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]

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.

Relaxation and tunnelling of structural units within the LTO phase of La2CuO4

The anelastic relaxation (elastic energy loss and Young modulus) of nearly stoichiometric La2CuO4+delta with LTO structure was measured. Extraordinarily intense effects are present below room temperature in the elastic dynamic susceptibility, indicating relaxational dynamics of a relevant fraction of the lattice. The involved degrees of freedom are identified as rotations of the CuO6 octahedra. Two distinct processes are found at frequencies around 1 kKz: one is observed around 150 K and is characterized by a mean activation energy of 2800 K; the second one occurs below 30 K and is governed by atomic tunnelling. Two explanations are proposed for the faster process: i) formation of fluctuating LTT domains on a scale of few atomic cells; ii) the LTO phase is a dynamical Jahn-Teller phase with all the octahedra tunneling between two LTT-like tilts. In both cases there would be important implications regarding the mechanisms giving rise to charge nanophase separation and strong electron-phonon coupling.

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated. © 1995.

Follicular dynamics in Mangalarga mares.

Ovarian follicular activity was studied by ultrasonography during 17 oestrous cycles in 9 Mangalarga mares during the second half of the ovulatory season. Sixteen oestrous cycles were considered normal and one 3-wave cycle showing a prolonged luteal phase was considered atypical. Daily ultrasonographic examinations were performed and the compiled data on follicular dynamics were studied retrospectively. One major wave of follicular growth was observed in 13 of the 16 normal cycles (81.25%), whereas 2 major waves occurred in 3 cycles (18.75%). The mean (+/- s.d.) days of emergence of the primary wave of follicular development in cycles containing one or 2 waves were Day 6.0 +/- 2.3 and Day 11.0 +/- 1.0, respectively. The secondary wave of follicular development in 2-wave cycles emerged on Day 0.0 +/- 3.6. The day of wave divergence for primary waves of follicular development in cycles which exhibited one or 2 major waves were Day 12.2 +/- 3.5 and Day 17.3 +/- 3.0, respectively. Divergence of secondary waves occurred in only one of the 3 cycles which exhibited 2 major follicular waves (Day 7). The mean (+/- s.d.) maximum diameters of the dominant follicle in the primary wave of oestrous cycles exhibiting one and 2 major waves were 39.0 +/- 3.9 mm and 34.7 +/- 2.5 mm, respectively. The mean (+/- s.d.) maximum diameter of the dominant follicle present in the secondary wave was 34.3 +/- 11.0 mm. The mean (+/- s.d.) lengths of the interovulatory intervals for cycles containing one and 2 major waves were 19.4 +/- 2.2 and 23.3 +/- 2.5 days, respectively. These data indicate that most Mangalarga mares show one major follicular wave during the oestrous cycle but a small percentage of mares show 2 major waves.

Smooth landscape solvent dynamics in electron transfer reactions

Solvent effects play a major role in controlling electron-transfer reactions. The solvent dynamics happens on a very high-dimensional surface, and this complex landscape is populated by a large number of minima. A critical problem is to understand the conditions under which the solvent dynamics can be represented by a single collective reaction coordinate. When this unidimensional representation is valid, one recovers the successful Marcus theory. In this study the approach used in a previous work [V. B. P. Leite and J. N. Onuchic; J. Phys. Chem. 100, 7680 (1996)] is extended to treat a more realistic solvent model, which includes energy correlation. The dynamics takes place in a smooth and well behaved landscape. The single shell of solvent molecules around a cavity is described by a two-dimensional system with periodic boundary conditions with nearest neighbor interaction. It is shown how the polarization-dependent effects can be inferred. The existence of phase transitions depends on a factor y proportional to the contribution from the two parameters of the model. For the present model, γ suggests the existence of weak kinetic phase transitions, which are used in the analysis of solvent effects in charge-transfer reactions. © 1999 American Institute of Physics.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

A contribution for nonlinear structural dynamics characterization of cantilever beams

Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.

