754 research outputs found
Dinâmica simbólica e ferradura de Smale
No full textDescrevemos a “ferradura de Smale”, um sistema dinâmico bem conhecido que apresenta um conjunto de propriedades muito importantes em Sistemas Dinâmicos. O estudo da dinâmica da “ferradura de Smale” permitenos entender a importância do conceito de dinâmica simbólica.We describe the Smale horseshoe, a well-known dynamical system that presents a set of properties which are very important in Dynamical Systems. The study of the dynamics of the Smale horseshoe allows us to
understand the importance of the notion of symbolic dynamics
Multi-scale patterns of spatial variability in sessile assemblage structure do not alter predictably with development time
No full textPatterns of benthic community structure are driven by a range of biological and physical processes that act over multiple spatial and temporal scales. Settlement panels were deployed in relatively ‘pristine’ subtidal habitats off southwest Australia, to examine spatial variability in assemblage structure at multiple spatial scales, from centimetres to 100s of kilometres. Panel assemblages were harvested after 3, 9 and 14 months of maturation, to test the following hypotheses: (i) that the magnitude of variability at large spatial scales increases with assemblage development time, (ii) that variability at the smallest spatial scales is consistently high regardless of assemblage development time, and (iii) that patterns of spatio-temporal variability differ between taxa. No clear trends in the magnitude of variability at each spatial scale examined, in relation to assemblage development time, were recorded. Sessile assemblages were highly variable at all spatial scales examined, and variability at the smallest-spatial scale (cms) was consistently high. As predicted, the magnitude of variability at the largest spatial scales (i.e. between locations 100s of km apart) was lowest for immature assemblages, but overall patterns of large-scale variability did not alter predictably with maturation time. Subtidal sessile assemblages in southwest Australia, like elsewhere, are structured by a complex, interacting suite of biological and physical processes that vary in their relative importance throughout assemblage maturation. As such, understanding variability patterns is challenging, and requires greater appreciation of variability in physical processes across multiple spatial and temporal scales and improved knowledge of the life histories and population structures of key taxa
Ice disturbance intensity structures benthic communities in nearshore Antarctic waters
No full textIce scouring is one of the 5 most significant natural forces acting on ecosystems, yet very few data exist linking the intensity of ice disturbance with parameters of benthic community structure. The benthos at 2 nearshore sites on Adelaide Island, Antarctica, was sampled at 3 resolutions to make novel links between biological data and empirical disturbance data from the literature. A total of 125 taxa and > 70 000 individuals were recorded. A total of 8 parameters of community structure were measured; all of them were negatively correlated to disturbance intensity at one site, whilst 6 significant relationships were found at the other site. At 2 of the 3 sampling resolutions, disturbance, rather than depth or the percentage cover of major substratum types, was the environmental variable most correlated with the patterns in community structure. Furthermore, biological samples were divided into 3 categories based on the disturbance data (low, moderate and high). Each group was statistically dissimilar and the relative abundance of sessile fauna decreased as disturbance intensity increased. The intensity of disturbance was broadly correlated with depth, but small-scale differences in topography and substratum type created small-scale refugia, which supported richer assemblages. Overall, both study sites were disturbed frequently and no evidence of a peak in richness at the moderately disturbed locations was recorded
Sistemas dinâmicos: dinâmica da ferradura de Smale
No full textSistemas Dinâmicos na matemática, é uma área ativa que estuda o movimento de partículas ao longo do tempo.
Ela é utilizada em diversas áreas do conhecimento, atraindo matemáticos, físicos, epidemiologistas, economistas
e biólogos. A pesquisa é de caráter Bibliográfica cuja foi desenvolvida durante um projeto de iniciação científica
em 2020/2021, com base em estudos de diversos autores, incluindo Villate (2007), Silva (2018), Ferreira (2007)
e Gelfert (2017). O objetivo da pesquisa é abordar a teoria dos Sistemas Dinâmicos deterministas, com ênfase
na Ferradura de Smale, uma forma geométrica que ajuda a descrever a imprevisibilidade em sistemas dinâmicos,
especialmente caóticos. Os objetivos específicos incluem a definição de conceitos introdutórios, a apresentação da
construção da Ferradura de Smale e a explicação da conexão topológica entre a ferradura e a dinâmica simbólica. A
primeira seção da pesquisa aborda definições importantes da teoria dos Sistemas Dinâmicos, como transformações
órbitas, pontos fixos, atratores e repulsores, preparando o leitor para a seção subsequente. Por fim, a pesquisa
explora o Sistema Dinâmico Ferradura e sua relação com a dinâmica simbólica
Dinâmica unidimensional: teoria da bifurcação, dinâmica simbólica e difeomorfismos Morse-Smale
No full textThe main objective in this work is introducing studies in dynamical systems by means of unidimensional dynamics. The principal topics covered are the hyperbolicity of fixed and periodic points, some results about the Schwarzian Derivative and its contributions to understand the dynamics of the quadratic family Fμ(x) = μx(1 − x), bifurcations in real functions, the dynamics on the circle and the rotation number, reaching the stability of Morse-Smale diffeomorphisms.Trabalho de Conclusão de Curso (Graduação)Este trabalho tem como principal objetivo introduzir os estudos na área de sistemas dinâmicos por meio da dinâmica unidimensional. Os principais tópicos abordados são a hiperbolicidade de pontos fixos e periódicos, alguns resultados acerca da Derivada Schwarziana e suas contribuições para compreensão da dinâmica da família quadrática Fμ(x) = μx(1 − x), bifurcações em funções reais, a dinâmica do círculo e o número de rotação, chegando até a estabilidade de difeomorfismos Morse-Smale
