C. P. Malta

Epileptic activity recognition in EEG recording

We apply Approximate Entropy (ApEn) algorithm in order to recognize epileptic activity in electroencephalogram recordings. ApEn is a recently developed statistical quantity for quantifying regularity and complexity. Our approach is illustrated regarding different types of epileptic activity. In all segments associated with epileptic activity analyzed here the complexity of the signal measured by ApEn drops abruptly. This fact can be useful for automatic recognition and detection of epileptic seizures.

Bifurcations of periodic trajectories in non-integrable Hamiltonian systems with two degrees of freedom: Numerical and analytical results

Numerical and analytical studies of the types of period n-upling bifurcations undergone by classsical periodic trajectories of non-intergrable Hamiltonians with two degrees of freedom are made. The Hamiltonians studied possess time reversal and reflexion symmetries and we found that these symmetries give rise to additional types of period n-upling bifurcations. The analytical study explains most of the numerically observed bifurcations.

Mechanical properties of amorphous nanosprings

Helical amorphous nanosprings have attracted particular interest due to their special mechanical properties. In this work we present a simple model, within the framework of the Kirchhoff rod model, for investigating the structural properties of nanosprings having asymmetric cross section. We have derived expressions that can be used to obtain the Youngs modulus and Poissons ratio of the nanospring material composite. We also address the importance of the presence of a catalyst in the growth process of amorphous nanosprings in terms of the stability of helical rods.

Classical aspects of the Pauli-Schrödinger equation

Abstract We derive a Pauli-Schrodinger type equation from the classical Liouville equation, for a neutral particle with arbitrary spin and magnetic dipole. Our derivation does not apply to a general classical phase-space distribution. Nevertheless, in certain particular cases we show that there is a correspondence between the classical equations and the Pauli-Schrodinger equation. Consequently, the results of the Stern-Gerlach, and also the Rabi type molecular beam experiments, can be interpreted classically, that is, in such a way that the particles have well-defined and continuous trajectory, and also continuous orientation of the spin vector. Theoretical and experimental implications of this conclusion are briefly commented.

Isochronous and period doubling bifurcations of periodic solutions of non-integrable Hamiltonian systems with reflexion symmetries

Abstract We analytically derive the possible types of isochronous and period doubling bifurcations undergone by periodic solutions of two degrees of freedom, non-integrable, Hamiltonian systems possessing reflexion and time-reversal symmetries. We find that one of the isochronous bifurcations numerically found in refs. [3] cannot exist. In the case of period-doubling we predict the existence of a type of bifurcation not found in refs. [2] and [3] but confirmed by further numerical investigation.

LYAPUNOV GRAPH FOR TWO-PARAMETERS MAP: APPLICATION TO THE CIRCLE MAP

In a Lyapunov graph the Lyapunov exponent, λ, is represented by a color in the parameter space. The color shade varies from black to white as λ goes from -∞ to 0. Some of the main aspects of the complex dynamics of the circle map (θn+1=θn+Ω+(1/2π)Ksin(2πθn)(mod 1)), can be obtained by analyzing its Lyapunov graph. For K>1 the map develops one maximum and one minimum and may exhibit bistability that corresponds to the intersection of topological structures (stability arms) in the Lyapunov graph. In the bistability region, there is a strong sensitivity to the initial condition. Using the fact that each of the coexisting stable solution is associated to one of the extrema of the map, we construct a function that allows to obtain the boundary separating the set of initial conditions converging to one stable solution, from the set of initial conditions converging to the other coexisting stable solution.

Elastic properties of nanowires

We present a model to study Young’s modulus and Poisson’s ratio of the composite material of amorphous nanowires. It is an extension of the model derived by two of us [da Fonseca and Galvao, Phys. Rev. Lett. 92, 175502 (2004)] to study the elastic properties of amorphous nanosprings. The model is based on twisting and tensioning a straight nanowire and we propose an experimental setup to obtain the elastic parameters of the nanowire. We used the Kirchhoff rod model to obtain the expressions for the elastic constants of the nanowire.

Nonlinear structures in electroencephalogram signals

We apply a nonlinear prediction algorithm to investigate the presence of nonlinear structure in electroencephalogram (EEG) recordings. The EEG signal could be modeled as a realization of a nonlinear model plus a residual noise (uncorrelated Gaussian noise). Using linear and nonlinear models we analyze the statistical nature of these residual noises in the case of epileptic patients and normal subjects. We found that the residual noise presents Gaussian distribution for epileptic patients if a nonlinear model is used whereas in the case of normal subjects the residual noise will exhibit a Gaussian distribution only if a linear model (autoregressive) is used. These results provide another evidence of the nonlinear character of the epileptic seizure recordings, while the normal EEG seems to be better described as linearly correlated noise.

Two important numbers in the Hénon-Heiles dynamics

Abstract We study the dynamics of a one parameter family of two degrees of freedom Hamiltonian systems that includes the Henon-Heiles system. We show that several dynamical properties of this family, like the existence of large stochastic regions in certain parts of the phase space, are related to two canonical invariants that can be explicitly computed. These two invariants characterize universality classes of two degrees of freedom Hamiltonian systems with orbits homoclinic (bi-asymptotic) to saddle-center equilibria (related to pairs of real and pure imaginary eigenvalues). Examples of systems that can be described by Hamiltonians in this universality class are the planar three-body system, charged particles in a magnetic dipole field (Stormer problem), buckled beams, some stationary plasma systems.

Resonant helical deformations in nonhomogeneous Kirchhoff filaments

We study the three-dimensional static configurations of nonhomogeneous Kirchhoff filaments with periodically varying Youngs modulus. We analyze the effects of the Youngs modulus frequency and amplitude of variation in terms of stroboscopic maps, and in the regular (non chaotic) spatial configurations of the filaments. Our analysis shows that the tridimensional conformations of long filaments may depend critically on the Youngs modulus frequency in case of resonance with other natural frequencies of the filament. As expected, far from resonance the shape of the solutions remain very close to that of the homogeneous case. In the case of biomolecules, although various other elements, besides sequence-dependent effects, combine to determine their conformation, our results show that sequence-dependent effects alone may have a significant influence on the shape of these molecules, including DNA.