Auto Resonance Research Articles

Detection of Fricatives in Continuous Speech Using Auto Resonance Networks

Detection of Fricatives in Continuous Speech Using Auto Resonance Networks

Humanoid Motion Control using Auto Resonance Neural Network

It has been proven difficult to control robots with many mechanical joints due to a variety of problems, including redundant configurations, non-linear displacement, dynamic user surroundings, etc. Iterative computations have been applied to address inverse kinematic problems of industrial robots with up to six Degrees of Freedom (DoF). With one to three degrees of freedom in each of more than hundred joints used by humans for locomotion, the complexity is unfathomable. Consequently, in humanoid structures, algorithmic and heuristic approaches have failed. Numerous research fields that were earlier thought to be challenging to solve with computers have seen interest piqued by recent advancements in artificial intelligence and machine learning. One such domain is humanoid motion. This paper presents a novel kind of Artificial Neural Network named as Auto Resonance Neural Network (ARN). ARN uses the pull-relax mechanism applied by biological systems to control musculoskeletal motion. A variety of functions can be employed to build the pull-relax model, contingent on variables such as range, necessary coverage, and tunability. When employing ARN for joint control, inverse kinematics or some other kind of repetitive solution is not required. Its application is not influenced by the DoF or joint count. The network can use the learning methods like reinforcement learning or supervised or unsupervised learning.

Tunability of auto resonance network

This paper proposes a new type of Artificial Neural Network called Auto-Resonance Network (ARN) derived from synergistic control of biological joints. The network can be tuned to any real valued input without any degradation of learning rate. Neuronal density of the network is low and grows at a linear or low order polynomial rate with input classification. Input coverage of the neuron can be tuned dynamically to match properties of input data. ARN can be used as a part of hierarchical structures to support deep learning applications.

Multidimensional topography sensing simulating an AFM

Atomic force microscopy (AFM) is used in the semiconductor industry for inspection and quality control. Frequency modulated AFM (FM-AFM) extracts surface topography by measuring the frequency shift created by the Van der Waals (VdW) interaction forces between the tip and the sample. To improve the measurement speed and address complex geometries emerging in industrial microchip constructions, several enhancements are introduced. While most FM-AFM devices operate in a single vibrating mode, this article proposes a method for multidimensional sensing using frequency modulation of 2 orthogonal vibration modes, simultaneously. The concept was tested on a large-scale experimental system, where VdW forces were replaced by magnetic forces, using a magnetic tip and ferromagnetic samples. To emulate the VdW forces accurately, the designed ratio between the base frequency and frequency shift was kept to mimic a Nano-scale AFM. By utilizing an Autoresonance (AR) control scheme for faster locking onto resonance and a curve fitting frequency estimation algorithm it is possible to sense the minute changes in frequency experienced by several modes, simultaneously. Experimental results employ 3D relevant topographies such as inclined surfaces, steep walls and trenches that were reconstructed experimentally with 4 (μm) resolution or better. Downscaling to typical AFM dimensions would theoretically yield sub-nanometer resolution.

Ladder climbing and autoresonant acceleration of the spherical plasma density wave

Ladder climbing (LC) and autoresonance (AR) of the spherical plasma density wave are studied for the first time. The governing equation of the perturbed spherical density wave in the energy level space based on a hydrodynamic model of the electron plasma is presented, and it is demonstrated that the quantum LC and classical AR transition can be achieved in the spherical plasma. The asymptotic thresholds of the LC and AR transition of the spherical plasma wave are obtained analytically and confirmed numerically. We find that the spherical wave energy is concentrated to the sphere center as the density wave climbs to the higher level, the spherical plasma behaves obvious compression character, and the perturbed density of the sphere center even can be amplified to 100 times larger of the initial perturbed density. Compared to the one-dimensional case, the energy spectrum of the spherical plasma wave shifts upward, and the energy level spacing of the spherical plasma wave is broadened. These result in the facts that the spherical plasma needs the larger driving strength to achieve the LC and AR, while the total perturbed density of the spherical plasma always is larger than that of the one-dimensional case.

