Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

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

Comments on a nonlinear and nonideal electromechanical damping vibration absorber, Sommerfeld effect and energy transfer

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

On energy transfer between vibrating systems under linear and nonlinear interactions

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

On energy transfer phenomena, in a nonlinear ideal and nonideal essential vibrating systems, coupled to a (MR) magneto-rheological damper

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

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

Energy gain induced by boundary crisis

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

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

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

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Follicular dynamics and production of oocytes in young Nellore heifers with energetic supplementation

To verify the effects of energy supplementation and fat on follicular dynamics, metabolic profile and the production of oocytes, 15 young heifers (Bos taurus indicus) with an average age of 14 months and with an initial weight of 256.35 kg were assigned to two treatments according to weight and follicular population as evaluated by ultrasonography: in T1 (1.0 × M), animals received 100% of the energy requirements for maintenance; in T2 (1.7 × M), animals received 170% of the energy requirements for maintenance, achieved by the addition of 200 g of Megalac®. After a period of adaptation to the diet, the treatments, blood collection and follicular aspirations were started using a randomized design. The dry matter intake and weight gain were lower in the 1.0 × M group than in the 1.7 × M group. No differences were found in the plasma progesterone concentrations, albumin, glucose, urea or gonadotropin (FSH and LH) levels between the groups. The mean concentrations of cholesterol were higher in the 1.7 × M group. The total number of small (<4 mm) and medium follicles (4-8 mm) was not altered by the treatments, but the number of small follicles increased on days 1 and 2 of the estrous cycle, with higher values found in the 1.7 × M group. The average of the oocytes also increased (9.50±2.1 and 12.5±4.4 for the 1.0 × M and 1.7 × M groups, respectively). The rapid increase in the amount of energy offered in the diet changes the amount of follicles and oocytes available for follicular aspiration (OPU) in young heifers without changing their metabolic profile.

Thermally activated dynamics in La2CuO4+delta: tilts of the CuO6 octahedra and interstitial O

An intense peak of the elastic energy loss versus temperature is found in La2CuO4 at 150 K (in the LTO phase), at a vibration frequency of similar to 280 Hz. From the dependence of the dissipation curve on frequency it is deduced that the relaxation rate has an activation enthalpy of 0.23 eV. The peak is ascribed to a thermally activated dynamics of the tilts of the CuO6 octahedra which form the La2CuO4 lattice, a fraction of which are supposed to be able to switch between energetically equivalent configurations. The peak is suppressed by interstitial O; this is explained by supposing that each interstitial atom can block several octahedra into a configuration that can accommodate the distortion due to its presence. Increasing the content of excess O, two new thermally activated processes develop, attributed to the hopping of interstitial O atoms which are isolated and which are paired or otherwise aggregated. The activation enthalpy for the diffusion of O at low values of 6 is 0.48 eV.

Energy localization in the Phi(4) oscillator chain

We study energy localization in a finite one-dimensional Phi(4) oscillator chain with initial energy in a single oscillator of the chain. We numerically calculate the effective number of degrees of freedom sharing the energy on the lattice as a function of time. We find that for energies smaller than a critical value, energy equipartition among the oscillators is reached in a relatively short time. on the other hand, above the critical energy, a decreasing number of particles sharing the energy is observed. We give an estimate of the effective number of degrees of freedom as a function of the energy. Our results suggest that localization is due to the appearance, above threshold, of a breather-like structure. Analytic arguments are given, based on the averaging theory and the analysis of a discrete nonlinear Schrodinger equation approximating the dynamics, to support and explain the numerical results.

Energy localization in the Peyrard-Bishop DNA model

We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup on a long time scale. We use a localization criterion based on the information entropy and verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter (mu>2.25) (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is mu=6.3). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.