Characterization of a 10-MHz quadrant APD for measuring frequency oscillations and tip displacements of microcantilevers

The room-temperature response of a 10-MHz quadrant avalanche photodiode (APD) is investigated for detection of high frequency oscillations and tip displacements of fabricated microcantilevers. Currently, no quadrant detectors with a response bandwidth in the megahertz range are available, and oscillations on the order of a few microseconds cannot be resolved. A comparison is made between optical and opto-mechanical measurements to characterize this detector by investigating the frequency response and signal-to-noise (SNR) of pulsed laser signals up to 10?MHz and reflected laser signals from freely vibrating microcantilevers up to 1.64?MHz. The power level of the minimum detectable signal incident on the APD is found to be 28.2?±?5.0?nW for optical measurements and 1.0???W?±?5.0?nW for opto-mechanical measurements.     

Theory of oscillations in average crisis-induced transient lifetimes

Analytical and numerical study of the roughly periodic oscillations emerging on the background of the well-known power law governing the scaling of the average lifetimes of crisis induced chaotic transients is presented. The explicit formula giving the amplitude of "normal" oscillations in terms of the eigenvalues of unstable orbits involved in the crisis is obtained using a simple geometrical model. We also discuss the commonly encountered situation when normal oscillations appear together with "anomalous" ones caused by the fractal structure of basins of attraction.     

Chaotic oscillations in a coupled system of bistable oscillators

The influence of the asymmetry of the nonlinear element characteristic on the chaotic oscillations of Chua’s bistable oscillator is studied. It is shown that such asymmetry causes asymmetry of a chaotic attractor that maps the switching of motions between two basins of attraction up to the concentration of oscillations in one basin. Oscillation control in a bistable chaotic self-oscillating system (two coupled Chua’s oscillators) is considered. It is demonstrated that oscillations excited in two basins of attraction may pass to one of them and that oscillations may build up in two basins when they are autonomously excited in different basins. It is also found that chaotic oscillations in a coupled system may be excited at parameter values for which the autonomous chaotic oscillations of partial oscillators are absent. The influence of external noiselike oscillations is investigated.     

Quantitative characterization of chaotic instabilities in semiconductors

A method for quantitative characterization of chaotic dynamical systems is discussed. An electronic instrument for determining the number of independent variablesk ^*, involved in the motion, is described. It allows one to obtain these in real time from a single observable. The suggested technique has been applied to quantification of strange attractors underlying chaotic instabilities in semi-insulating GaAsCr, and n-Ge, irradiated with high energy electrons. In n-Ge, for instance, the measured numbersk ^* range from 2 to 4 depending on control parameters. These measurements reveal the highly deterministic nature of the observed chaotic oscillations. The physical mechanisms responsible for the current instabilities and chaotic behaviour are discussed.     

Fano fingerprints of Majoranas in Kitaev dimers of superconducting adatoms

We investigate theoretically a Fano interferometer composed by STM and AFM tips close to a Kitaev dimer of superconducting adatoms, in which the adatom placed under the AFM tip, encloses a pair of Majorana fermions (MFs). For the binding energy Δ of the Cooper pair delocalized into the adatoms under the tips coincident with the tunneling amplitude t between them, namely Δ=t, we find that only one MF beneath the AFM tip hybridizes with the adatom coupled to the STM tips. As a result, a gate invariance feature emerges: the Fano profile of the transmittance rises as an invariant quantity depending upon the STM tips Fermi energy, due to the symmetric swap in the gate potential of the AFM tip.     

Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure

Opto-mechanical chaotic oscillation of an on-chip resonator is excited by the radiation-pressure nonlinearity. Continuous optical input, with no external feedback or modulation, excites chaotic vibrations in very different geometries of the cavity (both tori and spheres) and shows that opto-mechanical chaotic oscillations are an intrinsic property of optical microcavities. Measured phenomena include period doubling, a spectral continuum, aperiodic oscillations, and complex trajectories. The rate of exponential divergence from a perturbed initial condition (Lyapunov exponent) is calculated. Continuous improvements in cavities mean that such chaotic oscillations can be expected in the future with many other platforms, geometries, and frequency spans.     

