Schr\"odinger formalism for a particle constrained to a surface in R13\mathbb{R}_1^3

In this work it is studied the Schr\"odinger equation for a non-relativistic particle restricted to move on a surface $S$ in a three-dimensional Minkowskian medium $\mathbb{R}_1^3$, i.e., the space $\mathbb{R}^3$ equipped with the metric $\text{diag}(-1,1,1)$. After establishing the consistency of the interpretative postulates for the new Schr\"odinger equation, namely the conservation of probability and the hermiticity of the new Hamiltonian built out of the Laplacian in $\mathbb{R}_1^3$, we investigate the confining potential formalism in the new effective geometry. Like in the well-known Euclidean case, it is found a geometry-induced potential acting on the dynamics $V_S = - \frac{\hbar^{2}}{2m} \left(\varepsilon H^2-K\right)$ which, besides the usual dependence on the mean ($H$) and Gaussian ($K$) curvatures of the surface, has the remarkable feature of a dependence on the signature of the induced metric of the surface: $\varepsilon= +1$ if the signature is $(-,+)$, and $\varepsilon=1$ if the signature is $(+,+)$. Applications to surfaces of revolution in $\mathbb{R}^3_1$ are examined, and we provide examples where the Schr\"odinger equation is exactly solvable. It is hoped that our formalism will prove useful in the modeling of novel materials such as hyperbolic metamaterials, which are characterized by a hyperbolic dispersion relation, in contrast to the usual spherical (elliptic) dispersion typically found in conventional materials.Comment: 26 pages, 1 figure; comments are welcom

Enraizamento de estacas de mangostão com diferentes concentrações de auxinas.

Ensaio para verificar a possibilidade de obtencao de estacas enraizadas de mangostao sob nebulizacao intermitente de auxinas. Os resultados preliminares indicam a possibilidade de obtencao de mudas de estacas enraizadas de mangostao, embora haja necessidade de ensaios mais elaborados, onde serao estudados os tipos de estacas, epocas e dosagens de fitormonios. Mesmo obtendo-se taxas de enraizamento nao muito altas, o tamanho da muda obtida pelo tratamento com fitormonio equivale a uma muda de um ano proveniente de sementes apomiticas, o que valida os resultados obtidos e corrobora com a continuidade da pesquisa.bitstream/item/89231/1/PA-35.pd

Agrotóxicos: avaliação ambiental.

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Nematic liquid crystal dynamics under applied electric fields

In this paper we investigate the dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available LIquid CRystal Algorithm (LICRA) developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.Comment: 7 pages, 12 figure

Limitações nutricionais de mudas de mangostãozeiro.

Este trabalho teve o objetivo de avaliar, por meio da análise foliar, as limitações nutricionais para produção de mudas de mangostãozeiro. Após 12 meses do plantio, em condições de viveiro, com sombreamento no início do desenvolvimento, foi observado amarelecimento progressivo das folhas novas, com diminuição significativa dos teores foliares de Fe e Mn

Response of the parasitoid Telenomus podisi to induced volatiles from soybean damaged by stink bug herbivory and oviposition.

Egg parasitoids have a short time frame in which their host eggs are suitable for parasitism, and in several systems these parasitoids respond to plant volatiles induced by oviposition on the plant (either in isolation or in combination with feeding damage) as a means of finding suitable hosts. It is known that the parasitoid of pentatomid eggs Telenomus podisi responds to damage done to soybeans by female Euschistus heros, its preferred host. ln this study our aim was to determine the type of E. heros damage to soybean (herbivory, oviposition or a combination of both) necessary for attraction of T. podisi. ln a Y-tube olfactometer the parasitoid has shown to respond to the undamaged plant over clcan air and herbivory-damaged plants over undamaged plants. However, the parasitoids did not respond to the treatments wherc oviposition occurred, either in isolation or in combination with herbivory. Analysis of volatile blends revealed that herbivory plus oviposition damage to soybean induced a volatile blend different to those induced when herbivory or oviposition occurred separately. These results, along with other results from this system, suggest that T. podisi uses plant volatile cues associated with female E. heros damage in order to be present when E. heros lays its eggs, and thus ensure its resource is optimal for parasitism