Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. (C) 2010 Elsevier B.V. All rights reserved.

Fermi acceleration with memory-dependent excitation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

Velocity-dependent KAM islands

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

Suppressing Fermi acceleration in two-dimensional driven billiards

We consider a dissipative oval-like shaped billiard with a periodically moving boundary. The dissipation considered is proportional to a power of the velocity V of the particle. The three specific types of power laws used are: (i) F proportional to-V; (ii) F proportional to-V-2 and (iii) F proportional to-V-delta with 1 < delta < 2. In the course of the dynamics of the particle, if a large initial velocity is considered, case (i) shows that the decay of the particle's velocity is a linear function of the number of collisions with the boundary. For case (ii), an exponential decay is observed, and for 1 < delta < 2, an powerlike decay is observed. Scaling laws were used to characterize a phase transition from limited to unlimited energy gain for cases (ii) and (iii). The critical exponents obtained for the phase transition in the case (ii) are the same as those obtained for the dissipative bouncer model. Therefore near this phase transition, these two rather different models belong to the same class of universality. For all types of dissipation, the results obtained allow us to conclude that suppression of the unlimited energy growth is indeed observed.

Energy gain induced by boundary crisis

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

Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime. (C) 2011 American Institute of Physics. [doi:10.1063/1.3657917]

Parameter space for a dissipative Fermi-Ulam model

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)

Charge injection in an LED with a hybrid composite as the emissive layer

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

Potassium niobate thin films prepared through polymeric precursor method

Thin films of potassium niobate were deposited on (100) Si substrates by the polymeric precursor method (Pechini method). Annealing in static air was performed at 600degrees C for 20 h. The obtained films were characterized by X-ray diffraction and atomic force microscopy (AFM). Electrical characterization of the films pointed to ferroelectricity via hysteresis loop. The dielectric constant, dissipation factor and resistance were measured in frequency region from 10 Hz to 10 MHz. At 1 MHz, the dielectric constant was 158 and the dissipation factor was 0.11. (C) 2004 Elsevier B.V. All rights reserved.

LiNbO3 thin films prepared through polymeric precursor method

Thin films of lithium niobate were deposited on (100) silicon by the polymeric precursor method (Pechini method). Annealing in static air was performed at 500degreesC for 3 h. The films obtained were characterized by X-ray diffraction, scanning electron microscopy and transmission electron microscopy. Electrical characterization of the films pointed to ferroelectricity via hysteresis loop. The dielectric constant, dissipation factor and resistance were measured in the frequency region from 10 Hz to 10 MHz. At 1 MHz, the dielectric constant was 46 and the dissipation factor was 0.043. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Ferroelectric characteristics of SrBi4Ti4O15 thin films grown on Pt/Ti/SiO2/Si substrates by the soft chemical method

Ferroelectric SrBi4Ti4O15 thin films were successfully prepared on a Pt(111)/Ti/SiO2/Si(100) substrate for the first time by spin coating, using the polymeric precursor method. X-ray diffraction patterns of the films indicate that they are polycrystalline in nature. Atomic force microscopy (AFM) analyses showed that the surface of these films is smooth, dense and crack-free with low surface roughness (6.4 nm). At room temperature and at a frequency of 1 MHz, the dielectric constant and the dissipation factor were, respectively, 150 and 0.022. The C-V characteristics of perovskite thin film prepared at low temperature show normal ferrolectric behaviour. The remanent polarization and coercive field for the films deposited were 5.4 mu C/cm(2) and 8 5 kV/cm, respectively. All the capacitors showed good polarization fatigue characteristics at least up to 1 x 10(10) bipolar pulse cycles indicating that SrBi4Ti4O15 thin films can be a promising material for use in nonvolatile memories. (c) 2005 Elsevier B.V. All rights reserved.