Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

Effects of substrate type on plant growth and nitrogen and nitrate concentration in spinach

Abstract The effects of three commercial substrates (a mixture of forest residues, composted grape husks, and white peat, black peat and coir) on plant growth and nitrogen (N) and nitrate (NO3) concentration and content were evaluated in spinach (Spinacia oleracea L. cv. Tapir). Spinach seedlings were transplanted at 45 days after emergence into Styrofoam boxes filled with the substrates and were grown during winter and early spring in an unheated greenhouse with no supplemental lighting. Each planting box was irrigated daily by drip and fertilized with a complete nutrient solution. The NO3 content of the drainage water was lower in coir than in the other substrates. However, shoot NO3 concentration was not affected by substrate type, while yield and total shoot N and NO3 content were greater when plants were grown in peat than in the mixed substrate or the coir. Leaf chlorophyll meter readings provided a good indication of the amount of N in the plants and increased linearly with total shoot N. Keywords Spinacia oleracea; chlorophyll meter; coir; peat; soilless culture systems

Effects of substrate type on plant growth and nitrogen and nitrate concentration in spinach.

The effects of three commercial substrates (a mixture of forest residues, composted grape husks, and white peat, black peat and coir) on plant growth and nitrogen (N) and nitrate (NO3) concentration and content were evaluated in spinach (Spinacia oleracea L. cv. Tapir). Spinach seedlings were transplanted at 45 days after emergence into Styrofoam boxes filled with the substrates and were grown during winter and early spring in an unheated greenhouse with no supplemental lighting. Each planting box was irrigated daily by drip and fertilized with a complete nutrient solution. The NO3 content of the drainage water was lower in coir than in the other substrates. However, shoot NO3 concentration was not affected by substrate type, while yield and total shoot N and NO3 content were greater when plants were grown in peat than in the mixed substrate or the coir. Leaf chlorophyll meter readings provided a good indication of the amount of N in the plants and increased linearly with total shoot N.

Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.

Modelos estocásticos de crescimento individual e desenvolvimento de software de estimação e previsão

Os modelos de crescimento individual são geralmente adaptações de modelos de crescimento de populações. Inicialmente estes modelos eram apenas determinísticos, isto é, não incorporavam as flutuações aleatórias do ambiente. Com o desenvolvimento da teoria do cálculo estocástico podemos adicionar um termo estocástico, que representa a aleatoriedade ambiental que influencia o processo em estudo. Actualmente, o estudo do crescimento individual em ambiente aleatório é cada vez mais importante, não apenas pela vertente financeira, mas também devido às suas aplicações nas áreas da saúde e da pecuária, entre outras. Problemas como o ajustamento de modelos de crescimento individual, estimação de parâmetros e previsão de tamanhos futuros são tratados neste trabalho. São apresentadas novas aplicações do modelo estocástico monomolecular generalizado e um novo software de aplicação deste e de outros modelos. ABSTRACT: Individual growth models are usually adaptations of growth population models. Initially these models were only deterministic, that is, they did not incorporate the random fluctuations of the environment. With the development of the theory of stochastic calculus, we can add a stochastic term that represents the random environmental influences in the process under study. Currently, the study of individual growth in a random environment is increasingly important, not only by the financial scope but also because of its applications in health care and livestock production, among others. Problems such as adjustment of an individual growth model, estimation of parameters and prediction of future sizes are treated in this work. New applications of the generalized stochastic monomolecular model and a new software applied to this and other models are presented.

Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.