Detection the nonlinear ultrasonic signals based on modified Duffing equations

Zhang, Yuhua; Mao, Hanling; Mao, Hanying; Huang, Zhenfeng

doi:10.1016/j.rinp.2017.08.054

Cited by 12 publications

(10 citation statements)

References 11 publications

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“…One of the dynamical systems exhibiting chaos is the non-linear forced oscillator:

where

is an extensive variable such as the displacement or the charge,

is the damping parameter,

controls the linear stiffness,

controls the amount of non-linearity in the restoring force; if

, the Duffing equation describes a damped and driven simple harmonic oscillator, and

is the driving term, A is the amplitude of the periodic driving force and

the angular frequency. If

, the oscillator is a forced-damped Duffing oscillator (e.g., Figure 1 f,g) [ 46 , 47 ].…”

Section: Introductionmentioning

confidence: 99%

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes

Braga

2021

Materials

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Coherence is a major caveat in quantum computing. While phonons and electrons are weakly coupled in a glass, topological insulators strongly depend on the electron-phonon coupling. Knowledge of the electron−phonon interaction at conducting surfaces is relevant from a fundamental point of view as well as for various applications, such as two-dimensional and quasi-1D superconductivity in nanotechnology. Similarly, the electron−phonon interaction plays a relevant role in other transport properties e.g., thermoelectricity, low-dimensional systems as layered Bi and Sb chalcogenides, and quasi-crystalline materials. Glass-electrolyte ferroelectric energy storage cells exhibit self-charge and self-cycling related to topological superconductivity and electron-phonon coupling; phonon coherence is therefore important. By recurring to ab initio molecular dynamics, it was demonstrated the tendency of the Li3ClO, Li2.92Ba0.04ClO, Na3ClO, and Na2.92Ba0.04ClO ferroelectric-electrolytes to keep phonon oscillation coherence for a short lapse of time in ps. Double-well energy potentials were obtained while the electrolyte systems were thermostatted in a heat bath at a constant temperature. The latter occurrences indicate ferroelectric type behavior but do not justify the coherent self-oscillations observed in all types of cells containing these families of electrolytes and, therefore, an emergent type phenomenon where the full cell works as a feedback system allowing oscillations coherence must be realized. A comparison with amorphous SiO2 was performed and the specific heats for the various species were calculated.

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“…One of the dynamical systems exhibiting chaos is the non-linear forced oscillator:

where

is an extensive variable such as the displacement or the charge,

is the damping parameter,

controls the linear stiffness,

controls the amount of non-linearity in the restoring force; if

, the Duffing equation describes a damped and driven simple harmonic oscillator, and

is the driving term, A is the amplitude of the periodic driving force and

the angular frequency. If

, the oscillator is a forced-damped Duffing oscillator (e.g., Figure 1 f,g) [ 46 , 47 ].…”

Section: Introductionmentioning

confidence: 99%

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes

Braga

2021

Materials

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“…For example, [53] can detect low signal amplitude, and [54] can be immune. e noise is small, and [55] detects that the initial phase angle error of the signal is too large. Based on the above reasons, this paper proposes a new system:…”

Section: Coupled Chaotic System Model and Dynamic Analysismentioning

confidence: 99%

“…e system in [54] can detect signals with a size of 1 × 10 − 9 , but a noise signal that can be immune to it can only reach the order of 1 × 10 − 9 . e system in [55] can detect a signal with a wider frequency range, but the detection range of the initial phase angle of the signal is too large and thus is unfavorable for determining the signal parameters. At present, most of the researches on weak signals based on chaos theory use a single chaotic system for detection.…”

Section: Introductionmentioning

confidence: 99%

“…rough data analysis and experimental data, the system proposed in this paper can detect signals sized 1 × 10 − 6 , and the signal-to-noise ratio reaches −73.892 dB. Moreover, the immune signal reached the order of 3.5 × 10 − 3 , and the error range of the initial phase angle is ± 0.09. erefore, the detection performance of the coupled system proposed in this paper is better than the single chaotic system proposed in [45,46,[53][54][55].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a New Hidden Attractor Coupled Chaotic System and Application of Its Weak Signal Detection

Luo

et al. 2020

Mathematical Problems in Engineering

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In order to improve the complexity of the chaotic system and the accuracy of the weak signal detection, this paper propose a new hidden attractor coupled chaotic system and a corresponding weak signal detection system, which can be used to obtain the phase diagram of the proposed system using the fourth order of the Runge-Kutta method. The dynamic behavior of the chaotic system is analyzed through the bifurcation diagram, Lyapunov exponent, and power spectrum. The Lyapunov exponent is used to depict the basins of attraction for the system. After research, it is discovered that symmetry exists in the system. Comparative analysis has demonstrated that the system has higher detection accuracy and excellent antinoise performance. Finally, the circuit simulation and FPGA realization of the system indicated that the numerical simulation results are consistent with the FPGA implementation results, proving the theoretical analysis to be correct and the accuracy of the detection results.

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“…For example, Duffing oscillator based encryption devices have been proposed for secure communication systems [69,70]. Duffing oscillators can be used in weak signal detection in various cases like fatigue damage in materials [71,72] and down-hole acoustic telemetry in oilfield exploration [73]. Such broad applications of Duffing oscillators and progress in theory [59] as well as in experiments [70], makes Duffing chain a natural test-bed for studying spatio-temporal chaos in extended driven dissipative classical systems -an area yet largely unexplored.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach

Chatterjee,

Kundu,

Kulkarni

2020

Preprint

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Out-of-time-ordered correlators (OTOC) have been extensively used as a major tool for exploring quantum chaos and also recently, there has been a classical analogue. Studies have been limited to closed systems. In this work, we probe an open classical many-body system, more specifically, a spatially extended driven dissipative chain of coupled Duffing oscillators using the classical OTOC to investigate the spread and growth (decay) of an initially localized perturbation in the chain. Correspondingly, we find three distinct types of dynamical behavior, namely the sustained chaos, transient chaos and non-chaotic region, as clearly exhibited by different geometrical shapes in the heat map of OTOC. To quantify such differences, we look at instantaneous speed (IS), finite time Lyapunov exponents (FTLE) and velocity dependent Lyapunov exponents (VDLE) extracted from OTOC. Introduction of these quantities turn out to be instrumental in diagnosing and demarcating different regimes of dynamical behavior. To gain control over open nonlinear systems, it is important to look at the variation of these quantities with respect to parameters. As we tune drive, dissipation and coupling, FTLE and IS exhibit transition between sustained chaos and non-chaotic regimes with intermediate transient chaos regimes and highly intermittent sustained chaos points. In the limit of zero nonlinearity, we present exact analytical results for the driven dissipative harmonic system and we find that our analytical results can very well describe the non-chaotic regime as well as the late time behavior in the transient regime of the Duffing chain. We believe, this analysis is an important step forward towards understanding nonlinear dynamics, chaos and spatio-temporal spread of perturbations in many-particle open systems.

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Detection the nonlinear ultrasonic signals based on modified Duffing equations

Cited by 12 publications

References 11 publications

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes

Analysis of a New Hidden Attractor Coupled Chaotic System and Application of Its Weak Signal Detection

Spatio-temporal spread of perturbations in a driven dissipative Duffing chain: an OTOC approach

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