A note on statistical solutions of the three-dimensional Navier–Stokes equations: The stationary case

Stationary statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble average for turbulent flows in statistical equilibrium in time. They are also a generalization of the notion of invariant measure to the case of the three-dimensional Navier–Stokes equations, for which a global uniqueness result is not known to exist and a semigroup may not be well-defined in the classical sense. The two classical definitions of stationary statistical solutions are considered and compared, one of them being a particular case of the other and possessing a number of useful properties. Furthermore, the so-called time-average stationary statistical solutions, obtained as generalized limits of time averages of weak solutions as the averaging time goes to infinity are shown to belong to this more restrictive class. A recurrent type result is also obtained for statistical solutions satisfying an accretion condition. Finally, the weak global attractor of the three-dimensional Navier–Stokes equations is considered, and in particular it is shown that there exists a topologically large subset of the weak global attractor which is of full measure with respect to that particular class of stationary statistical solutions and which has a certain regularity property.Indisponível

Topological properties of the weak global attractor of the three-dimensional Navier-Stokes equations

The three-dimensional incompressible Navier-Stokes equations are considered along with its weak global attractor, which is the smallest weakly compact set which attracts all bounded sets in the weak topology of the phase space of the system (the space of square-integrable vector fields with divergence zero and appropriate periodic or no-slip boundary conditions). A number of topological properties are obtained for certain regular parts of the weak global attractor. Essentially two regular parts are considered, namely one made of points such that all weak solutions passing through it at a given initial time are strong solutions on a neighborhood of that initial time, and one made of points such that at least one weak solution passing through it at a given initial time is a strong solution on a neighborhood of that initial time. Similar topological results are obtained for the family of all trajectories in the weak global attractor.Indisponível

A note on statistical solutions of the three-dimensional Navier–Stokes equations: The time-dependent case

Time-dependent statistical solutions of the three-dimensional Navier–Stokes equations for incompressible fluids are considered. They are a mathematical formalization of the notion of ensemble averages in turbulence theory and form the backbone for a mathematical foundation of the theory of turbulence. The two main notions of statistical solutions, previously introduced, are revisited and a new formulation of one of them is given. An existence proof for this new formulation is given, along with a number of useful properties.Indisponível

Statistical estimates for channel flows driven by a pressure gradient

We present rigorous estimates for some physical quantities related to turbulent and non-turbulent channel flows driven by a uniform pressure gradient. Such results are based on the concept of stationary statistical solutions, which is related to the notion of ensemble averages for flows in statistical equilibrium. We provide a lower bound estimate for the mean skin friction coefficient and improve on a previous upper bound estimate for the same quantity; both estimates are derived in terms of the Reynolds number. We also present lower and upper bound estimates for the mean rate of energy dissipation, the mean longitudinal bulk velocity (in the direction of the pressure gradient), and the mean kinetic energy in terms of various physical parameters. In particular, we obtain an upper bound related to the energy dissipation law, namely that the mean rate of energy dissipation is essentially bounded by a non-dimensional universal constant times the cube of the mean longitudinal bulk velocity over a characteristic macro-scale length. Finally, we investigate the scale-by-scale energy injection due to the pressure gradient, proving an upper bound estimate for the decrease of this energy injection as the scale length decreases.Indisponível

Melhoria das medições indiretas do índice de área foliar com uso da altura do dossel