Optimization of TE11/TE04 mode converters for the cold test of a 250 GHz CARM source

Electron Cyclotron Resonance Heating (ECRH) systems in future fusion devices, like the DEMO-nstration reactor, foresee an operational frequency in the range 230–280 GHz to match the plasma characteristics. Cyclotron Auto Resonance Masers (CARMs) could represent an alternative to gyrotrons as effective source of mm and sub-mm waves and the project of a 250 GHz, 0.5 MW CARM has been undertaken at ENEA. Mode converters from the TE10 in WR3 rectangular waveguide to the operational mode (TE53) are required to perform the RF cold test of Bragg reflectors and cavities. In this paper an improved and feasible structure for the TE11 to TE04 conversion, in oversized circular waveguides, using only two transitions with profile and radius optimized in order to obtain high efficiencies and sufficient bandwidth, has been designed and the simulation results are presented. The first transition is a TE11/TE01 serpentine mode converter in circular waveguide (efficiency of 95%) with average radius of 1.48 mm and an appropriate number of geometrical periods. The second one, a TE01/TE04 rippled wall mode converter with efficiency of 97%, consists of a single conversion section with an average radius of 3 mm and sixteen sinusoidal periods instead of three conversion sections (TE01/TE02, TE02/TE03, TE03/TE04) in cascade, thus reducing the complexity and the length of the full transition chain.

Autoresonance in a strongly nonlinear chain driven at one end

This work examines the emergence of autoresonance (AR) in a one-dimensional chain of strongly nonlinear oscillators subjected to a harmonic force with a slowly varying frequency applied at the end of the chain. The dynamics of the chain is studied assuming 1:1 (fundamental) resonance, when the response of each nonlinear oscillator has a dominant harmonic component with the frequency close to the frequency of the external excitation. Explicit asymptotic equations describing the amplitudes and the phases of the oscillations are derived. These equations demonstrate that, in contrast to the chain with a linear attachment, the strongly nonlinear chain can be entirely captured into resonance provided that its structural and excitation parameters exceed certain critical thresholds but the frequency detuning rate is small enough. It is shown that at large times the amplitudes of all oscillators captured into AR converge to a common monotonically growing quasisteady backbone curve. This implies asymptotic equipartition of energy between the oscillators under the condition of AR. Numerical simulations have been performed for two-, four-, and 12-particle arrays with fixed forcing and coupling parameters and different detuning rates. The obtained results demonstrate the existence of two intervals of the rate's values corresponding to AR and small-amplitude oscillations in the entire chain, respectively, and a narrow gap between these two intervals, wherein each oscillator may escape from resonance individually or in combination with neighboring particles. This implies a negligibly small interval of energy localization in a part of the chain adjacent to the source of energy compared to the interval of the emergence of AR in the entire chain.

Autoresonant excitation of Bose-Einstein condensates.

Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters P_{1,2,3} are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the P_{1,2,3} parameter space, the system may exhibit two very different evolutions, i.e., the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analyzed both in theory and simulations with the emphasis on the effect of the interaction parameter P_{3}. In particular, the transition thresholds on the driving parameter P_{1} and their width in P_{1} in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and deexcitation of the condensate.

Autoresonance Cooling of Ions in an Electrostatic Ion Beam Trap.

Autoresonance (AR) cooling of a bunch of ions oscillating inside an electrostatic ion beam trap is demonstrated for the first time. The relatively wide initial longitudinal velocity distribution is reduced by at least an order of magnitude using AR acceleration and ramping forces. The hot ions escaping the bunch are not lost from the system but continue to oscillate in the trap outside of the bunch and may be further cooled by successive AR processes. Ion-ion collisions inside the bunch close to the turning points in the trap's mirrors contribute to the thermalization of the ions. This cooling method can be applied to any mass and any charge.

Cyclotron auto resonance maser and free electron laser devices: a unified point of view

We take advantage of previous research in the field of cyclotron auto resonance maser (CARM) and undulator-based free electron laser (U-FEL) sources to establish a common formalism for the relevant description of the underlying physical mechanisms. This strategy is aimed at stressing the deep analogies between the two devices and at providing a practical tool for their study based on the use of well-tested scaling formulae developed independently for the two systems.

Autoresonance versus localization in weakly coupled oscillators

We study formation of autoresonance (AR) in a two-degree of freedom oscillator array including a nonlinear (Duffing) oscillator (the actuator) weakly coupled to a linear attachment. Two classes of systems are studied. In the first class of systems, a periodic force with constant (resonance) frequency is applied to a nonlinear oscillator (actuator) with slowly time-decreasing stiffness. In the systems of the second class a nonlinear time-invariant oscillator is subjected to an excitation with slowly increasing frequency. In both cases, the attached linear oscillator and linear coupling are time-invariant, and the system is initially engaged in resonance. This paper demonstrates that in the systems of the first type AR in the nonlinear actuator entails oscillations with growing amplitudes in the linear attachment while in the system of the second type energy transfer from the nonlinear actuator is insufficient to excite high-energy oscillations of the attachment. It is also shown that a slow change of stiffness may enhance the response of the actuator and make it sufficient to support oscillations with growing energy in the attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.

