Effects of three-body interactions on structural phases of classical twodimensional cluster
Autor(a) principal: | |
---|---|
Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/41391 |
Resumo: | When a physical system has many interacting constituents, many-body terms will arise in the Hamiltonian, besides the usual two-body interactions. These terms are often ignored in numerical studies due to their high computational cost. However, many-body terms are responsible for important corrections in charged colloidal systems and promote structural changes in clusters of Abrikosov vortices in superconductors. The main goal of this work is to determine the effect the addition of a three-body term has on the properties of two-dimensional clusters of classical interacting particles. In order to understand such effect, we carried out semi-analytical calculations and numerical minimization of the system free energy, using a simulated annealing scheme based on the Langevin dynamics. We considered particles (3 ≤ ≤ 50) confined in a parabolic potential and interacting via a pair potential. We considered three of the most studied pair potentials: logarithmic, Coulomb and Yukawa. The novelty in our study consisted in the addition of a short-ranged Gaussian three-body interaction potential with tunable amplitude. The obtained configurations were compared with the typical case in which the particles interact only via a pair potential. In this last situation, we recover the typical concentric rings of particles, widely found in the literature. With the addition of the three-body interaction, our findings include changes in the ring occupation numbers and the emergence of a first-order like transition associated with the bistability phenomenon due to the competition between the two- and three-body potentials. This transition is accompanied by a sudden cluster compaction, especially in the > 20 range, for all two-body potentials, and a phase separation effect starting around = 40, in which the initial single cluster was divided into smaller ones. These results indicate that the three-body term in the interaction potential of many confined particles can induce dramatic changes in the equilibrium configurations and, therefore, should not be ignored in those particle systems. |
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CORREIA, Matheus Valençahttp://lattes.cnpq.br/7163730778616017http://lattes.cnpq.br/8076432608646837SILVA, Clécio Clemente de Souza2021-10-20T17:29:19Z2021-10-20T17:29:19Z2021-06-29CORREIA, Matheus Valença. Effects of three-body interactions on structural phases of classical twodimensional clusters. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021.https://repositorio.ufpe.br/handle/123456789/41391When a physical system has many interacting constituents, many-body terms will arise in the Hamiltonian, besides the usual two-body interactions. These terms are often ignored in numerical studies due to their high computational cost. However, many-body terms are responsible for important corrections in charged colloidal systems and promote structural changes in clusters of Abrikosov vortices in superconductors. The main goal of this work is to determine the effect the addition of a three-body term has on the properties of two-dimensional clusters of classical interacting particles. In order to understand such effect, we carried out semi-analytical calculations and numerical minimization of the system free energy, using a simulated annealing scheme based on the Langevin dynamics. We considered particles (3 ≤ ≤ 50) confined in a parabolic potential and interacting via a pair potential. We considered three of the most studied pair potentials: logarithmic, Coulomb and Yukawa. The novelty in our study consisted in the addition of a short-ranged Gaussian three-body interaction potential with tunable amplitude. The obtained configurations were compared with the typical case in which the particles interact only via a pair potential. In this last situation, we recover the typical concentric rings of particles, widely found in the literature. With the addition of the three-body interaction, our findings include changes in the ring occupation numbers and the emergence of a first-order like transition associated with the bistability phenomenon due to the competition between the two- and three-body potentials. This transition is accompanied by a sudden cluster compaction, especially in the > 20 range, for all two-body potentials, and a phase separation effect starting around = 40, in which the initial single cluster was divided into smaller ones. These results indicate that the three-body term in the interaction potential of many confined particles can induce dramatic changes in the equilibrium configurations and, therefore, should not be ignored in those particle systems.CNPqSistemas físicos com um grande número de componentes podem apresentar, além das interações usuais de dois corpos, contribuições de três, quatro ou mais corpos no Hamiltoniano. Frequentemente, esses termos de muitos corpos são ignorados em estudos numéricos devido ao alto custo de processamento que normalmente acarretam. No entanto, termos de muitos corpos são responsáveis por diversas correções de interesse em colóides carregados e também pela modificação estrutural de aglomerados de vórtices de Abrikosov em supercondutores. O objetivo deste trabalho é determinar o efeito do termo de três corpos nas propriedades de aglomerados bidimensionais de partículas clássicas interagentes. Para isso, realizamos estudos semi-analíticos e a minimização numérica da energia livre do sistema, utilizando um procedimento de recozimento (annealing) simulado baseado na dinâmica de Langevin. Foram consideradas partículas (3 ≤ ≤ 50) confinadas em um potencial parabólico e interagindo repulsivamente por meio de um potencial repulsivo de dois corpos. Alguns dos mais estudados potenciais de dois corpos foram considerados: logarítmico, Coulomb e Yukawa. A novidade deste trabalho consistiu em adicionar um potencial atrativo de três corpos Gaussiano de curto alcance, com intensidade variável. Os resultados foram comparados com o caso típico, quando as partículas interagem somente através do potencial de dois corpos. Nessa condição, obtivemos os típicos arranjos de partículas em anéis concêntricos, já amplamente registrados pela literatura. Com a adição da interação de três corpos, nossos achados incluíram a modificação dos números de ocupação dos anéis e o surgimento de uma transição do tipo primeira ordem associado ao fenômeno de biestabilidade devido à competição entre os potenciais de dois e três corpos. Essa transição foi acompanhada por uma abrupta compactação do sistema, especialmente para > 20, em todos os potenciais de dois corpos, e um efeito de separação de fase a partir de = 40, em que o aglomerado único foi dividido em outros menores. Esses resultados mostram que o termo de três corpos no potencial de interação de muitas partículas confinadas pode produzir mudanças dramáticas nas configurações de equilíbrio. Portanto, trata-se de contribuição que não deve ser ignorada nesses sistemas de partículas.