Facing fluid dynamics through a friendly shortcut though of limited validity: the superposition principle

O princípio da superposição é invocado de maneira ampla na física, mas o estudante deve ter em mente que sua validade limita-se às situações regidas por equações lineares. Tal é o caso do eletromagnetismo, em contraste com a dinâmica de fluidos. Nesta ultima, as equações são em geral não-lineares, podendo contudo se reduzir a equações lineares num caso particular de grande interesse, capaz inclusive de abranger situações dependentes do tempo. O objetivo desse artigo de cunho pedagógico é explorar as analogias deste caso com o eletromagnetismo, de forma a possibilitar uma introdução rápida à dinâmica de fluidos por parte do estudante não familiarizado com este ramo fascinante porém geralmente ausente da formação do físico. Nesse processo daremos ênfase ao traçado de linhas de corrente mediante o uso de ferramentas gráficas computacionais que, acreditamos, facilitarão ao estudante a percepção da analogia mencionada.The superposition principle is widely invoked in physics. However, the student should bear in mind that its validity implies that the system under focus is governed by linear equations. Such a condition is usually fulfilled in electromagnetism, but not in fluid dynamics, where the governing equations are generally non-linear ones. Nevertheless, such equations become linear in an important particular case, which applies even to time dependent situations. Our aim in this pedagogical article is to explore the analogies of such a case with electromagnetism. We believe that this approach can make easier to introduce fluid dynamics to a typical student, generally not acquainted at all with the principles of this branch of increasing importance in physics. We emphasize the plot of streamlines by making use of computational graphical tools which hopefully helps to clarify the proposed pedagogical strategy

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio