Minimal domain size necessary to simulate the field enhancement factor numerically with specified precision

In the literature about field emission, finite elements and finite differences techniques are being increasingly employed to understand the local field enhancement factor (FEF) via numerical simulations. In theoretical analyses, it is usual to consider the emitter as isolated, i.e, a single tip field emitter infinitely far from any physical boundary, except the substrate. However, simulation domains must be finite and the simulation boundaries influences the electrostatic potential distribution. In either finite elements or finite differences techniques, there is a systematic error ($\epsilon$) in the FEF caused by the finite size of the simulation domain. It is attempting to oversize the domain to avoid any influence from the boundaries, however, the computation might become memory and time consuming, especially in full three dimensional analyses. In this work, we provide the minimum width and height of the simulation domain necessary to evaluate the FEF with $\epsilon$ at the desired tolerance. The minimum width ($A$) and height ($B$) are given relative to the height of the emitter ($h$), that is, $(A/h)_{min} \times (B/h)_{min}$ necessary to simulate isolated emitters on a substrate. We also provide the $(B/h)_{min}$ to simulate arrays and the $(A/h)_{min}$ to simulate an emitter between an anode-cathode planar capacitor. At last, we present the formulae to obtain the minimal domain size to simulate clusters of emitters with precision $\epsilon_{tol}$. Our formulae account for ellipsoidal emitters and hemisphere on cylindrical posts. In the latter case, where an analytical solution is not known at present, our results are expected to produce an unprecedented numerical accuracy in the corresponding local FEF

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Recent analyses of the field enhancement factor (FEF) from multiple emitters have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest $0<c/h\lesssim5$ ($c$ being the separation and $h$ is the height of the emitters) and $c\rightarrow\infty$, has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this letter, we use first principles to derive a simple two-parameter formula for fractional reduction that can be of interest for experimentalists to modeling and interpret the FEF from small clusters of emitters or arrays in small and large separations. For the structures tested, the agreement between numerical and analytical data is $\sim1\%$

The rapid soybean growth in Brazil.

Título em francês: La rapide croissance du soja au Brésil

Zero-energy states in graphene quantum dots and rings

We present exact analytical zero-energy solutions for a class of smooth decaying potentials, showing that the full confinement of charge carriers in electrostatic potentials in graphene quantum dots and rings is indeed possible without recourse to magnetic fields. These exact solutions allow us to draw conclusions on the general requirements for the potential to support fully confined states, including a critical value of the potential strength and spatial extent.Comment: 8 pages, 3 figures, references added, typos corrected, discussion section expande

Dicas para uma produção sustentável de soja.

bitstream/item/214945/1/Folder-01-prod.sustentavel-soja-2020.pdf1 folder. Folder 01/2020 - 1ª impressão - junho de 2020 - CGPE 15908

Desenvolvimento, mercado, rentabilidade da soja brasileira.

O agronegócio e o desenvolvimento da soja no Brasil. O agronegócio brasileiro no contexto global. O Brasil na produção de alimentos e de bioenergia. O Brasil e alta do preço dos alimentos. A soja no mundo. A soja no Brasil. Mercado e rentabilidade da soja.bitstream/CNPSO-2010/30758/1/CT74-eletronica.pd

A Embrapa Soja no contexto do desenvolvimento da soja no Brasil: histórico e contribuições.

Introdução. Antecedentes da pesquisa agrícola no Brasil. Estabelecimento da Embrapa. Implantação da Embrapa soja. A pesquisa com soja no Brasil. Os primórdios da produção e a rápida expansão da soja no Brasil. Impactos da soja no mundo. O futuro do setor privado na pesquisa agrícola brasileira. Avanços tecnológicos na cultura da soja. Referências.bitstream/item/142568/1/Livro-EmbrapaSoja-desenvolvimento-BR-OL.pd