Physical Aging of Classical Oscillators

Ionita, Florin; Meyer‐Ortmanns, Hildegard

doi:10.1103/physrevlett.112.094101

Cited by 12 publications

(13 citation statements)

References 26 publications

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“…a Power-law 'on'/'off' waiting time [21] b finite mean 'on' time [21] c Lattice size 32 × 32, coupling strength κ = −4 [28]. d Intermediate regime (ii) (see details in [28]) e Saturation regime (iii) (see details in [28])…”

Section: Critical Exponents and Scaling Relationsmentioning

confidence: 99%

Aging Wiener-Khinchin theorem and critical exponents of 1/fβ noise

et al. 2016

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The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

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Section: Critical Exponents and Scaling Relationsmentioning

confidence: 99%

Aging Wiener-Khinchin theorem and critical exponents of 1/fβ noise

et al. 2016

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“…Introduction. -Collective behavior in a large ensemble of coupled oscillators has attracted great interest during the past decades [1][2][3][4][5]. The reason comes from the fact that modelling coupled oscillators serves as a simple but efficient way for understanding basic self-organized phenomena in a variety of disciplines of science.…”

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confidence: 99%

Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators

Liu¹,

Zou²,

Zhan³

et al. 2016

EPL

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We propose an effective method to enhance the dynamical robustness of networks of diffusively coupled oscillators experiencing aging transition. By introducing a new control parameter into the normal diffusive coupling, we demonstrate that the dynamical robustness of coupled oscillator networks can be efficiently improved by enhancing the tolerance of dynamic activity in the network to inactivation or deterioration of the individual oscillators. Even a tiny deviation from the normal diffusive coupling greatly strengthens the robustness of networks. Particularly, the strong coupling in our scheme is shown to be in favor of the dynamic activity, which is in sharp contrast to the normal form of diffusive coupling with the tendency to spoil the dynamical robustness. Our proposed approach serves as a rather simple and efficient way to recover dynamic activity in networks of diffusively coupled oscillators that has been lost due to some inactivated or damaged oscillator components.

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“…In the sociological phenomenon of interest to us here the role of inhibitory links is played by individuals called contrarians [7]. More recently an interesting connection has been established between the action of contrarians and the property of frustration found in spin glasses [8,9]. As the term frustration suggests, the action of contrarians is found to quench consensus or prevent its occurrence in accordance with the sociological conclusions of Crokidakis et al [10].…”

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confidence: 87%

The value of conflict in stable social networks

Pramukkul¹,

West²,

Grigolini³

2015

EPL

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A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that the transmission of information from a network B to a network A, with a small fraction of lookout members in A who adopt the behavior of B, becomes maximal when both networks are assigned the same critical percentage of contrarians.

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Physical Aging of Classical Oscillators

Cited by 12 publications

References 26 publications

Aging Wiener-Khinchin theorem and critical exponents of 1/fβ noise

Aging Wiener-Khinchin theorem and critical exponents of 1/fβ noise

Enhancing dynamical robustness in aging networks of coupled nonlinear oscillators

The value of conflict in stable social networks

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