Non-integrability of the Armbruster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory

We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. We use Poincar\'e sections to illustrate the breakdown of regular motion for some parameter values.Comment: Accepted for publication in SIAM Journal on Applied Dynamical Systems. Adapted version for arxiv with 19 pages and 11 figure

Variational Integrators for the Gravitational N-Body Problem

This paper describes a fourth-order integration algorithm for the gravitational N-body problem based on discrete Lagrangian mechanics. When used with shared timesteps, the algorithm is momentum conserving and symplectic. We generalize the algorithm to handle individual time steps; this introduces fifth-order errors in angular momentum conservation and symplecticity. We show that using adaptive block power of two timesteps does not increase the error in symplecticity. In contrast to other high-order, symplectic, individual timestep, momentum-preserving algorithms, the algorithm takes only forward timesteps. We compare a code integrating an N-body system using the algorithm with a direct-summation force calculation to standard stellar cluster simulation codes. We find that our algorithm has about 1.5 orders of magnitude better symplecticity and momentum conservation errors than standard algorithms for equivalent numbers of force evaluations and equivalent energy conservation errors.Comment: 31 pages, 8 figures. v2: Revised individual-timestepping description, expanded comparison with other methods, corrected error in predictor equation. ApJ, in pres

Sunki mandarin and Swingle citrumelo as rootstocks for rain-fed cultivation of late-season sweet orange selections in northern São Paulo state, Brazil.

In Brazilian regions affected by the citrus sudden death disease, sweet orange cultivation depends on the use of resistant rootstocks. Rangpur lime was mainly replaced by Swingle citrumelo and Sunki mandarin rootstocks, more drought-sensitive ones. The diversification of scion selections is also desirable aiming at the increasing demand for not from concentrate orange juice (NFC) that requires high-quality fruits. In this work, we evaluated the performance of 6 selections of Valencia (IAC, Dom João, Late Burjasot IVIA 35-2, Rhode Red SRA 360, Temprana IVIA 25 and Campbell) and Natal IAC sweet oranges grafted onto Swingle citrumelo and Sunki mandarin. The planting occurred in 2001 under rain-fed cultivation in Bebedouro, northern São Paulo state, Brazil. The outline was made through randomized blocks in a 7 × 2 factorial design (selections × rootstock), with 4 replications and 2 trees in unit. Both rootstocks performed well in the region. Sunki mandarin rootstock induced greater tree size and production per plant to the scion selections, 38 and 21%, respectively, plus higher precocity of production compared to Swingle citrumelo. The later determined a greater productive efficiency, as well as a greater percentage of juice in general, albeit with lower concentrations of soluble solids and acidity. Natal IAC, Valencia IAC and Rhode Red Valencia selections presented a higher accumulated production, on average, 218.6 kg?plant?1 (2004 ? 2008), and a higher productive efficiency (kg fruit?m?3 of canopy) due to their smaller tree size. All assessed selections produced fruits with high soluble solids content that were suitable for juice processing

Incidence of Huanglongbing on several sweet orange cultivars budded onto different rootstocks at the Citrus Experimental Station (EECB), Bebedouro, São Paulo, Brazil.

Huanglongbing (HLB), caused by Candidatus Liberibacter asiaticus and Ca. L. americanus and vectored by Diaphorina citri Kuwayama, was first reported in 2004 in Brazil and it is currently widespread in São Paulo State (Belasque et al., 2010). The EECB, in partnership with Embrapa Cassava & Fruits, conducts a citrus improvement program aimed to select scion and rootstock Citrus cultivars mainly focused on the resistance or tolerance to biotic and abiotic stresses

Reação da cultivar Navelina ISA 315 (Citrus sinensis L. Osb.), à clorose variegada dos citros em condições de campo.

A clorose variegada dos citros (CVC), causada pela bactéria Xylella fastidiosa, está presente no Estado de São Paulo desde 1987. Todas as variedades comerciais de laranjas doces são afetadas. Causa redução da produção, principalmente pela acentuada redução no tamanho dos frutos. (LARANJEIRA et al., 2005). A CVC é transmitida por meio de borbulhas contaminadas e por cigarrinhas das famílias Cicadellidae, em citros existem diversas espécies transmissoras de X. fastidiosa, porém a eficiência na transmissão é inferior a 15%, e este índice pode variar entre espécies em função de mecanismos fisiológicos e comportamentais (YAMAMOTO, 2007; LOPES, 1996). Os sintomas característicos da doença são cloroses internervais amareladas na face superior da folha com correspondente necroses de tons de marrom na face inferior, a frutificação tem tendência de ser em pencas onde os frutos tornam-se rígidos, pequenos e com uma concentração de açúcar maior que o normal (LARANJEIRA et al., 2005).pdf 12