Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page

Will ultrathin CIGS solar cells overtake the champion thin-film cells? Updated SCAPS baseline models reveal main differences between ultrathin and standard CIGS

Cu(In,Ga)Se2 (CIGS) solar cells are amongst the best performing thin-film technologies, with the latest performance gains being mainly due to recent years improvements obtained with post-deposition treatments (PDT). Moreover, thinning of the absorber layer down to sub-micrometre values (ultrathin absorbers) is of extreme importance for CIGS to be even more cost-effective and sustainable. However, electrical and optical limitations, such as rear interface recombination and insufficient light absorption, prevent the widespread implementation of ultrathin CIGS devices. The recent electrical CIGS simulation baseline models have failed to keep up with the experimental developments. Here an updated and experimentally based baseline model for electrical simulations in the Solar Cell Capacitor Simulator (SCAPS) software is presented and discussed with the incorporation of the PDT effects and increased optical accuracy with the support from Finite-Difference Time-Domain (FDTD) simulation results. Furthermore, a champion solar cell with an equivalent architecture validates the developed thin-film model. The baseline model is also applied to ultrathin CIGS solar cell devices, validated with the ultrathin champion cell. Ultimately, these ultrathin models pave the way for an ultrathin baseline model. Simulations results reveal that addressing these absorbers' inherent limitations makes it possible to achieve an ultrathin solar cell with at least 21.0% power conversion efficiency, with open-circuit voltage values even higher than the recent thin-film champion cells.This work was supported by the Fundação para a Ciência e Tecno-logia (FCT) grant numbers DFA/BD/7073/2020, DFA/BD/4564/2020, SFRH/BD/146776/2019, IF/00133/2015, UIDB/50025/2020, UIDP/50025/2020, UIDB/04730/2020, and UIDP/04730/2020. The authors want to acknowledge the funding from the project NovaCell (PTDC/ CTM-CTM/28075/2017). The authors also acknowledge the financial support of the project Baterias 2030, with the reference POCI-01-0247-FEDER-046109, co-funded by Operational Programme for Competitiveness and Internationalization (COMPETE 2020), under the Portugal 2020 Partnership Agreement, through the European Regional Development Fund (ERDFinfo:eu-repo/semantics/submittedVersio

Geostatistical characterization of the spatial distribution of Xylella fastidiosa sharpshooter vectors on citrus

A distribuição espacial das espécies de cigarrinhas (Dilobopterus costalimai Young, Acrogonia sp. e Oncometopia facialis Signoret), vetoras da Xylella fastidiosa, agente causal da Clorose Variegada dos Citros, foi estudada com o uso da geoestatística. As avaliações foram feitas em um pomar comercial de laranja 'Pêra' (Citrus sinensis [L.] Osb.), objetivando estabelecer meios para melhor controle dos vetores e da doença. O monitoramento da ocorrência das cigarrinhas no pomar foi feito através de amostragens mensais, utilizando-se armadilhas adesivas amarelas de 3 x 5, distribuídas uniformemente em 50 pontos na área, dispostas em laranjeiras à altura de 1,5 m do solo e substituídas mensalmente. Acrogonia sp. foi a espécie prevalente nas amostragens. Os resultados possibilitaram ajustar modelos aos semivariogramas da distribuição espacial das três espécies no pomar estudado. Durante os três anos consecutivos de amostragem, as populações de Acrogonia sp., D. costalimai e O. facialis apresentaram modelos de distribuição agregada somente nos meses de verão, inverno e primavera, respectivamente, mostrando a necessidade de monitoramento constante desses vetores para reduzir a sua população em épocas favoráveis ao seu desenvolvimento. Através de parâmetros geoestatísticos foi possível calcular a área de agregação das cigarrinhas no pomar. A espécie Acrogonia sp. apresentou área média de agregação de 15.760 m², enquanto para O. facialis e D. costalimai foi possível constatar áreas médias de agregação de 11.555 m² e 10.980 m², respectivamente. Esses resultados indicaram que para um levantamento seguro de cigarrinhas é necessário pelo menos dispor de uma armadilha por hectare.The spatial distribution of the three principal species of sharpshooter (Dilobopterus costalimai Young, Acrogonia sp. e Oncometopia facialis Signoret), vectors of Xylella fastidiosa causal agent of Citrus Variegated Chlorosis, was studied by using geostatistics. The evaluations were carried out in a commercial 'Pera' sweet orange (Citrus sinensis [L.] Osb.) grove budded on Rangpur lime (Citrus limonia Osb.) located at Bebedouro, São Paulo state, aiming to establish better means for vector and disease control. The sharpshooters were monitored using with 50 uniformly distributed 3 x 5 yellow sticky traps hanging down in branches at 1.5 m up to the ground, which were replaced monthly. Acrogonia sp. was the prevalent species sampled. The results were used to adjust population models to semivariograms of the spatial distribution of the three sharpshooters species in the grove. During the three consecutive years of sampling, the population of Acrogonia sp., D. costalimai and O. facialis showed an aggregated distribution only during summer, winter and spring, respectively, showing that intensive monitoring of these vectors is necessary to control their population in periods favorable to their development. The aggregation area of the sharpshooters within the orange grove was determined using geostatistic parameters. Acrogonia sp. showed a mean aggregation area of 15,760 m², whereas for O. facialis and D. costalimai, the corresponding areas were 11,555 m² and 10,980 m², respectively. Therefore, in order to obtain a reliable estimate of sharpshooter populations, at least one trap should be used per hectare