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Ronald Dickmanhttp://lattes.cnpq.br/0484982277336205Lucas Lages WardilHugues Chatéhttp://lattes.cnpq.br/4421130514407419Leonardo Santos Lopes2023-11-29T15:59:13Z2023-11-29T15:59:13Z2021-11-05http://hdl.handle.net/1843/61508Active matter is the branch of physics that studies systems of interacting self-propelled individuals. Some examples are a bird flocks and schools of fish. In the last few years much attention has been paid to this subject. The Vicsek model [Vicsek et al., Phys. Rev. Lett. 75, 1226(1995)] was the first and the simplest model to explain the collective movement and formation of herds using the phase transition perspective. This model has been shown to exhibit symmetry breaking, developing long-range order, even with only short-range interactions [Toner, Phys. Rev. E 86, 031918]. While the Vicsek model has been extensively studied over the years [Ginelli, Eur. Phys. J. Spec. Top. 225, 2099 (2016) ], a theoretical analysis has shown that it would be of interest to relax the conservation of the number of individuals [Toner, Phys. Rev. Lett. 108, 088102 (2011)]. In addition to its theoretical interest, there are experiments in which the number of individuals is not conserved, including colonies of bacteria and other systems in which individuals are created and destroyed as they move. In this work we study a system of active particles with Malthusian population dynamics, that is, the probability of a particle dying is proportional to local particle density. Using simulations, we seek to understand the relation between the stationary density and the noise intensity, how the formation of groups affects population size. Of prime interest is characterizing the phase diagram and determining whether the system exhibits banding.A matéria ativa é o ramo da física que estuda sistemas nos quais os indivíduos são autopropelidos, ou seja, não dependem de um agente externo para se movimentar. Alguns exemplos são bandos de pássaros e cardumes de peixes. Nos últimos anos, muita atenção tem sido dada a esse assunto. O modelo de Vicsek [Vicsek et al.,Phys.Rev.Lett.75,1226] foi o primeiro e o mais simples modelo para explicar o movimento coletivo e a formação de rebanhos usando a perspectiva de transição de fase. Este modelo recebeu muita atenção e demonstrou apresentar quebra de simetria, desenvolvendo ordenamento de longo alcance, mesmo com apenas interações de curto alcance [Toner e Tu, Phys. Rev. E 86, 031918]. Embora o modelo de Vicsek tenha sido extensivamente estudado ao longo dos anos [Ginelli, Eur. Phys. J. Spec. Top. 225, 2099–2117 ], uma análise teórica mostrou que seria de interesse relaxar a conservação do número de indivíduos [Toner, Phys. Rev. Lett. 108(8):088102]. Além de seu interesse teórico, existem experimentos em que o número de indivíduos não é conservado, incluindo colônias de bactérias e outros sistemas nos quais os indivíduos são criados e destruídos à medida que se movem. Neste trabalho estudamos um sistema com dinâmica populacional malthusiana (ou seja, a probabilidade de uma partícula morrer é proporcional à densidade na vizinhança da partícula) por meio de métodos computacionais, buscando entender como a densidade estacionária do sistema interage com a intensidade do ruído, como a formação de grupos interfere no número de indivíduos vivos, pois a aplicação do ruído interfere nas propriedades do sistema. Além disso, procuramos classificar a transição de fase e dizer se o sistema apresenta bandas.CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em FísicaUFMGBrasilICX - DEPARTAMENTO DE FÍSICADinâmica populacionalModelos matemáticosMalthusianismoPopulationDynamicMathematicalModelsMalthusianVicsek model with malthusian population dynamicsModelo de Vicsek com dinâmica populacional malthusianainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGORIGINALVICSEK MODEL WITH MALTHUSIAN POPULATION DYNAMICS.pdfVICSEK MODEL WITH MALTHUSIAN POPULATION DYNAMICS.pdfapplication/pdf14270949https://repositorio.ufmg.br/bitstream/1843/61508/1/VICSEK%20MODEL%20WITH%20MALTHUSIAN%0d%0aPOPULATION%20DYNAMICS.pdf28066798018ab7eeacdd2fdd77ee4febMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/61508/2/license.txtcda590c95a0b51b4d15f60c9642ca272MD521843/615082023-11-29 12:59:13.767oai:repositorio.ufmg.br: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ório InstitucionalPUBhttps://repositorio.ufmg.br/oaiopendoar:2023-11-29T15:59:13Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
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