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.

Scaling attractors in interacting teleparallel dark energy

It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found. Here we consider a model in which the non-minimal coupling is ruled by a dynamically changing coefficient α≡f,φ/(f)1/2, with f(φ) an arbitrary function of the scalar field φ. It is shown that in this case the existence of scaling attractors is possible, which means that the universe will eventually enter these scaling attractors, regardless of the initial conditions. As a consequence, the cosmological coincidence problem could be alleviated without fine-tunings. © 2013 IOP Publishing Ltd and Sissa Medialab srl.

Cortical representation of the horizon in V1 and peripheral scaling in mammals with lateral eyes

In the present investigation we mapped the primary visual area of the South American diurnal rodent, Dasyprocta aguti, by standardized electrophysiological mapping techniques. In particular, we performed a series of mapping experiments of the visual streak in the primary visual cortex. We found that the representation of the visual streak in V1 is greatly expanded, the nasal 10 degrees of the visual streak representation occupies ten times more cortical area than equivalent areas in the central or temporal representation. Comparison of these data with those on the density of ganglion cells in the retina at corresponding locations in the visual field reveal a significant mismatch between these two variables. The nasal representation is greatly expanded along the horizontal meridian in V1 as compared to the central and temporal regions whereas the density of ganglion cells decreases with progression along the visual streak from central region towards the nasal or temporal visual field. A review of the available data reveals that all lateral-eyed mammals exhibit a similar mismatch between the retinal and cortical representation of the visual field, and this mismatches is greater in those species with well defined visual streaks such as rabbit and agouti.

Temporal and Spatial Scaling of the Genetic Structure of a Vector-Borne Plant Pathogen

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monitoring scaling and dental calculus removal with an optical fluorescence system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Intraspecific scaling of arterial blood pressure in the Burmese python

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

Dynamical properties of a dissipative discontinuous map: A scaling investigation

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

Fractal scaling exponents of heart rate variability association with linear indices and Poincaré Plot

The literature indicated that the fractal analysis of heart rate variability (HRV) is related to the chaos theory. However, it is not clear if the both short and long-term fractal scaling exponents of HRV are reliable for short period analysis in women. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV. We evaluated 65 healthy women between 18 and 30 years old. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains, the geometric index were also analyzed (triangular indexRRtri, triangular interpolation of RR intervals-TINN and Poincaré plot-SD1, SD2 and SD1/SD2) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). No significant correlation was observed for alpha-2 exponent with all indices. There was significant correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu and ms2 ), LF/HF ratio, SD1 and SD1/SD2 ratio. Our data does not indicate the alpha-2 exponent to be used for 256 RR intervals and we support the alpha-1 exponent to be used for HRV analysis in this condition.

Trimer-Tetramer Interwoven States in the Scaling Limit

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

Scaling properties and universality in a ratchet system

Critical exponents that describe a transition from unlimited to limited diffusion for a ratchet system are obtained analytically and numerically. The system is described by a two dimensional nonlinear mapping with three relevant control parameters. Two of them control the non-linearity while the third one controls the intensity of the dissipation. Chaotic attractors appear in the phase space due to the dissipation and considering large non-linearity are characterised by the use of Lyapunov exponents. The critical exponents are used to overlap different curves of average momentum (dynamical variable) onto a single plot confirming a scale invariance. The formalism used is general and the procedure can be extended to different systems.

A microscopic analysis of the effects of root surface scaling with different power parameters of er,cr: YSGG laser

The aim of this study was to evaluate the effects of different power parameters of an Erbium, Cromium: Yttrium, Scandium, Gallium, Garnet laser (Er,Cr:YSGG laser) on the morphology, attachment of blood components (ABC), roughness, and wear on irradiated root surfaces. Sixty-five incisive bovine teeth were used in this study, 35 of which were used for the analysis of root surface morphology and ABC. The remaining 30 teeth were used for roughness and root wear analysis. The samples were randomly allocated into seven groups: G1: Er,Cr:YSGG laser, 0.5 W; G2: Er,Cr:YSGG laser, 1.0 W; G3: Er,Cr:YSGG laser, 1.5 W; G4: Er,Cr:YSGG laser, 2.0 W; G5: Er,Cr:YSGG laser, 2.5 W; G6: Er,Cr:YSGG laser, 3.0 W; G7: scaling and root planning (SRP) with manual curettes. The root surfaces irradiated by Er,Cr:YSGG at 1.0 W and scaling with manual curettes presented the highest degrees of ABC. The samples irradiated by the Er,Cr:YSGG laser were rougher than the samples treated by the manual curette, and increasing the laser power parameters caused more root wear and greater roughness on the root surface. The Er,Cr:YSGG laser is safe to use for periodontal treatment, but it is not appropriate to use irradiation greater than 1.0 W for this purpose. Microsc. Res. Tech. 78:529–535, 2015. © 2015 Wiley Periodicals, Inc.

The smear layer created by scaling and root planing is physiologically eliminated in a biphasic process

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Convergence towards asymptotic state in 1-D mappings: a scaling investigation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Vereda and Murundu wetlands and changes in Brazilian environmental laws: challenges to conservation

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