An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation

In the present work we show that planetary mean distances can be calculated with the help of a Schrodinger-type diffusion equation. The obtained results are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, with only three empty states. Furthermore, the equation solutions predict a fundamental orbit at 0.05 AU from solar-type stars, a result confirmed by recent discoveries. In contrast to other similar approaches previously presented in the literature, we take into account the flatness of the solar system, by considering the flat solutions of the Schrodinger-type equation. The model has just one input parameter, given by the mean distance of Mercury.Comment: 6 pages. Version accepted for publication in Chaos, Solitons & Fractal

On geometry-dependent vortex stability and topological spin excitations on curved surfaces with cylindrical symmetry

We study the Heisenberg Model on cylindrically symmetric curved surfaces. Two kinds of excitations are considered. The first is given by the isotropic regime, yielding the sine-Gordon equation and $\pi$-solitons are predicted. The second one is given by the XY model, leading to a vortex turning around the surface. Helical states are also considered, however, topological arguments can not be used to ensure its stability. The energy and the anisotropy parameter which stabilizes the vortex state are explicitly calculated for two surfaces: catenoid and hyperboloid. The results show that the anisotropy and the vortex energy depends on the underlying geometry.Comment: 10 pages, 2 figures, Accepted for publication in Phys. Lett A (2013

The influence of self‐weight of elastic 2D structures in topology optimization via numerical technique Smooth Evolutionary Structural Optimization (SESO)

O presente artigo aborda a otimização topológica em problemas de elasticidade plana linear considerando a influência do peso próprio nos esforços em elementos estruturais. Utiliza‐se para este fim uma técnica numérica denominada Smooth ESO (SESO) que se baseia no procedimento de diminuição progressiva da contribuição de rigidez de elementos ineficientes com menores tensões até que ele não tenha mais influência. As aplicações do SESO são feitas com o método dos elementos finitos e considera‐se um elemento finito triangular e de alta ordem. Neste trabalho estende‐se a técnica SESO para a aplicação do peso próprio onde o programa, no cômputo de seu volume e peso específico, gera automaticamente uma força concentrada equivalente para cada nó do elemento. A avaliação é finalizada com a definição de um modelo de bielas e tirantes resultante das regiões de concentração de tensões. Nos exemplos de aplicação são apresentadas topologias ótimas de uma estrutura suspensa, de viga baixa e de viga parede considerando o peso próprio e obtendo‐se ótimas configurações e demonstrando que a consideração do peso próprio leva a maior robustez ao processo de otimização.This paper deals with topology optimization in plane elastic‐linear problems considering the influence of the self weight in efforts in structural elements. For this purpose it is used a numerical technique called SESO (Smooth ESO), which is based on the procedure for progressive decrease of the inefficient stiffness element contribution at lower stresses until he has no more influence. The SESO is applied with the finite element method and is utilized a triangular finite element and high order. This paper extends the technique SESO for application its self weight where the program, in computing the volume and specific weight, automatically generates a concentrated equivalent force to each node of the element. The evaluation is finalized with the definition of a model of strut‐and‐tie resulting in regions of stress concentration. Examples are presented with optimum topology structures obtaining optimal settings.Peer Reviewe

Kantoswki-Sachs model with a running cosmological constant and radiation

The simplest anisotropic model of the early Universe is the one with two conformal factors, which can be identified as Kantowski-Sachs metric, or the reduced version of the Bianchi-I metric. To fit the existing observational data, it is important that the anisotropy is washed out in the early stage of the evolution. We explore the possible effect of the running cosmological constant (RCC) on the dynamics of isotropy, in the case of the space filled by radiation.Comment: The paper has 16 pages and 16 figure

Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrodinger equations

In this work we derive the Hamiltonian formalism of the O(N) non-linear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrodinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrodinger representation.Comment: Revtex version, 17 pages, substantial change

Canonical transformation for stiff matter models in quantum cosmology

In the present work we consider Friedmann-Robertson-Walker models in the presence of a stiff matter perfect fluid and a cosmological constant. We write the superhamiltonian of these models using the Schutz's variational formalism. We notice that the resulting superhamiltonians have terms that will lead to factor ordering ambiguities when they are written as operators. In order to remove these ambiguities, we introduce appropriate coordinate transformations and prove that these transformations are canonical using the symplectic method.Comment: Revtex4 Class, 3 pages, No Figure