Dynamics of change of mathematics education in Brazil and a scenario of current research

Mathematics education in Brazil, if we consider what one may call the scientific phase, is about 30 years old. The papers for this special issue focus mainly on this period. During these years, many trends have emerged in mathematics education to address the complex problems facing Brazilian society. However, most Brazilian mathematics educators feel that the separation of research into trends is a theoretical idealization that does not respond to the dynamics of the problems we face. We raise the conjecture that the complexity of Brazilian society, where pockets of wealth coexist with the most shocking poverty, has contributed to the adoption and generation of different strands in mathematics education, crossing the boundaries between trends. At a more micro level, we also raise the conjecture that Brazilian trends in research are interwoven because of the way that Brazilian mathematics educators have experienced the process of globalization over these 30 years. This tapestry of trends is a predominant characteristic of mathematics education in Brazil. © FIZ Karlsruhe 2009.

Single-phase current-source-boost inverter for renewable energy sources

This paper presents a new methodology for the operation and control of a single-phase current-source (CS) Boost Inverter, considering that the conventional CS boost inverter has a right-half-plane (RHP) zero in its control-to-output transfer function, and this RHP zero causes the known non-minimum-phase effects. In this context, a special design with low boost inductance and a multi-loop control is developed in order to assure stable and very fast dynamics. Furthermore, the proposed inverter presents output voltage with very low total harmonic distortion (THD), reduced components and high power density. Therefore, this paper presents the inverter operation, the proposed control technique, the main simulation results and a prototype in order to demonstrate the feasibility of the proposal. © 2011 IEEE.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Dynamics of foraging and recruitment behavior in the Asian subterranean termite Coptotermes gestroi (Rhinotermitidae)

The present study investigated the trail-following behavior of the subterranean termite Coptotermes gestroi (Wasmann Rhinotermitidae) under laboratory conditions. The results showed that workers were the first to initiate the exploration to the food source. When food was discovered they returned to the nest laying a trail for recruiting nestmates to the food source. In this situation, workers always traveled significantly faster when returning from the arenas. Both workers and soldiers were recruited to the food source; however, the soldier/worker proportion was higher during the first phase of the recruitment. When no food was available, the number of recruited nestmates and the speed on their way back to the nest were significantly lower. The results also showed that scout foragers always laid trail pheromones when entering into unknown territories, and that chemical signals found in the food could induce workers of C. gestroi to increase their travel speed. Copyright © 2012 Alberto Arab et al.

Nonlinear dynamics of a flexible portal frame under support excitation

This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams. © 2012 American Institute of Physics.

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

Electrocatalytic activity under oscillatory regime: The electro-oxidation of formic acid on ordered Pt3Sn intermetallic phase

Despite the considerable progress in the understanding of the mechanistic aspects of the oscillatory electro-oxidation of C1 molecules, there are apparently no systematic studies concerning the impact of surface modifiers on the oscillation dynamics. Herein we communicate on the oscillatory electro-oxidation of formic acid on ordered Pt3Sn intermetallic phase, and compare the results with those obtained on a polycrystalline platinum electrode. Overall, the obtained results were very reproducible, robust and allowed a detailed analysis on the correlation between the catalytic activity and the oscillation dynamics. The presence of Sn in the intermetallic electrode promotes drastic effects on the oscillatory dynamics. The decrease in the mean electrode potential and in the oscillation frequency, as well as the pronounced increase in the number oscillations (and also in the oscillation time), was discussed in connection with the substantial catalytic enhancement of the Pt3Sn towards the electro-oxidation of formic acid. The self-organized potential oscillations were used to probe the electrocatalytic activity of the Pt3Sn electrode and compare it with that for polycrystalline Pt. The presence of Sn resulted in a significant decrease (2-11 times, depending on the applied current) of the rate of surface poisoning. © 2012 Elsevier B.V.