Asymptotic Analysis of Autoresonant Oscillator Chains

This paper investigates the emergence of autoresonance (AR) with growing energy in a chain of time-invariant linear oscillators weakly coupled to a nonlinear actuator (the Duffing oscillator) driven by an external periodic force. Two types of forcing are studied: (1) harmonic forcing with constant frequency is applied to an actuator with slowly-varying parameters; (2) harmonic forcing with a slowly increasing frequency is applied to an actuator with constant parameters. In both cases, the linear attachment is time-invariant, and the system is initially engaged in resonance. It is shown that in case (1) AR the nonlinear oscillator generates oscillations with growing amplitudes in the attached chain, while in case (2) energy transfer from the nonlinear oscillator is insufficient to excite high-energy motion in the attachment. The difference in the dynamical behavior is explained by different resonance properties of the systems. It is also shown that a slow change of stiffness may enhance the response of the nonlinear oscillator and make it sufficient to support oscillations with growing energy in the linear attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained.

Autoresonant dynamics of weakly coupled oscillators

This paper studies the emergence of autoresonance (AR) in a two-degrees-of-freedom system consisting of an excited nonlinear actuator (the Duffing oscillator) linearly coupled to a passive linear oscillator. Two classes of system are considered: (1) In the system of the first type, a periodic force with constant (resonance) frequency is applied to the nonlinear (Duffing) oscillator with slowly time-decreasing linear stiffness; (2) in the system of the second type, the nonlinear oscillator with constant parameters is excited by a force with slowly increasing frequency. In both cases, the linear oscillator and the linear coupling are time-invariant, and the system is initially engaged in resonance. In the first step, the dynamics of the undamped system is analyzed. It is shown here that in the system of the first type, AR may occur in both oscillators, but in the system of the second type, the amount of energy transferred from the nonlinear oscillator is insufficient to excite high-energy motion in the attached oscillator. Different dynamical behavior arises due to different resonance properties of the systems. In the next step, an effect of viscous damping in the oscillators and the coupling is investigated. As this paper demonstrates, the response enhancement may be observed in the system of the first type on a bounded time interval provided that dissipation is weak enough. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is proved.

Response enhancement in an oscillator chain

This paper investigates the emergence of autoresonance (AR) oscillations with permanently growing energy in a chain of time-invariant linear oscillators weakly coupled to a nonlinear actuator (the Duffing oscillator) driven by an external force. Two types of forcing are studied: (1) harmonic forcing with constant frequency is applied to the actuator with slowly-varying parameters; (2) harmonic forcing with a slowly increasing frequency is applied to the nonlinear actuator with constant parameters. In both cases, the linear chain is time-invariant, and the system is initially engaged in resonance. It has been proved in earlier works that a slow increase of the forcing frequency or an equivalent decrease of stiffness play a similar role in the emergence of AR in a single Duffing oscillator. This paper shows that in the system of the first type AR the nonlinear oscillator generates oscillations with growing amplitudes in the chain, but in the system of the second type energy transfer from the nonlinear oscillator is insufficient to excite high-energy motion in the attachment. The difference in the dynamical behavior is explained by different resonance properties of the systems. It is also shown that a slow change of stiffness may enhance the response of the nonlinear oscillator and make it sufficient to support oscillations with growing energy in the linear attachment even beyond the linear resonance. Explicit asymptotic approximations of the solutions are obtained. Close proximity of the derived approximations to exact (numerical) results is demonstrated.

First-harmonic approximation in nonlinear chirped-driven oscillators

Nonlinear classical oscillators can be excited to high energies by a weak driving field provided the drive frequency is properly chirped. This process is known as autoresonance (AR). We find that for a large class of oscillators, it is sufficient to consider only the first harmonic of the motion when studying AR, even when the dynamics is highly nonlinear. The first harmonic approximation is also used to relate AR in an asymmetric potential to AR in a "frequency equivalent" symmetric potential and to study the autoresonance breakdown phenomenon.

