Global Analytic Solutions for the Nonlinear Schr\"odinger Equation

We prove the existence of global analytic solutions to the nonlinear Schr\"odinger equation in one dimension for a certain type of analytic initial data in $L^2$.Comment: Corrected errors in proofs in section

A Remark on Unconditional Uniqueness in the Chern-Simons-Higgs Model

The solution of the Chern-Simons-Higgs model in Lorenz gauge with data for the potential in $H^{s-1/2}$ and for the Higgs field in $H^s \times H^{s-1}$ is shown to be unique in the natural space $C([0,T];H^{s-1/2} \times H^s \times H^{s-1})$ for $s \ge 1$, where $s=1$ corresponds to finite energy. Huh and Oh recently proved local well-posedness for $s > 3/4$, but uniqueness was obtained only in a proper subspace $Y^s$ of Bourgain type. We prove that any solution in $C([0,T];H^{1/2} \times H^1 \times L^2)$ must in fact belong to the space $Y^{3/4+\epsilon}$, hence it is the unique solution obtained by Huh and Oh

Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces

We obtain an asymptotic rate of decay for the radius of spatial analyticity of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces

Low genetic but high morphological variation over more than 1000 km coastline refutes omnipresence of cryptic diversity in marine nematodes

Background: The resilience of ecosystems to negative impacts is generally higher when high gene flow, species diversity and genetic diversity are present. Population genetic studies are suitable to investigate genetic diversity and estimate gene flow between populations. Seaweed beds form a dynamic shallow water ecosystem influenced by climate change and human exploitation, as such, seaweed beds are a particularly powerful model to investigate ecosystem resilience in coastal areas. We studied the population genetic structure of the new nematode species Paracanthonchus gynodiporata associated with seaweeds in northeastern Brazil. Nematodes are generally believed to have a limited dispersal capacity because of the lack of planktonic larvae. Yet, they can drift on seaweeds, and water currents might be a natural barrier for their dispersal. Populations of P. gynodiporata were sampled over more than 1000 km coastline in regions across major oceanic currents with and without historical exploitation of seaweed. Results: P. gynodiporata is described in an integrative way using mitochondrial and nuclear sequences and morphological data. The 3D model of the head region shows for the first time a detailed view of the ventrosublateral teeth, a character often overlooked in older taxonomic studies of the genus. A total of 17 mitochondrial COI haplotypes were found with one haplotype representing 63 to 83% of the frequencies in each population. AMOVA showed overall little population genetic structure (F-ST = 0.05204), and no genetic subdivision between the populations under the influence of the two different water currents were found. Effects of historical seaweed exploitation on population genetic diversity were not detected. In contrast, significant differences between populations were found in morphometric characters. This discrepancy in genetic and morphological differentiation between populations across 1000 km of coastline is surprising in view of the frequently observed presence of several cryptic species at small geographical scale in other macroalgal associated nematodes. Conclusions: Our results show that cryptic species are not omnipresent in marine nematode species, suggesting that nematodes associated with seaweeds have been able to disperse over large distances across well-known biogeographic barriers

Well-posedness for a molecular beam epitaxy model

We study a general molecular beam epitaxy (MBE) equation modeling the epitaxial growth of thin films. We show that, in the deterministic case, the associated Cauchy problem admits a unique smooth solution for all time, given initial data in the space $X_0 = L^{2}(R^{d}) \cap \dot{W}^{1,4}(R^{d})$ with $d = 1, 2$. This improves a recent result by Ag\'elas, who established global existence in $H^{3}(R^{d})$. Moreover, we investigate the local existence and uniqueness of solutions in the space $X_0$ for the stochastic MBE equation, with an additive noise that is white in time and regular in the space variable

Projeto e análise Vof transiente de rotores Pelton

This work presents a methodology for the conceptual design of Pelton turbines, where configurations or dimensions are determined as a function of the nominal load condition. To determine the energy and hydraulic efficiency of the turbine, losses in terms of specific energy are introduced, and leakage and mechanical losses are then considered. This methodology allows obtaining the spatial coordinates that represent the concave surface of the bucket. The preliminary results of the project are compared with a numerical model in transient regime (CFD), procedures and methodologies for the simulation are presented in details, such as the construction of the mesh in the non-inertial domain, represented by five buckets and sliding mixing interfaces between the inertial and non-inertial domains. The multiphase, VOF and turbulence k-ω / SST models were selected considering step time values around 0.000185 s., in order to represent the instantaneous torque resulting from the interaction between the buckets and the jet. Simulation results were extended to analysis of hydraulic efficiency, at the design point and at part load.Este trabalho apresenta uma metodologia para o projeto conceitual de turbinas Pelton, onde as configurações ou dimensões são determinadas em função da condição de carga nominal. Para a determinação da energia e eficiência hidráulica da turbina, são introduzidas as perdas em termos de energia específica, sendo posteriormente consideradas as fugas e as perdas mecânicas. Esta metodologia permite obter as coordenadas espaciais que representam a superfície côncava da concha. Os resultados preliminares do projeto são comparados com um modelo numérico em regime transiente (CFD), procedimentos e metodologias para a simulação são apresentados em detalhes, como a construção da malha no domínio não inercial, representado por cinco conchas e interfaces de mistura deslizantes entre os domínios inerciais e não inercial. Os modelos multifásico, VOF e turbulência k-ω / SST foram selecionados considerando valores de passo tempo em torno de 0,000185 s., a fim de representar o torque instantâneo resultante da interação entre as conchas e o jato. Resultados da simulação foram estendidos para analises da eficiência hidráulica, no ponto de projeto e em carga parcial

Avaliação do nível de flexibilidade de idosos

Este estudo se propôs a verificar o nível da flexibilidade de idosos ativos praticantes de hidroginástica. Participaram da pesquisa 16 sujeitos do sexo feminino, com idade acima de 60 anos que praticavam hidroginástica regularmente. O grupo foi submetido a três testes: Teste do banco de Wells, Teste de Sentar e levantar e o Teste de Preensão manual. Os resultados não demonstramresultados significantes quando comparados a tabela padrão de flexibilidade em praticantes de hidroginástica, mas demonstram um resultado moderado quando correlacionaram os testes de sentar e levantar com o teste de Preensão manual. Os dados nos levam a concluir que a hidroginástica não refletiu em melhores resultados de flexibilidade e que a preensão manual tem relação com a flexibilidade, o que pode ser uma medida interessante para idosos, pois a força e flexibilidade os ajudam a manter as atividades do dia a dia