Antioxidant activity of flavonols

In this work we use a single new electronic index to describe the antioxidant activity of the flavonols, a special class of flavonoids. We also try to predict theoretically the antioxidant activity of some yet nonisolated flavonols. © 2003 Wiley Periodicals, Inc.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Plasma confinement in tokamaks with robust torus

We present a non-linear symplectic map that describes the alterations of the magnetic field lines inside the tokamak plasma due to the presence of a robust torus (RT) at the plasma edge. This RT prevents the magnetic field lines from reaching the tokamak wall and reduces, in its vicinity, the islands and invariant curve destruction due to resonant perturbations. The map describes the equilibrium magnetic field lines perturbed by resonances created by ergodic magnetic limiters (EMLs). We present the results obtained for twist and non-twist mappings derived for monotonic and non-monotonic plasma current density radial profiles, respectively. Our results indicate that the RT implementation would decrease the field line transport at the tokamak plasma edge. © 2010 Elsevier B.V. All rights reserved.

Locating invariant tori for a family of two-dimensional Hamiltonian mappings

The location of invariant tori for a two-dimensional Hamiltonian mapping exhibiting mixed phase space is discussed. The phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori. Given the mapping considered is parameterised by an exponent γ in one of the dynamical variables, a connection with the standard mapping near a transition from local to global chaos is used to estimate the position of the invariant tori limiting the size of the chaotic sea for different values of the parameter γ. © 2011 Elsevier B.V. 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.

A rescaling of the phase space for Hamiltonian map: Applications on the Kepler map and mappings with diverging angles in the limit of vanishing action

A rescale of the phase space for a family of two-dimensional, nonlinear Hamiltonian mappings was made by using the location of the first invariant Kolmogorov-Arnold-Moser (KAM) curve. Average properties of the phase space are shown to be scaling invariant and with different scaling times. Specific values of the control parameters are used to recover the Kepler map and the mapping that describes a particle in a wave packet for the relativistic motion. The phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant KAM curves whose position of the first of them depends on the control parameters. The transition from local to global chaos is used to estimate the position of the first invariant KAM curve, leading us to confirm that the chaotic sea is scaling invariant. The different scaling times are shown to be dependent on the initial conditions. The universality classes for the Kepler map and mappings with diverging angles in the limit of vanishing action are defined. © 2013 Published by Elsevier Inc. All rights reserved.

Equação de Fokker-Planck, supersimetria e enovelamento de proteína

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

Estudo de sistemas quânticos não-hermitianos com espectro real

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo clássico completo do formalismo de Hamilton-Jacobi

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

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

Conservation laws for Z(N) symmetric quantum spin models and their exact ground state energies

We derive an infinite set of conserved charges for some Z(N) symmetric quantum spin models by constructing their Lax pairs. These models correspond to the Potts model, Ashkin-Teller model and the particular set of self-dual Z(N) models solved by Fateev and Zamolodchikov [6]. The exact ground state energy for this last family of hamiltonians is also presented. © 1986.

Renormalization-group calculation of dynamical properties for impurity models

The numerical renormalization-group method was originally developed to calculate the thermodynamical properties of impurity Hamiltonians. A recently proposed generalization capable of computing dynamical properties is discussed. As illustrative applications, essentially exact results for the impurity specttral densities of the spin-degenerate Anderson model and of a model for electronic tunneling between two centers in a metal are presented. © 1991.

Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians. (C) 2012 Elsevier B.V. All rights reserved.

Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

Schrodinger and Dirac operators with the Aharonov-Bohm and magnetic-solenoid fields

We construct all self-adjoint Schrodinger and Dirac operators (Hamiltonians) with both the pure Aharonov-Bohm (AB) field and the so-called magnetic-solenoid field (a collinear superposition of the AB field and a constant magnetic field). We perform a spectral analysis for these operators, which includes finding spectra and spectral decompositions, or inversion formulae. In constructing the Hamiltonians and performing their spectral analysis, we follow, respectively, the von Neumann theory of self-adjoint extensions of symmetric operators and the Krein method of guiding functionals.