Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scien- tific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science

The growth of matter perturbations in f(R) models

We consider the linear growth of matter perturbations on low redshifts in some $f(R)$ dark energy (DE) models. We discuss the definition of dark energy (DE) in these models and show the differences with scalar-tensor DE models. For the $f(R)$ model recently proposed by Starobinsky we show that the growth parameter $\gamma_0\equiv \gamma(z=0)$ takes the value $\gamma_0\simeq 0.4$ for $\Omega_{m,0}=0.32$ and $\gamma_0\simeq 0.43$ for $\Omega_{m,0}=0.23$, allowing for a clear distinction from $\Lambda$CDM. Though a scale-dependence appears in the growth of perturbations on higher redshifts, we find no dispersion for $\gamma(z)$ on low redshifts up to $z\sim 0.3$, $\gamma(z)$ is also quasi-linear in this interval. At redshift $z=0.5$, the dispersion is still small with $\Delta \gamma\simeq 0.01$. As for some scalar-tensor models, we find here too a large value for $\gamma'_0\equiv \frac{d\gamma}{dz}(z=0)$, $\gamma'_0\simeq -0.25$ for $\Omega_{m,0}=0.32$ and $\gamma'_0\simeq -0.18$ for $\Omega_{m,0}=0.23$. These values are largely outside the range found for DE models in General Relativity (GR). This clear signature provides a powerful constraint on these models.Comment: 14 pages, 7 figures, improved presentation, references added, results unchanged, final version to be published in JCA

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

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

Electrostatic self-force in (2+1)-dimensional cosmological gravity

Point sources in (2+1)-dimensional gravity are conical singularities that modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge in the presence of point masses in (2+1)-dimensional gravity with a cosmological constant.Comment: 9 pages, Late

Anticarsia gemmatalis Hübner, 1818 (Lepidoptera: Noctuidae) biologia, amostragem e métodos de controle.

A lagarta da soja, Anticarsia gemmatalis Hübner, 1818 (Lepidoptera: Noctuidae) é a principal desfolhadora da soja no Brasil, sendo encontrada em todos os locais de produção, representando um risco à produção e à qualidade dos cultivos brasileiros (GAZZONI e YORINIORI, 1995; MOSCARDI e SOUZA, 2002). Este inseto causa grandes danos à lavoura de soja, que vão desde o desfolhamento até a destruição completa da planta. A lagarta da soja é um inseto mastigador e se alimenta de folhas jovens. Quando a folhagem é removida, ataca outras partes da planta, como pecíolos e a haste. O desfolhamento compromete o enchimento das vagens, devido à diminuição da área foliar responsável pela fotossíntese, com conseqüente redução da produção de grãos. Quando se alimentam, além de remover os tecidos vegetais, que contem nutrientes, as lagartas injetam toxinas nas plantas (SILVA et al., 2002). Existem, também, outras culturas em que a lagarta da soja causa prejuízos como cultura da alfafa, do amendoim, do arroz, da ervilha, do feijão, do feijão-vagem e do trigo, atacando durante a fase vegetativa e, em alguns casos, até no período da floração (PRATISSOLI, 2002). A lagarta da soja costuma atacar as lavouras nas regiões setentrionais e a partir de janeiro no extremo sul do País e chega a ocasionar 100% de destruição foliar (HOFFMANN et al., 1979; GAZZONI e YORINIORI, 1995), sendo, portanto, de grande importância conhecer o comportamento desta praga e os métodos utilizados para o seu controle.bitstream/CENARGEN/27983/1/doc196.pd