An implicit symplectic solver for high-precision long term integrations of the Solar System

We present FCIRK16, a 16th-order implicit symplectic integrator for long-term high precision Solar System simulations. Our integrator takes advantage of the near-Keplerian motion of the planets around the Sun by alternating Keplerian motions with corrections accounting for the planetary interactions. Compared to other symplectic integrators (the Wisdom and Holman map and its higher order generalizations) that also take advantage of the hierarchical nature of the motion of the planets around the central star, our methods require solving implicit equations at each time-step. We claim that, despite this disadvantage, FCIRK16 is more efficient than explicit symplectic integrators for high precision simulations thanks to: (i) its high order of precision, (ii) its easy parallelization, and (iii) its efficient mixed-precision implementation which reduces the effect of round-off errors. In addition, unlike typical explicit symplectic integrators for near Keplerian problems, FCIRK16 is able to integrate problems with arbitrary perturbations (non necessarily split as a sum of integrable parts). We present a novel analysis of the effect of close encounters in the leading term of the local discretization errors of our integrator. Based on that analysis, a mechanism to detect and refine integration steps that involve close encounters is incorporated in our code. That mechanism allows FCIRK16 to accurately resolve close encounters of arbitrary bodies. We illustrate our treatment of close encounters with the application of FCIRK16 to a point mass Newtonian 15-body model of the Solar System (with the Sun, the eight planets, Pluto, and five main asteroids) and a 16-body model treating the Moon as a separate body. We also present some numerical comparisons of FCIRK16 with a state-of-the-art high order explicit symplectic scheme for 16-body model that demonstrate the superiority of our integrator when very high precision is required.Consolidated Research Group MATHMODE (IT1294-19

An implicit symplectic solver for high-precision long term integrations of the Solar System

Compared to other symplectic integrators (the Wisdom and Holman map and its higher order generalizations) that also take advantage of the hierarchical nature of the motion of the planets around the central star, our methods require solving implicit equations at each time-step. We claim that, despite this disadvantage, FCIRK16 is more efficient than explicit symplectic integrators for high precision simulations thanks to: (i) its high order of precision, (ii) its easy parallelization, and (iii) its efficient mixed-precision implementation which reduces the effect of round-off errors. In addition, unlike typical explicit symplectic integrators for near Keplerian problems, FCIRK16 is able to integrate problems with arbitrary perturbations (non necessarily split as a sum of integrable parts). We present a novel analysis of the effect of close encounters in the leading term of the local discretization errors of our integrator. Based on that analysis, a mechanism to detect and refine integration steps that involve close encounters is incorporated in our code. That mechanism allows FCIRK16 to accurately resolve close encounters of arbitrary bodies. We illustrate our treatment of close encounters with the application of FCIRK16 to a point mass Newtonian 15-body model of the Solar System (with the Sun, the eight planets, Pluto, and five main asteroids) and a 16-body model treating the Moon as a separate body. We also present some numerical comparisons of FCIRK16 with a state-of-the-art high order explicit symplectic scheme for 16-body model that demonstrate the superiority of our integrator when very high precision is required

An Intrinsic Description of the Nonlinear Aeroelasticity of Very Flexible Wings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90662/1/AIAA-2011-1917-972.pd

Host and pathogen autophagy are central to the inducible local defences and systemic response of the giant kelp Macrocystis pyrifera against the oomycete pathogen Anisolpidium ectocarpii

Acknowledgements: We thank Gillian Milne (Aberdeen Microscopy Facility) for her support in TEM preparations, and Martina Strittmatter, Cecilia Rad‐Menendez and Marie‐Mathilde Perrineau (CCAP/SAMS) for contributing with some algal/pathogen strains. PM was funded by Conicyt (Becas Chile no. 72130422) for PhD studies at the University of Aberdeen. CMMG and PM were funded by the NERC IOF Pump priming (scheme NE/L013223/1), the UKRI GCRF grant BB/P027806/1 and the H2020 project GENIALG (contract no. 727892). ME was funded by the Austrian Science Fund (FWF), grant Y801‐B16. Funding Information: Conicyt. Grant Number: 72130422 NERC. Grant Number: NE/L013223/1 UKRI GCRF. Grant Number: BB/P027806/1 H2020 project GENIALG. Grant Number: 727892 Austrian Science Fund. Grant Number: Y801‐B16Peer reviewedPublisher PD

Overwintering of <i>Spodoptera frugiperda</i> (Smith) (Lep.: Noctuidae) in the Tucuman province corn area (Argentina)

Spodoptera frugiperda (Smith) (Lepidoptera: Noctuidae), "el cogollero del maíz (Zea mays L.)", es una plaga ampliamente distribuida en América que puede sobrevivir durante todo el año en áreas tropicales y, a medida que las condiciones ambientales se lo permiten, coloniza zonas subtropicales no infestadas. Debido a la falta de información sobre la actividad invernal del cogollero en el noroeste argentino y considerando la localización geográfica de Tucumán (Argentina), se planificaron estudios con trampas de feromonas para determinar la presencia de la plaga en el área maicera de la provincia durante los meses fríos (julio-setiembre) de 2001 y 2002. Asimismo, se realizaron monitoreos durante la época de cultivo para calcular el porcentaje de ataque de la plaga. Se comprobó la actividad de adultos del cogollero durante los meses más fríos del año, con marcadas diferencias poblacionales entre las dos temporadas estudiadas, estimándose que estas se debieron a la acción de un factor climático, mayormente por las temperaturas mínimas y ocurrencia de heladas durante mayo y junio. El porcentaje de ataque por la plaga en los cultivos, no tendría relación con el número de adultos capturados en los meses invernales previos. Estos resultados preliminares sugieren que la zona de estudio se encuentra en el límite austral de distribución permanente de la plaga, por lo cual se propone la realización de estudios más exhaustivos para tener un acabado conocimiento de estos aspectos de comportamiento.Spodoptera frugiperda (Smith) (Lepidoptera: Noctuidae), “fall armyworm (FAW)”, is an important pest widely distributed in America that survives year round in tropical areas. When climactic conditions are favorable, FAW populat ions colonize subt ropical (not infested) areas. Because of the lack information about FAW overwintering in Northwestern Argentinean Region, and considering the geographical location of Tucumán (Argentina), performed studies to determine the presence of FAW in the Tucumán maize (Zea mays L.) crops area using pheromone traps during cold months (JulySeptember) of 2001 and 2002 were tested. Furthermore, during the crop-growing season, sampled for FAW to calculate the attack percentage were realized. The FAW adult activity during the cold months was confirmed, recording important population differences among the two sampling periods. We estimated that the differences were caused by climatic factors, such as minimum temperature and frost occurrence during May and June. The pest attack percentages calculated in the summer have no relation with the number of moths collected during the previous coldest months. The data gathered suggest that the study area belongs to the austral limit of the pest’s distribution, and further studies to elucidate the overwintering behavior of FAW in the region were suggested.Facultad de Ciencias Agrarias y Forestale

An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications

We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series Z = \log(\e^X \e^Y) in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when $X$ and $Y$ are real or complex matrices.Comment: 30 page