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

Mouse tracking to explore motor inhibition processes in go/no-go and stop signal tasks

Response inhibition relies on both proactive and reactive mechanisms that exert a synergic control on goal-directed actions. It is typically evaluated by the go/no-go (GNG) and the stop signal task (SST) with response recording based on the key-press method. However, the analysis of discrete variables (i.e., present or absent responses) registered by key-press could be insufficient to capture dynamic aspects of inhibitory control. Trying to overcome this limitation, in the present study we used a mouse tracking procedure to characterize movement profiles related to proactive and reactive inhibition. A total of fifty-three participants performed a cued GNG and an SST. The cued GNG mainly involves proactive control whereas the reactive component is mainly engaged in the SST. We evaluated the velocity profile from mouse trajectories both for responses obtained in the Go conditions and for inhibitory failures. Movements were classified as one-shot when no corrections were observed. Multi-peaked velocity profiles were classified as non-one-shot. A higher proportion of one-shot movements was found in the SST compared to the cued GNG when subjects failed to inhibit responses. This result suggests that proactive control may be responsible for unsmooth profiles in inhibition failures, supporting a differentiation between these tasks

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 time-scale 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.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulations developed by Chirikov is applied to the Nesvorn\'{y}-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid system). In particular, we investigate the diffusion \emph{along} and \emph{across} the separatrices of the (5,-2,-2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to $10^{8}$ years.Comment: 27 pages, 6 figure

Phytochemical constituents, antioxidant activity, and toxicity assessment of the aerial part extracts from the infraspecific taxa of Matthiola fruticulosa (Brassicaceae) endemic to Sicily

In a project designed to investigate the specific and infraspecific taxa of Matthiola endemic to Sicily (Italy) as new potential sources of bioactive compounds in this work, the infraspecific taxa of Matthiola fruticulosa were studied, namely, subsp. fruticulosa and subsp. coronopifolia. HPLC-PDA/ESI-MS and SPME-GC/MS analyses of hydroalcoholic extracts obtained from the aerial parts of the two subspecies led to the detection of 51 phenolics and 61 volatile components, highlighting a quite different qualitative-quantitative profile. The antioxidant properties of the extracts were explored through in vitro methods: 1,1-diphenyl-2-picrylhydrazyl (DPPH), reducing power and Fe2+ chelating activity assays. The results of the antioxidant tests showed that the extracts possess a different antioxidant ability: Particularly, the extract of M. fruticulosa subsp. fruticulosa exhibited higher radical scavenging activity than that of subsp. coronopifolia (IC50 = 1.25 ± 0.02 mg/mL and 2.86 ± 0.05 mg/mL), which in turn displayed better chelating properties (IC50 = 1.49 ± 0.01 mg/mL and 0.63 ± 0.01 mg/mL). Lastly, Artemia salina lethality bioassay was performed for toxicity assessment. The results of the bioassay showed lack of toxicity against brine shrimp larvae for both extracts. The data presented indicate the infraspecific taxa of M. fruticulosa as new and safe sources of antioxidant compounds

On the relevance of chaos for halo stars in the solar neighbourhood II

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time

On the relevance of chaos for halo stars in the solar neighbourhood II

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time

Models of cuspy triaxial stellar systems. I. Stability and chaoticity

We used the N-body code of Hernquist and Ostriker (1992) to build a dozen cuspy ({\gamma}\approx 1) triaxial models of stellar systems through dissipationless collapses of initially spherical distributions of 10^6 particles. We chose four sets of initial conditions that resulted in models morphologically resembling E2, E3, E4 and E5 galaxies, respectively. Within each set, three different seed numbers were selected for the random number generator used to create the initial conditions, so that the three models of each set are statistically equivalent. We checked the stability of our models using the values of their central densities and of their moments of inertia, which turned out to be very constant indeed. The changes of those values were all less than 3 per cent over one Hubble time and, moreover, we show that the most likely cause of those changes are relaxation effects in the numerical code. We computed the six Lyapunov exponents of nearly 5,000 orbits in each model in order to recognize regular, partially and fully chaotic orbits. All the models turned out to be highly chaotic, with less than 25 per cent of their orbits being regular. We conclude that it is quite possible to obtain cuspy triaxial stellar models that contain large fractions of chaotic orbits and are highly stable. The difficulty to build such models with the method of Schwarzschild (1979) should be attributed to the method itself and not to physical causes.Comment: 10 pages, 5 figures, published in MNRAS (The definitive version is available at www.blackwell-synergy.com

A possible activity cycle in Proxima Centauri

Several late-type stars present activity cycles resembling the Solar one. This fact has been observed mostly in stars ranging from F to K, i.e., in stars with a radiative core and an outer convective layer. This work aims at studying whether an activity cycle can be detected in the dM5.5e star Proxima Centauri, which is supposed to be completely convective. We present periodical medium-resolution echelle observations covering the complete visual range, which were taken at the CASLEO Argentinean Observatory. These observations are distributed over 7 years. We discarded the spectra that present flare activity, and analyze the remaining activity levels using four different statistical techniques to look for a period of activity. We find strong evidence of a cyclic activity, with a period of around 442 days. We also estimate that the Ca II S index varies around 130% due to activity variations outside of flares.Comment: 7 pages, including 8 figures and 2 table