Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple self-propelled particle (SPP) model of collective motion. In our SPP model, a focal individual can interact with k randomly chosen neighbours within an interaction radius. We consider k = 1 (called stochastic pairwise interactions), k = 2 (stochastic ternary interactions), and k equalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). The data-driven mesoscopic equations reveal that the stochastic pairwise interaction model produces a novel form of collective motion driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, yield collective motion driven primarily by the deterministic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasizes the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies

An?lisis de la participaci?n renovable en el SEIN considerando los aspectos de competitividad, seguridad y sostenibilidad

Esta tesis brinda un orden y metodolog?a para desarrollar las pautas de la pol?tica energ?tica nacional y aprovechar eficientemente los recursos naturales tomando en consideraci?n la afectaci?n m?nima hacia los usuarios finales, preservando las condiciones de seguridad y el cuidado al medio ambiente, todo ello a un m?nimo costo. Esta metodolog?a servir? para delimitar el mix ?ptimo de generaci?n en el SEIN considerando los aspectos de sostenibilidad, seguridad y competitividad al 2040, aspectos analizados por el WEF en su informe ?Fostering Effective Energy Transition?, el cual sirve de referencia para visualizar los avances en materia energ?tica de cada pa?s. De esta manera, frente a la inminente inserci?n de energ?as renovables no convencionales, se busca conocer c?mo estas impactaran al SEIN; como en materia econ?mica, es el desplazamiento en el despacho el?ctrico de las centrales convencionales por tecnolog?as como la solar o e?lica; en materia de seguridad del sistema es la disminuci?n de inercia y aumento de intermitencia; y por ?ltimo, en materia de sostenibilidad ambiental, es determinar si realmente estas causan gran reducci?n de emisiones de CO2, ya que el mix de generaci?n actual es uno de los m?s limpios en la regi?n

50 Years of Quantum Chromodynamics

International audienceThis paper presents a comprehensive review of both the theory and experimental successes of Quantum Chromodynamics, starting with its emergence as a well defined theory in 1972-73 and following developments and results up to the present day. Topics include a review of the earliest theoretical and experimental foundations; the fundamental constants of QCD; an introductory discussion of lattice QCD, the only known method for obtaining exact predictions from QCD; methods for approximating QCD, with special focus on effective field theories; QCD under extreme conditions; measurements and predictions of meson and baryon states; a special discussion of the structure of the nucleon; techniques for study of QCD at high energy, including treatment of jets and showers; measurements at colliders; weak decays and quark mixing; and a section on the future, which discusses new experimental facilities or upgrades currently funded. The paper is intended to provide a broad background for Ph.D. students and postdocs starting their career. Some contributions include personal accounts of how the ideas or experiments were developed