Numerical simulations with the Galerkin least squares finite element method for the Burgers' equation on the real line

In this work we present an efficient Galerkin least squares finite element scheme to simulate the Burgers’ equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by considering a sequence of auxiliary spatially dimensionless Dirichlet’s problems parameterized by its numerical support ˜K . Gaining advantage from the well-known convective-diffusive effects of the Burgers’ equation, computations start by choosing ˜K so it contains the support of the initial condition and, as solution diffuses out, ˜K is increased appropriately. By direct comparisons between numerical and analytic solutions and its asymptotic behavior, we conclude that the proposed scheme is accurate even for large times, and it can be applied to numerically investigate properties of this and similar equations on unbounded domains

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

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 understanding 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,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 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 underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities 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 organism 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 neglected 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 lost

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 understanding 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,5,6,7 vast areas of the tropics remain understudied.8,9,10,11 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 underrepresented in biodiversity databases.13,14,15 To worsen this situation, human-induced modifications16,17 may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities 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 organism 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 neglected 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 lost

Análise assintótica de um problema de transporte radiativo

Neste trabalho, consideramos um modelo de transporte radiativo e sua aproximação SP1, que chamamos de problema reduzido. Ambos sistemas são expandidos em torno da aproximação de Rosseland, que serve como aproximação de ordem zero. A expansão é realizada empregando a teoria de perturbações singulares e analisamos as aproximações para o interior, fronteira e dado inicial para a solução. A teoria de existência é estabelecida para o problema reduzido e para várias equações diferenciais que aparecem ao longo da análise, o que inclui a resolução de um problema unidimensional oriundo da expansão das camadas de fronteira. A aproximação SP1 obtida depende de um parâmetro positivo livre b, cuja existência é estudada numericamente.In this work, we consider a model of radiative transfer and its SP1 approximation, which we call the reduced problem. Both systems are expanded near the Rosseland approximation, which serves as their zero order approximation. The expansion is carried out employing singular perturbation theory and we look for boundary and interior approximations to the solution as well as approximations for the initial data. A theory of existence is established for the reduced problem and for various differential equations which appear on the course of the analysis, including the resolution of a one-dimensional problem arising from the boundary layer expansion. The aproximation depends on a free positive parameter b, whose existence is studied numerically

Estudo de um modelo [alpha]-ω-b para o dínamo solar

O problema do campo magnético gerado nos fluidos condutores de uma estrela como o Sol ainda é campo de investigações e muitos modelos têm sido estudados. Neste trabalho realizamos o estudo de um destes modelos para a evolução destes campos em conjunto com o campo de velocidades do fluido, considerando a interação entre eles. Neste contexto, deduzimos as equação do dínamo α-ω. A partir de equação da teoria eletromagnética e da física de plasma. Demonstramos também, a existência de quotas a priori para a soluções destas equações, estabelecemos resultados de existência e unicidade de soluções. Finalmente, demonstramos uma estimativa local de truncamento para método espectral aplicado ao sistema em questão e apresentamos resultados de simulação.The magnetic field generated in conducting fluids inside a star like the Sun is yet an open problem and many models have been studied. In this work we analyze one of these model for the evolution of magnetic fields interacting with the field of velocity in the fluid. In this context, we derive the α-ω dynamo equations from the classical electromagnetic theory and plasma physics. We establish as well some a priori bounds for their solutions, showing a theorem of existence and uniqueness. Finally we demonstrate an estimate of the local truncation error for the espectral method applied to the system in study and we present some results from simulation

Análise assintótica de um problema de transporte radiativo

Neste trabalho, consideramos um modelo de transporte radiativo e sua aproximação SP1, que chamamos de problema reduzido. Ambos sistemas são expandidos em torno da aproximação de Rosseland, que serve como aproximação de ordem zero. A expansão é realizada empregando a teoria de perturbações singulares e analisamos as aproximações para o interior, fronteira e dado inicial para a solução. A teoria de existência é estabelecida para o problema reduzido e para várias equações diferenciais que aparecem ao longo da análise, o que inclui a resolução de um problema unidimensional oriundo da expansão das camadas de fronteira. A aproximação SP1 obtida depende de um parâmetro positivo livre b, cuja existência é estudada numericamente.In this work, we consider a model of radiative transfer and its SP1 approximation, which we call the reduced problem. Both systems are expanded near the Rosseland approximation, which serves as their zero order approximation. The expansion is carried out employing singular perturbation theory and we look for boundary and interior approximations to the solution as well as approximations for the initial data. A theory of existence is established for the reduced problem and for various differential equations which appear on the course of the analysis, including the resolution of a one-dimensional problem arising from the boundary layer expansion. The aproximation depends on a free positive parameter b, whose existence is studied numerically