Limiting phase trajectories and emergence of autoresonance in nonlinear oscillators

Existence of stable autoresonance (AR) with continuously growing energy is directly connected with the inherent property of nonlinear systems to remain in resonance when the driving frequency varies in time. However, the physical mechanism underlying the transformation of bounded oscillations into AR remains unclear. As this paper demonstrates, the emergence of AR from stable bounded oscillations is basically analogous to the transition from quasilinear to nonlinear oscillations in the time-invariant oscillator driven by an external harmonic excitation with constant frequency, and AR can occur as a result of the loss of stability of the so-called limiting phase trajectory. We obtain the parametric threshold, which determines the transition from bounded oscillations to AR in the time-dependent system. The accuracy of the obtained approximations is confirmed by numerical simulations.

Driven Spatially Autoresonant Stimulated Raman Scattering in the Kinetic Regime

The autoresonant behavior of Langmuir waves excited by stimulated Raman scattering (SRS) is clearly identified in particle-in-cell (PIC) simulations in an inhomogeneous plasma. As previously shown via a 3-wave coupling model [T. Chapman et al., Phys. Plasmas 17, 122317 (2010)], weakly kinetic effects such as trapping can be described via an amplitude-dependent frequency shift that compensates the dephasing of the resonance of SRS due to the inhomogeneity. The autoresonance (AR) leads to phase locking and to growth of the Langmuir wave beyond the spatial amplification expected from Rosenbluth's model in an inhomogeneous profile [M. N. Rosenbluth, Phys. Rev. Lett. 29, 565 (1972)]. Results from PIC simulations and from a 3-wave coupling code show very good agreement, leading to the conclusion that AR arises even beyond the so-called weakly kinetic regime.

Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator

Classical and quantum-mechanical phase-locking transition in a nonlinear oscillator driven by a chirped-frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters ${P}_{1}=\ensuremath{\varepsilon}/\sqrt{2m\ensuremath{\hbar}{\ensuremath{\omega}}_{0}\ensuremath{\alpha}}$ and ${P}_{2}=(3\ensuremath{\hbar}\ensuremath{\beta})/(4m\sqrt{\ensuremath{\alpha}})$ ($\ensuremath{\varepsilon},$ $\ensuremath{\alpha},$ $\ensuremath{\beta}$, and ${\ensuremath{\omega}}_{0}$ being the driving amplitude, the frequency chirp rate, the nonlinearity parameter, and the linear frequency of the oscillator). It is shown that, for ${P}_{2}\ensuremath{\ll}{P}_{1}+1$, the passage through the linear resonance for ${P}_{1}$ above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for ${P}_{2}\ensuremath{\gg}{P}_{1}+1$, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in ${P}_{1}$ in both AR and LC limits are calculated. The theoretical results are tested by solving the Schr\"odinger equation in the energy basis and illustrated via the Wigner function in phase space.

Current drive generation based on autoresonance and intermittent trapping mechanisms.

Two mechanisms for generating streams of high-velocity electrons are presented. One has its origin in auto resonance (AR) interaction, which takes place in the system after a trapping conditioning stage, the second being dominated by the trapping process itself. These mechanisms are revealed from the study of the relativistic motion of an electron in a configuration consisting of two counterpropagating electromagnetic waves along a constant magnetic field in a dispersive medium. Using a Hamiltonian formalism, we have numerically solved the equations of motion and presented the results in a set of figures showing the generation of streams of electrons having high parallel velocities. Insight into these numerical results is gained from a theoretical analysis, which consists of a reformulation of the equations of motion. The operation of these mechanisms was found to circumvent the deterioration of the electron acceleration process that is characteristic for a dispersive medium, thus allowing for an effective generation of a current drive. Discussion of the results follows.

A 250 GHz CARM oscillator experiment driven by an induction linac

A 250 GHz cyclotron auto resonance maser (CARM) oscillator has been designed and constructed and will be tested using a 1 kA, 2 MeV electron beam produced by the induction linac at the Accelerator Research Center (ARC) facility of Lawrence Livermore National Laboratory (LLNL). The oscillator circuit was made to operate in the TE 11 mode at 10 times cutoff using waveguide Bragg reflectors to create an external cavity Q of 8000. Theory predicts cavity fill times of less than 30 ns (pulse length) and efficiencies approaching 20% if sufficiently low transverse electron velocity spreads are maintained (2%).