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua??s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.     

Chaos generated by the cutting process

Due to nonlinearity and coupling forces chaotic oscillations take place in an elastic manufacturing machine. A transition from quasiperiodic via chaotic to synchronised anharmonic oscillations with increasing cutting intensity is demonstrated by spectral distributions and the correlation exponent.     

Nonstationary theory and simulation of the backward wave peniotron oscillator

The oscillations build-up process from raising until reaching steady-state in the backward wave peniotron oscillator (BWPO) are analased in the frame of the nonstationary nonlinear theory. By analytical and numerical calculations it is indicated that single-frequency and multi-frequency oscillations including chaotic ones can be generated by BWOP with high efficiency.     

Spike-burst synchronization in an ensemble of electrically coupled discrete model neurons

In this paper, we study the dynamics of a system of two model neurons interacting via the electrical synapse. Each neuron is described by a two-dimensional discontinuous map. A chaotic relaxational-type attractor, which corresponds to the spiking-bursting chaotic oscillations of neurons is shown to exist in a four-dimensional phase space. It is found that the dynamical mechanism of formation of chaotic bursts is based on a new phenomenon of generation of transient chaotic oscillations. It is demonstrated that transition from the chaotic-burst generation to the state of relative rest occurs with a certain time delay. A new characteristic which estimates the degree of synchronization of the spiking-bursting oscillations is introduced. The dependence of the synchronization degree on the strength of coupling of the ensemble elements is studied.     

Images of synchronized chaos: Experiments with circuits

Synchronization of oscillations underlies organized dynamical behavior of many physical, biological and other systems. Recent studies of the dynamics of coupled systems with complex behavior indicate that synchronization can occur not only in case of periodic oscillations, but also in regimes of chaotic oscillations. Using experimental observations of chaotic oscillations in coupled nonlinear circuits we discuss a few forms of cooperative behavior that are related to the regimes of synchronized chaos. This paper is prepared under the request of the editors of the special focus issue of Chaos and contains the materials for the lecture at the International School in Nonlinear Science, "Nonlinear Waves: Synchronization and Patterns," Nizhniy Novgorod, Russia, 1995. The main goal of the paper is to outline the collection of examples that illustrate the state of the art of chaos synchronization. (c) 1996 American Institute of Physics.     

Nonlinear nonstationary processes in a pair of coupled gyro-backward-wave oscillators

The nonlinear dynamics of a pair of unidirectionally coupled gyro-backward-wave oscillators is studied numerically. When the control parameters vary, both developed chaotic oscillations and steady single-frequency oscillations may arise in this pair. The ranges of parameters within which the pair of gyro-oscillators exhibits developed chaotic oscillations are found. Physical processes complicating chaotic processes in the active medium are considered.     

Conductance through atomic point contacts between fcc(100) electrodes of gold

Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E_F evolves from G ≈ 3G₀ to G ≈ 1G₀ (G₀ = 2e/h²). Formation of a true one-atom point contact, with G ≈ 1G₀ and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E_F, and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 ≤ E-E_F ≤ 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear “gold molecule" between the electrodes, and a weak coupling of this “molecule" to the tips.     

Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma

Glow discharge plasmas exhibit various types of self-excited oscillations for different initial conditions like discharge voltages and filling pressures. The behavior of such oscillations associated with the anode glow has been investigated using nonlinear techniques like correlation dimension, largest Lyapunov exponent, etc. It is seen that these oscillations go to an ordered state from a chaotic state with an increase in input energy, i.e., with discharge voltages implying occurrence of inverse bifurcations. These results are different from the other observations wherein the fluctuations have been observed to go from ordered to chaotic state.     

