Vicsek model with malthusian population dynamics

• Autor(a) principal: Leonardo Santos Lopes
• Data de Publicação: 2021
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/61508
• topic: Population; Dynamic; Mathematical; Models; Malthusian; Dinâmica populacional; Modelos matemáticos; Malthusianismo

Active 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.