Stochastic approach to diffusion inside the chaotic layer of a resonance

We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus in the diffusion process in the action, $I$, of the FR, obtaining a semi--numerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case the numerically computed probability density function for the action $I$ is well interpolated by the solution of a Fokker-Planck (F-P) equation, whereas it presents a non--constant time delay respect to the concomitant F-P solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in Celestial Mechanics and Accelerator Physics.Comment: This is the author's version of a work that was submitted to Physical Review E (http://pre.aps.org

Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov's 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov's formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev's theorem. On the other hand, Chirikov's formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.Comment: 25 pages, 9 figures. NOTICE: this is the author's version of a work that was accepted for publication in Physica D. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publicatio

On the relevance of chaos for halo stars in the Solar Neighbourhood

We show that diffusion due to chaotic mixing in the Neighbourhood of the Sun may not be as relevant as previously suggested in erasing phase space signatures of past Galactic accretion events. For this purpose, we analyse Solar Neighbourhood-like volumes extracted from cosmological simulations that naturally account for chaotic orbital behaviour induced by the strongly triaxial and cuspy shape of the resulting dark matter haloes, among other factors. In the approximation of an analytical static triaxial model, our results show that a large fraction of stellar halo particles in such local volumes have chaos onset times (i.e., the timescale at which stars commonly associated with chaotic orbits will exhibit their chaotic behaviour) significantly larger than a Hubble time. Furthermore, particles that do present a chaotic behaviour within a Hubble time do not exhibit significant diffusion in phase space.Comment: 20 pages, 16 figures. Accepted for publication in MNRA

Testeo del "MEGNO": indicador rápido de la dinámica

Fil: Maffione, Nicolás P. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Giordano, Claudia.Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Cincotta, Pablo.Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.We extend a previous work (Maffione, Giordano & Cincotta, 2007) where the Lyapunov characteristic exponents and the Mean Exponential Growth factor of Nearby Orbits (MEGNO), introduced by Cincotta & Simó (2000), are compared. Some differences in their classifications appeared and one of the main possible causes of the discrepancy was discussed. Now, with the implementation of another technique closely related with the fast Lyapunov indicator (Froeschlé et al., 1997) and an analysis of the involved orbits’ neighborhoods, we understood the reasons for the discrepancy, reaching a detailed evaluation of the MEGNO efficiency.Extendemos un trabajo previo (Maffione, Giordano & Cincotta, 2007) donde se comparan los exponentes característicos de Lyapunov y el Mean Exponential Growth factor of Nearby Orbits (MEGNO), introducido por Cincotta & Simó (2000). Se observaron algunas diferencias en sus respectivas clasificaciones y se discutió una de las posibles causas de la discrepancia. Ahora, con la implementación de otra técnica estrechamente relacionada con el indicador rápido de Lyapunov (Froeschlé et al., 1997) y el análisis de los entornos de las órbitas involucradas, logramos entender el por qué de la discrepancia, obteniendo así una evaluación detallada del rendimiento del MEGNO

On the comparison of two different techniques for the study of chaos in galactic dynamics

Fil: Maffione, Nicolás P. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica de La Plata. CONICET; Argentina.Fil: Giordano, Claudia M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica de La Plata. CONICET; Argentina.Fil: Cincotta, Pablo M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaRealistic models in Galactic Dynamics seem to present a divided phase space (Giordano & Cincotta, 2004). Therefore, it is necessary to rely on efficient techniques to study the global dynamical behaviour in order to split as well as to identify the complex nature of the orbital structure. Herein we present some results of an exhaustive comparison between two of such techniques: the well–known Lyapunov characteristic exponents, and a rather new one, introduced by Cincotta & Simó (2000), the Mean Exponential Growth factor of Nearby Orbits (MEGNO).Los modelos realistas en Dinámica Galáctica parecen contar con un espacio de fases dividido (Giordano & Cincotta, 2004). Por lo tanto, es necesario disponer de técnicas eficientes para el estudio de la dinámica global, que separen e identifiquen la compleja naturaleza del movimiento orbital. En este trabajo se realizó una comparación exhaustiva entre dos de tales herramientas numéricas: una ya clásica, los exponentes característicos de Lyapunov, y otra más reciente, presentada por Cincotta & Simó (2000), el Mean Exponential Growth factor of Nearby Orbits (MEGNO)

La relevancia del caos en estrellas del halo local

Fil: Maffione, Nicolás P. Universidad Nacional de Río Negro. Sede Antina. Laboratorio de Procesamiento de Señales Aplicadas y Computación de Alto Rendimiento; Argentina.Fil: Gómez, Facundo A. Universidad de La Serena. Departamento de Física y Astronomía; Chile.Fil: Cincotta, Pablo M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Giordano, Claudia G. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. IALP-UNLP-CONICET; Argentina.Fil: Maffione, Nicolás P. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaWe show compelling numerical evidence that chaos is undoubtedly active in the local stellar halo, however, its effect might not be large enough to foster chaotic mixing processes that can erase crucial dynamical information to detect stellar streams that are necessary to rebuild the formation history of our galaxy. Therefore, the lack of positive identifications of such coherent substructures in the neighbourhood of the Sun seems to be given, at least at first order, to the lack of precision in the observations.Con el presente trabajo mostramos evidencia numérica que el caos, si bien indudablemente activo en el halo estelar local, no parece ser suficientemente abundante como para que los procesos de mezcla caótica puedan eliminar información dinámica esencial para la detección de corrientes estelares, necesarias para reconstruir la historia de formación de nuestra galaxia. Luego, la falta de identificaciones de estas subestructuras coherentes en la vecindad solar parece deberse, al menos a primer orden, a la falta de precisión en las observaciones

Mammal responses to global changes in human activity vary by trophic group and landscape

Wildlife must adapt to human presence to survive in the Anthropocene, so it is critical to understand species responses to humans in different contexts. We used camera trapping as a lens to view mammal responses to changes in human activity during the COVID-19 pandemic. Across 163 species sampled in 102 projects around the world, changes in the amount and timing of animal activity varied widely. Under higher human activity, mammals were less active in undeveloped areas but unexpectedly more active in developed areas while exhibiting greater nocturnality. Carnivores were most sensitive, showing the strongest decreases in activity and greatest increases in nocturnality. Wildlife managers must consider how habituation and uneven sensitivity across species may cause fundamental differences in human–wildlife interactions along gradients of human influence.Peer reviewe