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

Multi-objective heuristics applied to robot task planning for inspection plants

Robotics are generally subject to stringent operational conditions that impose a high degree of criticality on the allocation of resources and the schedule of operations in mission planning. In this regard the so-called cost of a mission must be considered as an additional criterion when designing optimal task schedules within the mission at hand. Such a cost can be conceived as the impact of the mission on the robotic resources themselves, which range from the consumption of battery to other negative effects such as mechanic erosion. This manuscript focuses on this issue by presenting experimental results obtained over realistic scenarios of two heuristic solvers (MOHS and NSGA-II) aimed at efficiently scheduling tasks in robotic swarms that collaborate together to accomplish a mission. The heuristic techniques resort to a Random-Keys encoding strategy to represent the allocation of robots to tasks whereas the relative execution order of such tasks within the schedule of certain robots is computed based on the Traveling Salesman Problem (TSP). Experimental results in three different deployment scenarios reveal the goodness of the proposed technique based on the Multi-objective Harmony Search algorithm (MOHS) in terms of Hypervolume (HV) and Coverage Rate (CR) performance indicators

Using a Bayesian modelling approach (INLA‑SPDE) to predict the occurrence of the Spinetail Devil Ray (Mobular mobular)

To protect the most vulnerable marine species it is essential to have an understanding of their spatiotemporal distributions. In recent decades, Bayesian statistics have been successfully used to quantify uncertainty surrounding identified areas of interest for bycatch species. However, conventional simulation-based approaches are often computationally intensive. To address this issue, in this study, an alternative Bayesian approach (Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation, INLA-SPDE) is used to predict the occurrence of Mobula mobular species in the eastern Pacific Ocean (EPO). Specifically, a Generalized Additive Model is implemented to analyze data from the Inter-American Tropical Tuna Commission’s (IATTC) tropical tuna purse-seine fishery observer bycatch database (2005–2015). The INLA-SPDE approach had the potential to predict both the areas of importance in the EPO, that are already known for this species, and the more marginal hotspots, such as the Gulf of California and the Equatorial area which are not identified using other habitat models. Some drawbacks were identified with the INLA-SPDE database, including the difficulties of dealing with categorical variables and triangulating effectively to analyze spatial data. Despite these challenges, we conclude that INLA approach method is an useful complementary and/or alternative approach to traditional ones when modeling bycatch data to inform accurately management decisions.En prensa2,92