Revisiting high-order Taylor methods for astrodynamics and celestial mechanics

We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution of ordinary differential equations. Detailed numerical tests focused on difficult high-precision gravitational problems in astrodynamics and celestial mechanics show how our general-purpose integrator is competitive with and often superior to state-of-the-art specialised symplectic and non-symplectic integrators in both speed and accuracy. In particular, we show how Taylor methods are capable of satisfying Brouwer’s law for the conservation of energy in long-term integrations of planetary systems over billions of dynamical timescales. We also show how close encounters are modelled accurately during simulations of the formation of the Kirkwood gaps and of Apophis’ 2029 close encounter with the Earth (where heyoka surpasses the speed and accuracy of domain-specific methods). heyoka can be used from both C++ and Python, and it is publicly available as an open-source project.

Evapotranspiration Model-based Scheduling Strategy for Baby Pakchoi Irrigation in Greenhouse

Water management is one of the most important operations in greenhouse baby leaf production. However, growers mainly irrigate the plants based on experience, which generally leads to yield loss, uneven quality, and low water-use efficiency. This study evaluated four evapotranspiration (ET) models, such as Radsum, Penman methods, FAO Penman-Monteith, and Priestley-Taylor, for irrigation strategy by predicting the ET level of greenhouse baby pakchoi [Brassica rapa L. ssp. chinensis (L.) Hanelt] under different plant densities (72-, 128-, 200-, and 288-plug tray). Among environmental factors, net radiation and photosynthetically active radiation (PAR) had the highest correlation with ET, with R2 of 0.93 and 0.94, respectively. Plant growth period was divided into different stages according to canopy development and substrate surface coverage. The corresponding crop coefficient (Kc) was introduced into ET prediction models. The result shows overestimation of ETc (crop evapotranspiration) by the Radsum and Penman methods. FAO Penman-Monteith and Priestley-Taylor methods performed the best with R2 ≈0.7 for all planting densities. These two methods are recommended for greenhouse irrigation scheduling in baby pakchoi production.