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 formulation developed by Chirikov is applied to the NesvornA1/2-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and 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.

Controle de dinâmica caótica com toros robustos

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Circular, elliptic and oval billiards in a gravitational field

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Scaling invariance of the diffusion coefficient in a family of two-dimensional Hamiltonian mappings

We consider a family of two-dimensional nonlinear area-preserving mappings that generalize the Chirikov standard map and model a variety of periodically forced systems. The action variable diffuses in increments whose phase is controlled by a negative power of the action and hence effectively uncorrelated for small actions, leading to a chaotic sea in phase space. For larger values of the action the phase space is mixed and contains a family of elliptic islands centered on periodic orbits and invariant Kolmogorov-Arnold-Moser (KAM) curves. The transport of particles along the phase space is considered by starting an ensemble of particles with a very low action and letting them evolve in the phase until they reach a certain height h. For chaotic orbits below the periodic islands, the survival probability for the particles to reach h is characterized by an exponential function, well modeled by the solution of the diffusion equation. On the other hand, when h reaches the position of periodic islands, the diffusion slows markedly. We show that the diffusion coefficient is scaling invariant with respect to the control parameter of the mapping when h reaches the position of the lowest KAM island. © 2013 American Physical Society.

Diffusion-Weighted MRI Helps Predict Outcome in Basilar Artery Occlusion Patients Treated with Intra-Arterial Thrombolysis

Intra-arterial thrombolysis (IAT) can improve clinical outcome in patients with acute basilar artery occlusion (BAO). The purpose of this study was to determine whether the severity of neurological symptoms, the extent of early ischemic damage on pretreatment diffusion-weighted MRI (DWI), and the lesion progression or regression on post-treatment MRI can predict functional outcome in patients with BAO treated with IAT.

Younger Stroke Patients With Large Pretreatment Diffusion-Weighted Imaging Lesions May Benefit From Endovascular Treatment.

BACKGROUND AND PURPOSE Lesion volume on diffusion-weighted magnetic resonance imaging (DWI) before acute stroke therapy is a predictor of outcome. Therefore, patients with large volumes are often excluded from therapy. The aim of this study was to analyze the impact of endovascular treatment in patients with large DWI lesion volumes (>70 mL). METHODS Three hundred seventy-two patients with middle cerebral or internal carotid artery occlusions examined with magnetic resonance imaging before treatment since 2004 were included. Baseline data and 3 months outcome were recorded prospectively. DWI lesion volumes were measured semiautomatically. RESULTS One hundred five patients had lesions >70 mL. Overall, the volume of DWI lesions was an independent predictor of unfavorable outcome, survival, and symptomatic intracerebral hemorrhage (P<0.001 each). In patients with DWI lesions >70 mL, 11 of 31 (35.5%) reached favorable outcome (modified Rankin scale score, 0-2) after thrombolysis in cerebral infarction 2b-3 reperfusion in contrast to 3 of 35 (8.6%) after thrombolysis in cerebral infarction 0-2a reperfusion (P=0.014). Reperfusion success, patient age, and DWI lesion volume were independent predictors of outcome in patients with DWI lesions >70 mL. Thirteen of 66 (19.7%) patients with lesions >70 mL had symptomatic intracerebral hemorrhage with a trend for reduced risk with avoidance of thrombolytic agents. CONCLUSIONS There was a growing risk for poor outcome and symptomatic intracerebral hemorrhage with increasing pretreatment DWI lesion volumes. Nevertheless, favorable outcome was achieved in every third patient with DWI lesions >70 mL after successful endovascular reperfusion, whereas after poor or failed reperfusion, outcome was favorable in only every 12th patient. Therefore, endovascular treatment might be considered in patients with large DWI lesions, especially in younger patients.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.