Satellite-derived SST data as a proxy for water temperature in nearshore benthic ecology
No full textSatellite-derived sea surface temperatures (SSTs) are increasingly being used as a proxy for water temperature in nearshore marine ecology, but there have been very few evaluations of how accurately SSTs reflect actual temperatures experienced by subtidal organisms. Here, we describe the benthic temperature climatology of 4 coastal locations along a ~1000 km latitudinal gradient in ocean temperature in Western Australia (WA), and compare temperature records from in situ loggers at 10 to 12 m depth with records from 2 independent satellite-derived SST datasets over 2 years. Satellite-derived SSTs were significantly correlated with in situ logger data at all locations, which demonstrate their overall ability to detect general patterns of ecological importance. However, SSTs were also significantly different from benthic water temperatures (usually 1 to 2°C higher), and they did not adequately detect ecologically important small-scale variability or provide reliable information on temperature extremes. Furthermore, rank orders of the study locations differed between the methodologies, especially in winter. We emphasize the need to carefully consider whether the accuracy and resolution of satellite-derived SSTs are appropriate for the specific ecological hypothesis being tested in nearshore subtidal habitats, and advocate the use of in situ loggers otherwise. We also highlight the suitability of the WA coastline for experimental work on the effects of temperature (and synergistic factors) on marine organisms
Morse-Smale Flows on a Tilted Torus
No full textEducação Superior::Ciências Exatas e da Terra::MatemáticaEsta demonstração mostra os fluxos de gradiente das funções de altura em um toro inclinado. Ela ilustra os conceitos básicos da teoria de Morse: os pontos críticos de uma função de Morse-Smale e suas variedades estáveis e instáveis. A posição de um ponto sobre o toro inclinado é determinada por duas parametrizações de ângulos (-π ≤ α ≤ π) e (-π ≤ β ≤ π), que definem um sistema de coordenadas locais em cada ponto do toro. O parâmetro 't' (que pode ser negativo) controla a duração do toro. Mais detalhes podem ser visualizados na descrição original da demonstraçã
Control to flocking of the kinetic Cucker-Smale model
No full textThe well-known Cucker-Smale model is a macroscopic system reflecting flocking, i.e. the alignment of velocities in a group of autonomous agents having mutual interactions. In the present paper, we consider the meanfield limit of that model, called the kinetic Cucker-Smale model, which is a transport partial differential equation involving nonlocal terms. It is known that flocking is reached asymptotically whenever the initial conditions of the group of agents are in a favorable configuration. For other initial configurations, it is natural to investigate whether flocking can be enforced by means of an appropriate external force, applied to an adequate time-varying subdomain. In this paper we prove that we can drive to flocking any group of agents governed by the kinetic Cucker-Smale model, by means of a sparse centralized control strategy, and this, for any initial configuration of the crowd. Here, “sparse control” means that the action at each time is limited over an arbitrary proportion of the crowd, or, as a variant, of the space of configurations; “centralized” means that the strategy is computed by an external agent knowing the configuration of all agents. We stress that we do not only design a control function (in a sampled feedback form), but also a time-varying control domain on which the action is applied. The sparsity constraint reflects the fact that one cannot act on the whole crowd at every instant of time. Our approach is based on geometric considerations on the velocity field of the kinetic Cucker-Smale PDE, and in particular on the analysis of the particle flow generated by this vector field. The control domain and the control functions are designed to satisfy appropriate constraints, and such that, for any initial configuration, the velocity part of the support of the measure solution asymptotically shrinks to a singleton, which means flocking.First published in SIAM Journal on Mathematical Analysis, 47(6), 2015, published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.Peer reviewe
The realization of Smale solenoid type attractors in 3-manifolds
No full textAbstractWe study how to realize Smale solenoid type attractors in 3-manifolds. It is already known that we can restrict the 3-manifolds to lens spaces. We get all Smale solenoids realized in a given lens space through an inductive construction. We turn this around to address the question of how to decide whether a closed braid is a trivial knot in S3. For a diffeomorphism f of a 3-manifold M that realizes a Smale solenoid, it is natural to ask whether f−1 also realizes a Smale solenoid. We relate this question to exchangeable braids, and for some special positive case, we describe the relation between the two Smale solenoids of f and f−1
Interpretação eletrostática e a conjectura se Smale
No full textNesta dissertação estudamos a conjectura de Smale junto com a maioria dos resultados sobre este assunto e sua interpretação eletrostática. Mostramos alguns testes numéricos sobre a citada conjectura, para podermos analisar sua interpretação eletrostática.In this dissertation we study a conjecture of smale together with majority of results about this topic and its electrostatic interpretation. We show some numerical tests concerning the conjecture in order to analise its electrostatic interpretation.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq
- …
