Chaotic Diffusion in Delay Systems: Giant Enhancement by Time Lag Modulation

Albers, Tony; Müller-Bender, David; Hille, Lukas; Radons, Günter

doi:10.1103/physrevlett.128.074101

Cited by 12 publications

(6 citation statements)

References 78 publications

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“…A first observation is that both quantities roughly get halved if the value of Θ is doubled. This is in agreement with a previous finding of the authors in [45], where it was shown that the diffusion coefficient asymptotically vanishes as D ∼ 1/Θ. Furthermore, we can see that for larger values of µ, the diffusion coefficient and the variance of the increments coincide, whereas for smaller values of µ, there are distinct discrepancies between these two quantities that can only be explained by taking the anti-persistence into account.…”

Section: Anti-persistent Random Walksupporting

confidence: 93%

“…which shows chaotic diffusion for µ > µ c = 0.732644... [5]. In a previous article [45], we discussed that the resulting DDE, Eq. ( 1) with Eq.…”

Section: Delay Equationmentioning

confidence: 97%

“…An integrated version of the Ikeda DDE [42] was considered in [43,44]. Recently, we demonstrated that introducing a modulation of the time delay, i.e., τ = τ (t), can lead to a giant increase of the diffusion constant over several orders of magnitudes [45], which is associated with certain types of chaos induced by the time-varying delay [46,47]. In this paper, we show that, even if the delay is constant, chaotic diffusion in time-delay systems exhibits interesting features, where we focus on anti-persistence.…”

Section: Introductionmentioning

confidence: 99%

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Anti-persistent random walks in time-delayed systems

Albers,

Müller-Bender,

Radons

2022

Preprint

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We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the dependence of all relevant quantities characterizing the random walk on the strength of the nonlinearity and on the delay. With the help of analytical considerations, we show that for a decreasing nonlinearity parameter the resulting dependence of the diffusion coefficient is well described by Markov processes of increasing order.

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Section: Anti-persistent Random Walksupporting

confidence: 93%

“…which shows chaotic diffusion for µ > µ c = 0.732644... [5]. In a previous article [45], we discussed that the resulting DDE, Eq. ( 1) with Eq.…”

Section: Delay Equationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Anti-persistent random walks in time-delayed systems

Albers,

Müller-Bender,

Radons

2022

Preprint

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“…There exists a trivial solution to the system of equations given by eqs. ( 3), ( 12), (13), which is the isotropic concentration profile c = 1/r, corresponding to the quiescent state of zero phoretic velocity and no fluid motion at all times. Beyond Pe = 4, however, the quiescent state becomes unstable with respect to dipolar perturbations in the concentration field [1,7], and the autophoretic particle sets into motion.…”

Section: Problem Formulationmentioning

confidence: 99%

“…More broadly, it is known that chaotic maps can lead to either normal [9] or anomalous diffusion [10,11]. Delay-differential equations, used to model phenomena such as blood cell production and the transmission of light from optical ring cavities, have also been shown to exhibit chaotic diffusion [12,13]. Given the differing theoretical and experimental results mentioned above, it is not evident what the MSD scaling of autophoretic particles in the chaotic regime is.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of forced and unforced autophoretic particles

Kailasham¹,

Khair²

2022

Preprint

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Chemically active, or autophoretic, particles that isotropically emit or absorb solute molecules are known to undergo spontaneous self-propulsion when their activity is increased beyond a critical Péclet number (Pe). Here, we conduct numerical simulations of a spherical rigid autophoretic particle in unsteady rectilinear translation, which reveal that its motion progresses through four regimes, as Pe is increased: quiescent, steady, stirring, and chaos. The particle is stationary in the quiescent regime, and the solute profile is isotropic about the particle. At P e = 4 the foreaft symmetry in the solute profile is broken, resulting in its steady self-propulsion, as has been shown in previous studies. A further increase in Pe gives rise to the stirring regime at Pe ≈ 27, where the fluid undergoes recirculation, as the particle remains essentially stationary in a state of dynamic arrest. As the Péclet number is increased further, the dynamics of the particle is marked by chaotic oscillations at Pe ≈ 55 and higher, where its velocity undergoes rapid reorientations. The mean square displacement of particles in the chaotic regime exhibits a subdiffusive behavior with an apparently universal scaling exponent at long times for all values of Pe studied. However, the time-scale for the decorrelation of the swimming velocity decreases with an increase in Pe, and this time-scale also governs the transition in the mean square displacement from early-time ballistic to long-time subdiffusive motion.

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