The objective of this work was to evaluate the use of plant height as a calibration variable for improving indirect measurements of the leaf area index (LAI). Three experiments were conducted with different crops – corn (Zea mays), soybean (Glycine max), and sugarcane (Saccharum officinarum) –, to compare the performance of the LAI measured indirectly (LAIind) and corrected by the calibration variable with the LAI measured directly (LAIref). Without the proposed correction, the LAIind tended to be overestimated by 20%, on average, compared with the LAIref, for the three crops. After crop height was used to adjust the LAIind, a strong positive relationship was observed between the LAIref and the corrected LAIind (R2 = 0.96); overestimation was reduced to 4% and the mean square error decreased to 0.07 m2 m-2. The variable canopy height is promising for the correction of the LAI of the soybean, corn, and sugarcane crops.O objetivo deste trabalho foi avaliar o uso da altura do dossel da planta como variável de ajuste para melhorar as medições indiretas do índice de área foliar (IAF). Três experimentos foram conduzidos com diferentes culturas – milho (Zea mays), soja (Glycine max) e cana-de-açúcar (Saccharum officinarum) –, para comparar o desempenho do IAF medido indiretamente (IAFind) e corrigido pela variável de ajuste com o IAF medido diretamente (IAFref). Sem a correção proposta, o IAFind tendeu a ser superestimado em 20%, em média, em relação ao IAFref, para as três culturas. Após o uso da altura da colheita para ajustar o IAFind, observaram-se fortes relações positivas entre o IAFref e o IAFind corrigido (R2 = 0,96); a superestimação foi reduzida para 4% e o erro médio quadrático diminuiu para 0,07 m2 m-2. A variável altura do dossel mostra-se promissora para correção do IAF das culturas de soja, milho e cana-de-açúcar

Secondary syphilis presenting as a corymbiform syphilide: case report and review

It is essential that healthcare providers are familiar with the full spectrum of clinical presentations of syphilis. A rare manifestation of secondary syphilis is the corymbiform (or corymbose) arrangement, in which a central greater papule is surrounded by smaller satellite lesions. Very few reports of corymbiform syphilis are available in current biomedical databases. We present the case of a 28 year-old HIV-infected male patient on regular, successful antiretroviral therapy who developed an asymptomatic corymbiform maculopapular lesion in the medial aspect of the right thigh. There were also a few brownish macular lesions on the left sole. New serological tests for syphilis (which had been negative in the past) were reactive. The coymbiform lesion slowly regressed and the non-treponemal test reverted to negative after benzathine penicillin G treatment. A review of the literature is provided. This is the first report of corymbiform syphilis in an HIV-infected patient

Towards Generating Richer Code by Binding Security Abstractions to BPMN Task Types

This paper presents an approach for binding security requirements to different BPMN task types to create secure executable business processes.This paper presents an approach for binding security requirements to different BPMN task types to create secure executable business processes

An Approach for Reducing the Gap between BPMN Models and Implementation Artifacts

The need for using high-level modeling tools (e.g. BPMN) isincreasing considerably. The proliferation of the service oriented architectures (SOA) is also apparent. In this context, there is a gap between the developed model and its execution. This work introduces the MoSC Translator which translates models produced in BPMN into executable WS-BPEL processes

Antiplatelet, Antithrombotic, and Fibrinolytic Activities of Campomanesia xanthocarpa

In a previous work based on popular belief, Campomanesia xanthocarpa Berg., popularly known as “guavirova”, showed to have a potential effect in the control of a number of conditions associated with cardiovascular diseases. The aim of the present work was to investigate the effects of C. xanthocarpa extract (CXE) on antiplatelet, antithrombotic and fibrinolytic activities in mice and in human blood. Mice were treated orally for 5 days with CXE or acetylsalicylic acid and at the end of the treatment period animals were challenged for bleeding, acute thromboembolism and ulcerogenic activity. In addition, we have assessed the prothrombin time and activated partial thromboplastin time (aPTT) after oral administration. In in vitro assays, antiplatelet effects of CXE was evaluated on platelet aggregation, and fibrinolytic activity of the extract was observed by mice or human artificial blood clot degradation. Platelet citotoxicity of the extract was also determined by the LDH assay. Results demonstrated that CXE has a significant protective effect on thrombosis. It also inhibits platelet aggregation without demonstrating cytotoxicity on platelets. CXE slightly prolonged aPTT and showed no ulcerogenic activity after oral administration. In addition, CXE showed a fibrinolytic activity. Thus, C. xanthocarpa showed antiplatelet, antithrombotic and fibrinolytic activities in mice