Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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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.

Feasibility And Reproducibility Of Diffusion-weighted Magnetic Resonance Imaging Of The Fetal Brain In Twin-twin Transfusion Syndrome.

The aim of this study is to test the feasibility and reproducibility of diffusion-weighted magnetic resonance imaging (DW-MRI) evaluations of the fetal brains in cases of twin-twin transfusion syndrome (TTTS). From May 2011 to June 2012, 24 patients with severe TTTS underwent MRI scans for evaluation of the fetal brains. Datasets were analyzed offline on axial DW images and apparent diffusion coefficient (ADC) maps by two radiologists. The subjective evaluation was described as the absence or presence of water diffusion restriction. The objective evaluation was performed by the placement of 20-mm(2) circular regions of interest on the DW image and ADC maps. Subjective interobserver agreement was assessed by the kappa correlation coefficient. Objective intraobserver and interobserver agreements were assessed by proportionate Bland-Altman tests. Seventy-four DW-MRI scans were performed. Sixty of them (81.1%) were considered to be of good quality. Agreement between the radiologists was 100% for the absence or presence of diffusion restriction of water. For both intraobserver and interobserver agreement of ADC measurements, proportionate Bland-Altman tests showed average percentage differences of less than 1.5% and 95% CI of less than 18% for all sites evaluated. Our data demonstrate that DW-MRI evaluation of the fetal brain in TTTS is feasible and reproducible.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Reaction-diffusion stochastic lattice model for a predator-prey system

We have the purpose of analyzing the effect of explicit diffusion processes in a predator-prey stochastic lattice model. More precisely we wish to investigate the possible effects due to diffusion upon the thresholds of coexistence of species, i. e., the possible changes in the transition between the active state and the absorbing state devoid of predators. To accomplish this task we have performed time dependent simulations and dynamic mean-field approximations. Our results indicate that the diffusive process can enhance the species coexistence.

Evaluation of the diffusion capacity of calcium hydroxide pastes through the dentinal tubules

This study aimed to evaluate the diffusion capacity of calcium hydroxide pastes with different vehicles through dentinal tubules. The study was conducted on 60 extracted single-rooted human teeth whose crowns had been removed. The root canals were instrumented and divided into 4 groups according to the vehicle of the calcium hydroxide paste: Group I - distilled water; Group II - propylene glycol; Group III - 0.2% chlorhexidine; Group IV - 2% chlorhexidine. After placement of the root canal dressings, the teeth were sealed and placed in flasks containing deionized water. After 1, 2, 7, 15, 30, 45 and 60 days, the pH of the water was measured to determine the diffusion of calcium hydroxide through the dentinal tubules. The data were recorded and statistically compared by the Tukey test. The results showed that all pastes presented a similar diffusion capacity through dentin. Group IV did not present difference compared to group I. Group II presented difference compared to the other groups, as did Group III. In conclusion, groups I and IV presented a better diffusion capacity through dentin than groups II and III; 2% chlorhexidine can be used as a vehicle in calcium hydroxide pastes.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Artificial Lighting as a Vector Attractant and Cause of Disease Diffusion

BACKGROUND: Traditionally, epidemiologists have considered electrification to be a positive factor. In fact, electrification and plumbing are typical initiatives that represent the integration of an isolated population into modern society, ensuring the control of pathogens and promoting public health. Nonetheless, electrification is always accompanied by night lighting that attracts insect vectors and changes people's behavior. Although this may lead to new modes of infection and increased transmission of insect-borne diseases, epidemiologists rarely consider the role of night lighting in their surveys. OBJECTIVE: We reviewed the epidemiological evidence concerning the role of lighting in the spread of vector-borne diseases to encourage other researchers to consider it in future studies. DISCUSSION: We present three infectious vector-borne diseases-Chagas, leishmaniasis, and malaria-and discuss evidence that suggests that the use of artificial lighting results in behavioral changes among human populations and changes in the prevalence of vector species and in the modes of transmission. CONCLUSION: Despite a surprising lack of studies, existing evidence supports our hypothesis that artificial lighting leads to a higher risk of infection from vector-borne diseases. We believe that this is related not only to the simple attraction of traditional vectors to light sources but also to changes in the behavior of both humans and insects that result in new modes of disease transmission. Considering the ongoing expansion of night lighting in developing countries, additional research on this subject is urgently needed.

Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]