Rangel Rios Douglas Jardim Weslley Luiz da Silva Assis Tatiana Caneda Salazar Elena Villa |
| author_facet | Paulo Rangel Rios Douglas Jardim Weslley Luiz da Silva Assis Tatiana Caneda Salazar Elena Villa |
| author_sort | Paulo Rangel Rios |
| collection | DOAJ |
| description | Microstructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical. |
| first_indexed | 2024-04-13T09:14:32Z |
| format | Article |
| id | doaj.art-8bea879daaf94ee081af8af27ce87083 |
| institution | Directory Open Access Journal |
| issn | 1516-1439 |
| language | English |
| last_indexed | 2024-04-13T09:14:32Z |
| publishDate | 2009-06-01 |
| publisher | Associação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol) |
| record_format | Article |
| series | Materials Research |
| spelling | doaj.art-8bea879daaf94ee081af8af27ce870832022-12-22T02:52:47ZengAssociação Brasileira de Metalurgia e Materiais (ABM); Associação Brasileira de Cerâmica (ABC); Associação Brasileira de Polímeros (ABPol)Materials Research1516-14392009-06-0112221922410.1590/S1516-14392009000200017Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulationPaulo Rangel RiosDouglas JardimWeslley Luiz da Silva AssisTatiana Caneda SalazarElena VillaMicrostructural evolution in three dimensions of nucleation and growth transformations is simulated by means of cellular automata (CA). In the simulation, nuclei are located in space according to a heterogeneous Poisson point processes. The simulation is compared with exact analytical solution recently obtained by Rios and Villa supposing that the intensity is a harmonic function of the spatial coordinate. The simulated data gives very good agreement with the analytical solution provided that the correct shape factor for the growing CA grains is used. This good agreement is auspicious because the analytical expressions were derived and thus are exact only if the shape of the growing regions is spherical.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392009000200017microstructureanalytical methodsphase transformationsrecrystallizationcellular automata |
| spellingShingle | Paulo Rangel Rios Douglas Jardim Weslley Luiz da Silva Assis Tatiana Caneda Salazar Elena Villa Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation Materials Research microstructure analytical methods phase transformations recrystallization cellular automata |
| title | Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation |
| title_full | Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation |
| title_fullStr | Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation |
| title_full_unstemmed | Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation |
| title_short | Inhomogeneous Poisson point process nucleation: comparison of analytical solution with cellular automata simulation |
| title_sort | inhomogeneous poisson point process nucleation comparison of analytical solution with cellular automata simulation |
| topic | microstructure analytical methods phase transformations recrystallization cellular automata |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1516-14392009000200017 |
| work_keys_str_mv | AT paulorangelrios inhomogeneouspoissonpointprocessnucleationcomparisonofanalyticalsolutionwithcellularautomatasimulation AT douglasjardim inhomogeneouspoissonpointprocessnucleationcomparisonofanalyticalsolutionwithcellularautomatasimulation AT weslleyluizdasilvaassis inhomogeneouspoissonpointprocessnucleationcomparisonofanalyticalsolutionwithcellularautomatasimulation AT tatianacanedasalazar inhomogeneouspoissonpointprocessnucleationcomparisonofanalyticalsolutionwithcellularautomatasimulation AT elenavilla inhomogeneouspoissonpointprocessnucleationcomparisonofanalyticalsolutionwithcellularautomatasimulation |