Transient times, resonances and drifts of attractors in dissipative rotational dynamics

In a dissipative system the time to reach an attractor is often influenced by the peculiarities of the model and in particular by the strength of the dissipation. In particular, as a dissipative model we consider the spin-orbit problem providing the dynamics of a triaxial satellite orbiting around a central planet and affected by tidal torques. The model is ruled by the oblateness parameter of the satellite, the orbital eccentricity, the dissipative parameter and the drift term. We devise a method which provides a reliable indication on the transient time which is needed to reach an attractor in the spin-orbit model; the method is based on an analytical result, precisely a suitable normal form construction. This method provides also information about the frequency of motion. A variant of such normal form used to parametrize invariant attractors provides a specific formula for the drift parameter, which in turn yields a constraint - which might be of interest in astronomical problems - between the oblateness of the satellite and its orbital eccentricity.Comment: 21 pages, 7 figures, colo

Second order perturbation theory for spin-orbit resonances

We implement Lie transform perturbation theory to second order for the planar spin-orbit problem. The perturbation parameter is the asphericity of the body, with the orbital eccentricity entering as an additional parameter. We study first and second order resonances for different values of these parameters. For nearly spherical bodies like Mercury and the Moon first order perturbation theory is adequate, whereas for highly aspherical bodies like Hyperion the spin is mostly chaotic and perturbation theory is of limited use. However, in between, we identify a parameter range where second order perturbation theory is useful and where as yet unidentified objects may be in second order resonances.Comment: To appear in A

Effective stability of the Trojan asteroids

We study the spatial circular restricted problem of three bodies in the light of Nekhoroshev theory of stability over large time intervals. We consider in particular the Sun-Jupiter model and the Trojan asteroids in the neighborhood of the Lagrangian point $L_4$. We find a region of effective stability around the point $L_4$ such that if the initial point of an orbit is inside this region the orbit is confined in a slightly larger neighborhood of the equilibrium (in phase space) for a very long time interval. By combining analytical methods and numerical approximations we are able to prove that stability over the age of the universe is guaranteed on a realistic region, big enough to include one real asteroid. By comparing this result with the one obtained for the planar problem we see that the regions of stability in the two cases are of the same magnitude.Comment: 9 pages, 2 figures, Astronomy & Astrophysics in pres

Promoting post-stroke recovery through focal or whole body vibration: criticisms and prospects from a narrative review

Objective: Several focal muscle vibration (fMV) and whole body vibration (WBV) protocols have been designed to promote brain reorganization processes in patients with stroke. However, whether fMV and WBV should be considered helpful tools to promote post-stroke recovery remains still largely unclear. Methods: We here achieve a comprehensive review of the application of fMV and WBV to promote brain reorganization processes in patients with stroke. By first discussing the putative physiological basis of fMV and WBV and then examining previous observations achieved in recent randomized controlled trials (RCT) in patients with stroke, we critically discuss possible strength and limitations of the currently available data. Results: We provide the first systematic assessment of fMV studies demonstrating some improvement in upper and lower limb functions, in patients with chronic stroke. We also confirm and expand previous considerations about the rather limited rationale for the application of current WBV protocols in patients with chronic stroke. Conclusion: Based on available information, we propose new recommendations for optimal stimulation parameters and strategies for recruitment of specific stroke populations that would more likely benefit from future fMV or WBV application, in terms of speed and amount of post-stroke functional recovery

Persistence of Diophantine flows for quadratic nearly-integrable Hamiltonians under slowly decaying aperiodic time dependence

The aim of this paper is to prove a Kolmogorov-type result for a nearly-integrable Hamiltonian, quadratic in the actions, with an aperiodic time dependence. The existence of a torus with a prefixed Diophantine frequency is shown in the forced system, provided that the perturbation is real-analytic and (exponentially) decaying with time. The advantage consists of the possibility to choose an arbitrarily small decaying coefficient, consistently with the perturbation size.Comment: Several corrections in the proof with respect to the previous version. Main statement unchange

Evolution and stability of Laplace-like resonances under tidal dissipation

AbstractThe Laplace resonance is a configuration that involves the commensurability between the mean motions of three small bodies revolving around a massive central one. This resonance was first observed in the case of the three inner Galilean satellites, Io, Europa, and Ganymede. In this work the Laplace resonance is generalised by considering a system of three satellites orbiting a planet that are involved in mean motion resonances. These Laplace-like resonances are classified in three categories: first-order (2:1&2:1, 3:2&3:2, 2:1&3:2), second-order (3:1&3:1) and mixed-order resonances (2:1&3:1). In order to study the dynamics of the system we implement a model that includes the gravitational interaction with the central body, the mutual gravitational interactions of the satellites, the effects due to the oblateness of the central body and the secular interaction of a fourth satellite and a distant star. Along with these contributions we include the tidal interaction between the central body and the innermost satellite. We study the survival of the Laplace-like resonances and the evolution of the orbital elements of the satellites under the tidal effects. Moreover, we study the possibility of capture into resonance of the fourth satellite

Early and late follow-up of untreated traumatic aortic lesion: a support to delayed surgery

Fuente Fuente, Carlos;Montes Gil, Antonio;Periel Piquer, Montserra

Short-term effects of focal muscle vibration on motor recovery after acute stroke: a pilot randomized sham-controlled study

Repetitive focal muscle vibration (rMV) is known to promote neural plasticity and long-lasting motor recovery in chronic stroke patients. Those structural and functional changes within the motor network underlying motor recovery occur in the very first hours after stroke. Nonetheless, to our knowledge, no rMV-based studies have been carried out in acute stroke patients so far, and the clinical benefit of rMV in this phase of stroke is yet to be determined. The aim of this randomized double-blind sham-controlled study is to investigate the short-term effect of rMV on motor recovery in acute stroke patients. Out of 22 acute stroke patients, 10 were treated with the rMV (vibration group–VG), while 12 underwent the sham treatment (control group–CG). Both treatments were carried out for 3 consecutive days, starting within 72 h of stroke onset; each daily session consisted of three 10-min treatments (for each treated limb), interspersed with a 1-min interval. rMV was delivered using a specific device (Cro®System, NEMOCO srl, Italy). The transducer was applied perpendicular to the target muscle's belly, near its distal tendon insertion, generating a 0.2–0.5 mm peak-to-peak sinusoidal displacement at a frequency of 100 Hz. All participants also underwent a daily standard rehabilitation program. The study protocol underwent local ethics committee approval (ClinicalTrial.gov NCT03697525) and written informed consent was obtained from all of the participants. With regard to the different pre-treatment clinical statuses, VG patients showed significant clinical improvement with respect to CG-treated patients among the NIHSS (p < 0.001), Fugl-Meyer (p = 0.001), and Motricity Index (p < 0.001) scores. In addition, when the upper and lower limb scales scores were compared between the two groups, VG patients were found to have a better clinical improvement at all the clinical end points. This study provides the first evidence that rMV is able to improve the motor outcome in a cohort of acute stroke patients, regardless of the pretreatment clinical status. Being a safe and well-tolerated intervention, which is easy to perform at the bedside, rMV may represent a valid complementary non-pharmacological therapy to promote motor recovery in acute stroke patients