Geometric Approach to Lyapunov Analysis in Hamiltonian Dynamics

As is widely recognized in Lyapunov analysis, linearized Hamilton's equations of motion have two marginal directions for which the Lyapunov exponents vanish. Those directions are the tangent one to a Hamiltonian flow and the gradient one of the Hamiltonian function. To separate out these two directions and to apply Lyapunov analysis effectively in directions for which Lyapunov exponents are not trivial, a geometric method is proposed for natural Hamiltonian systems, in particular. In this geometric method, Hamiltonian flows of a natural Hamiltonian system are regarded as geodesic flows on the cotangent bundle of a Riemannian manifold with a suitable metric. Stability/instability of the geodesic flows is then analyzed by linearized equations of motion which are related to the Jacobi equations on the Riemannian manifold. On some geometric setting on the cotangent bundle, it is shown that along a geodesic flow in question, there exist Lyapunov vectors such that two of them are in the two marginal directions and the others orthogonal to the marginal directions. It is also pointed out that Lyapunov vectors with such properties can not be obtained in general by the usual method which uses linearized Hamilton's equations of motion. Furthermore, it is observed from numerical calculation for a model system that Lyapunov exponents calculated in both methods, geometric and usual, coincide with each other, independently of the choice of the methods.Comment: 22 pages, 14 figures, REVTeX

Cálculo do custo da monta natural e da inseminação artificial: Versão 2004.1

bitstream/item/82581/1/Calculo-do-custo-da-monta.pdfAcompanha 1 CD: Sistema para cálculo do custo da Monta Natural e da Inseminação Artificial, versão 2004.

Charge-Density-Wave Ordering in the Metal-Insulator Transition Compound PrRu4P12

X-ray and electron diffraction measurements on the metal-insulator (M-I) transition compound PrRu$_4$P$_{12}$ have revealed the emergence of a periodic ordering of charge density around the Pr atoms. It is found that the ordering is associated with the onset of a low temperature insulator phase. These conclusions are supported by the facts that the space group of the crystal structure transforms from Im$\bar{3}$ to Pm$\bar{3}$ below the M-I transition temperature and also that the temperature dependence of the superlattice peaks in the insulator phase follows the squared BCS function. The M-I transition could be originated from the perfect nesting of the Fermi surface and/or the instability of the $f$ electrons.Comment: 4 pages, 5 figures, Phys. Rev. B (2004) (in press

Evolution of a global string network in a matter dominated universe

We evolve the network of global strings in the matter-dominated universe by means of numerical simulations. The existence of the scaling solution is confirmed as in the radiation-dominated universe but the scaling parameter $\xi$ takes a slightly smaller value, $\xi \simeq 0.6 \pm 0.1$, which is defined as $\xi = \rho_{s} t^{2} / \mu$ with $\rho_{s}$ the energy density of global strings and $\mu$ the string tension per unit length. The change of $\xi$ from the radiation to the matter-dominated universe is consistent with that obtained by Albrecht and Turok by use of the one-scale model. We also study the loop distribution function and find that it can be well fitted with that predicted by the one-scale model, where the number density $n_{l}(t)$ of the loop with the length $l$ is given by $n_{l}(t) = \nu/[t^2 (l + \kappa t)^2]$ with $\nu \sim 0.040$ and $\kappa \sim 0.48$. Thus, the evolution of the global string network in the matter-dominated universe can be well described by the one-scale model as in the radiation-dominated universe.Comment: 10 pages, 5 figure

Ciclagem de nutrientes em cultivo de terceira soca de cana-de-açúcar.

Resumo: O objetivo do trabalho foi avaliar a liberação de macronutrientes em função de níveis de palhada mantida sobre o solo, na terceira soca de cana-de-açúcar, e sua contribuição para ciclos posteriores. O ensaio foi instalado em Araras ?SP, safra 2011-2012 (variedade RB-845210). Os tratamentos foram os níveis de palhada 25% - 50% - 75% - 100% (2,8 - 5,7 - 8,5 -11,3 t ha-1 em base seca) dispostos em blocos ao acaso, 4 repetições. Foi utilizado o método dos ?litter bags? para avaliar a decomposição da biomassa e sua respectiva ciclagem de nutrientes. Determinou-se as concentrações (g kg-1) de N, P, K, Ca, Mg e S e as quantidades (kg ha-1) liberadas após um ciclo de cultivo. Utilizou-se a análise de variância e regressão. As concentrações de N, P, Ca e S diferiram com níveis de palhada; já o K e Mg não responderam aos tratamentos. O modelo linear melhor se ajustou para as concentrações do N, P, K e Ca, com exceção do Mg e S. Houve maior liberação de nutrientes nos maiores níveis de palhada, porém esta diferença foi atribuída ao aumento da massa entre os tratamentos. Os elementos Ca, K e N, respectivamente, foram os mais liberados, independente dos tratamentos. Conclui-se que variações na quantidade de palhada deixadas sobre o solo apresentam comportamentos diferentes de mineralização de nutrientes durante um ciclo de cultivo da cana-de-açúcar. Há maior liberação de nutrientes nos maiores níveis de palhada, sendo os elementos Ca, K e N, respectivamente, os mais liberados