A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

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

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent 1 is observed. (C) 2011 Elsevier B.V. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

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

Instability zones for satellites of asteroids: The example of the (87) Sylvia system

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 chaotic behavior of a fixed offshore structure

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

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. 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 were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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]

Temperature-dependent vortex motion in a square mesoscopic superconducting cylinder: Ginzburg-Landau calculations

In this work we investigate the dynamics of vortices in a square mesoscopic superconductor. As time evolves we show how the vortices are nucleated into the sample to form a multivortex, single vortex, and giant vortex states. We illustrate how the vortices move around at the transition fields before they accommodate into an equilibrium configuration. We also calculate the magnetization and the free energy as functions of the applied magnetic field for several values of temperature. In addition, we evaluate the upper critical field.

Intra-articular pressure profiles of the cadaveric equine fetlock joint in motion

The study of the influence of motion and initial intra-articular pressure (IAP) on intra-articular pressure profiles in equine cadaver metatarsophalangeal (MTP) joints was undertaken as a prelude to in vivo studies, Eleven equine cadaver MTP joints were submitted to 2 motion frequencies of 5 and 10 cycles/min of flexion and extension, simulating the condition of lower and higher (double) rates of passive motion. These frequencies were applied and pressure profiles generated with initial normal intra-articular pressure (-5 mmHg) and subsequently 30 mmHg intra-articular pressure obtained by injection of previously harvested synovial fluid.The 4 trials performed were 1) normal IAP; 5 cyles/min; 2) normal IAP; 10 cycles/min; 3) IAP at 30 mmHg; 5 cycles/min and 4) IAP at 30 mmHg; 10 cycles/min. The range of joint motion applied (mean +/- s.e.) was 67.6 +/- 1.61 degrees with an excursion from 12.2 +/- 1.2 degrees in extension to 56.2 +/- 2.6 degrees in flexion, Mean pressure recorded in mmHg for the first and last min of each trial, respectively, were 1) -5.7 +/- 0.9 and -6.3 +/- 1.1; 2) -5.3 +/- 1.1 and -6.2 +/- 1.1; 3) 58.8 +/- 8.0 and 42.3 +/- 7.2; 4) 56.6 +/- 3.7 and 40.3 +/- 4.6. Statistical analyses showed a trend for difference between the values for the first and last minute in trial 3 (0.05>P<0.1) with P = 0.1 and significant difference (P = 0.02) between the mean IAP of the first and last min in trial 4. The loss of intra-articular pressure associated with time and motion was 10.5, 16.9, 28.1 and 28.9% for trials 1-4, respectively. As initial intraarticular pressure and motion increased, the percent loss of intra-articular pressure increased.The angle of lowest pressure was 12.2 +/- 1.2 (mean +/- s.e.) in extension in trials 1 and 2, In trials 3 and 4, the lowest pressures were obtained in flexion with the joints at 18.5 +/- 2.0 degrees (mean +/- s.e.). This demonstrated that the joint angle of least pressure changed as the initial intra-articular pressure changed and there would not be a single angle of least pressure for a given joint.The volume of synovial fluid recovered from the MTP joints in trial 3 compared to 4 (trials in which fluid was injected to attain IAP of 30 mmHg) was not significantly different, supporting a soft tissue compliance change as a cause for the significant loss of intra-articular pressure during the 15 min of trial 4.The pressure profiles generated correlate well with in vivo values and demonstrated consistent pressure profiles. Our conclusions are summarised as follows:1. Clinically normal equine MTP joints which were frozen and then later thawed were found to have mostly negative baseline intra-articular pressures, as would be expected in living subjects,2. Alternate pressure profiles of the dorsal and plantar pouch at baseline intra-articular pressure document the presence of pressure forces that would support 'back and forth' fluid movement between joint compartments. This should result in movement of joint fluid during motion, assisting in lubrication and nutrition of articular cartilage,3. If joint pressure was initially greater than normal (30 mmHg), as occurs in diseased equine MTP joints, joint motion further increased joint capsule relaxation (compliance) and, therefore, reduced intra-articular pressure.4. Peak intra-articular pressures reached extremely high values (often >100 mmHg) in flexion when initial pressure was 30 mmHg. Joint effusion pressures recorded for clinical MCP joints are frequently 30 mmHg. These IAP values are expected to produce intermittent synovial ischaemia in clinical cases during joint flexion.5, Additional in vivo studies are necessary to confirm our conclusions from this study and to identify the contributions of fluid absorption and the presence of ischaemia in a vascularised joint.

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).