Complex oscillations and chaos in electrostatic microelectromechanical systems under superharmonic excitations

In this Letter, the formation of complex oscillations of the type 2n M oscillations per period at the Mth superharmonic excitation is reported for electrostatic microelectromechanical systems. A dc bias (beyond "dc symmetry breaking") and an ac signal (at the Mth superharmonic frequency) with an amplitude around "ac symmetry breaking" gives rise to M oscillations per period or period M response. On increasing the ac voltage, a cascade of period doubling bifurcations take place giving rise to 2n M oscillations per period. An interesting chaotic transition (1-band and 2-band chaos) is observed during the first period doubling bifurcation. The nonlinear nature of the electrostatic force is shown to be responsible for the reported observations.     

Temperature effects of GaAs/Al_(0.45)Ga_(0.55)As superlattices on chaotic oscillation

For widespectrum chaotic oscillation, superlattice cryptography is an autonomous controllable brand-new technology.Originating from sequential resonance tunneling of electrons, the chaotic oscillation is susceptible to temperature change,which determines the performance of superlattices. In this paper, the temperature effects of chaotic oscillations are investigated by analyzing the randomness of a sequence at different temperatures and explained with superlattice microstates.The results show that the bias voltage at different temperatures makes spontaneous chaotic oscillations vary. With the temperature of superlattices changing, the sequence dives in entropy value and randomness at specific bias. This work fills the gap in the study of temperature stability and promotes superlattice cryptography for practice.     

Micro-mechanical analysis of dynamic processes of nanomanipulation

In this study, atomic force microscope (AFM) tips are used as tools to cut and manipulate carbon nanotubes on various surfaces. The lateral forces acting on AFM tips during manipulation are also recorded and analyzed from the perspective of micro-mechanics. It is found that differences in surface conditions can lead to obvious increase in micro-friction between nanotube and substrate. And also due to rehybridization, carbon nanotubes present excellent resilience when undergoing different degrees of strain. Finally, carbon nanotubes can complexly deform from elastic stage to plastic stage before complete rupture.     

Chaos in the quantum double well oscillator: the Ehrenfest view revisited

We treat the double well quantum oscillator from the standpoint of the Ehrenfest equation but in a manner different from Pattanayak and Schieve. We show that for short times there can be chaotic motion due to quantum fluctuations, but over sufficiently long time there will be quantum noise induced oscillations between the two wells, thus providing an alternative approach to the quantum noise induced chaotic oscillations found recently by Bag and Ray.     

Micro-mechanical analysis of dynamic processes of nanomanipulation

In this study, atomic force microscope (AFM) tips are used as tools to cut and manipulate carbon nanotubes on various surfaces. The lateral forces acting on AFM tips during manipulation are also recorded and analyzed from the perspective of micro-mechanics. It is found that differences in surface conditions can lead to obvious increase in micro-friction between nanotube and substrate. And also due to rehybridization, carbon nanotubes present excellent resilience when undergoing different degrees of strain. Finally, carbon nanotubes can complexly deform from elastic stage to plastic stage before complete rupture.     

Laser decal transfer of freestanding microcantilevers and microbridges

Freestanding silver microcantilevers and microbridges were fabricated over trenches in Si substrates by the laser decal transfer process without the use of sacrificial layers or subsequent etch processes. Single laser pulses (355 nm, 30 ns FWHM) were used to directly transfer 200 nm thick silver nanopaste layers (5 ?m wide×25 ?m long) over prepatterned Si substrates with 15 ?m wide trenches. By adjusting the position of the laser spot over the substrate, it was possible to directly deposit freestanding microcantilevers 7 to 9 ?m in length or 15-?m long microbridges over the trenches. Subsequent oven curing at 250°C resulted in sintering of the Ag nanoparticles without greatly affecting the shape and form of the transfers. Laser vibrometry experiments yielded fundamental resonance frequencies in vacuum of ?1–2 MHz for the microcantilevers and ?3 MHz for the microbridges. The fitted Q-factors averaged 1500 for the microcantilevers and 1400 for the microbridges. Overall, the measured resonances of the microbridges deviated from theoretical predictions in a manner suggesting a tensile residual stress state.