9 research outputs found
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, , 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 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
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