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em FisicaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessTheoretical and computational physicsThree-body interactionsClassical clustersCharged colloidsEffects of three-body interactions on structural phases of classical twodimensional clusterinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesismestradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPECC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufpe.br/bitstream/123456789/41391/2/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82310https://repositorio.ufpe.br/bitstream/123456789/41391/3/license.txtbd573a5ca8288eb7272482765f819534MD53ORIGINALDISSERTAÇÃO Matheus Valença 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dc.title.pt_BR.fl_str_mv |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
title |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
spellingShingle |
Effects of three-body interactions on structural phases of classical twodimensional cluster CORREIA, Matheus Valença Theoretical and computational physics Three-body interactions Classical clusters Charged colloids |
title_short |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
title_full |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
title_fullStr |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
title_full_unstemmed |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
title_sort |
Effects of three-body interactions on structural phases of classical twodimensional cluster |
author |
CORREIA, Matheus Valença |
author_facet |
CORREIA, Matheus Valença |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/7163730778616017 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/8076432608646837 |
dc.contributor.author.fl_str_mv |
CORREIA, Matheus Valença |
dc.contributor.advisor1.fl_str_mv |
SILVA, Clécio Clemente de Souza |
contributor_str_mv |
SILVA, Clécio Clemente de Souza |
dc.subject.por.fl_str_mv |
Theoretical and computational physics Three-body interactions Classical clusters Charged colloids |
topic |
Theoretical and computational physics Three-body interactions Classical clusters Charged colloids |
description |
When a physical system has many interacting constituents, many-body terms will arise in the Hamiltonian, besides the usual two-body interactions. These terms are often ignored in numerical studies due to their high computational cost. However, many-body terms are responsible for important corrections in charged colloidal systems and promote structural changes in clusters of Abrikosov vortices in superconductors. The main goal of this work is to determine the effect the addition of a three-body term has on the properties of two-dimensional clusters of classical interacting particles. In order to understand such effect, we carried out semi-analytical calculations and numerical minimization of the system free energy, using a simulated annealing scheme based on the Langevin dynamics. We considered particles (3 ≤ ≤ 50) confined in a parabolic potential and interacting via a pair potential. We considered three of the most studied pair potentials: logarithmic, Coulomb and Yukawa. The novelty in our study consisted in the addition of a short-ranged Gaussian three-body interaction potential with tunable amplitude. The obtained configurations were compared with the typical case in which the particles interact only via a pair potential. In this last situation, we recover the typical concentric rings of particles, widely found in the literature. With the addition of the three-body interaction, our findings include changes in the ring occupation numbers and the emergence of a first-order like transition associated with the bistability phenomenon due to the competition between the two- and three-body potentials. This transition is accompanied by a sudden cluster compaction, especially in the > 20 range, for all two-body potentials, and a phase separation effect starting around = 40, in which the initial single cluster was divided into smaller ones. These results indicate that the three-body term in the interaction potential of many confined particles can induce dramatic changes in the equilibrium configurations and, therefore, should not be ignored in those particle systems. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-10-20T17:29:19Z |
dc.date.available.fl_str_mv |
2021-10-20T17:29:19Z |
dc.date.issued.fl_str_mv |
2021-06-29 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CORREIA, Matheus Valença. Effects of three-body interactions on structural phases of classical twodimensional clusters. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/41391 |
identifier_str_mv |
CORREIA, Matheus Valença. Effects of three-body interactions on structural phases of classical twodimensional clusters. 2021. Dissertação (Mestrado em Física) - Universidade Federal de Pernambuco, Recife, 2021. |
url |
https://repositorio.ufpe.br/handle/123456789/41391 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
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openAccess |
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Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Fisica |
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UFPE |
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Brasil |
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Universidade Federal de Pernambuco |
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