Time-delayed feedback control of shear-driven micellar systems

Lospichl, Benjamin von; Klapp, Sabine H. L.

doi:10.1103/physreve.98.042605

Cited by 3 publications

(3 citation statements)

References 55 publications

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“…The characteristic function for that system is derived by solving the spatiotemporal problem explicitly. It contains Bessel functions, which play a similar role as the exponentials in equation (10). Furthermore, the diffusive response function (compare equation (20) in appendix A with a  0), has an initial increase and then decays to zero, just as in our model.…”

Section: Stability-to-instability Transitionmentioning

confidence: 75%

“…From mixing two liquids [1], sorting colloids [2,3], controlling reaction rates [4] and heat transport in microfluidic devices [5], to fluid optics [1] and spiral patterns in liquid crystals [6], soft matter systems often display their most useful or interesting properties under external stresses. Several control and driving schemes have already been applied to these systems, including optimal control [7], hysteresis control [8], and time-delayed feedback [8][9][10]. These methods sense the characteristic response of a material and adapt their control to it.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier theoretical studies [8,10,20] and experiments [9,21] applied delayed feedback to the spatiotemporal dynamics of specific systems. One study showed that a system with two delay times can be mapped to the complex Ginzburg-Landau equation [13].…”

Section: Introductionmentioning

confidence: 99%

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Dissipative systems with nonlocal delayed feedback control

et al. 2018

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We present a linear model, which mimics the response of a spatially extended dissipative medium to a distant perturbation, and investigate its dynamics under delayed feedback control. The time a perturbation needs to propagate to a measurement point is captured by an inherent delay time (or latency). A detailed linear stability analysis demonstrates that a nonzero system delay acts to destabilize the otherwise stable fixed point for sufficiently large feedback strengths. The imaginary part of the dominant eigenvalue is bounded by twice the feedback strength. In the relevant parameter space it changes discontinuously along specific lines when switching between eigenvalues. When the feedback control force is bounded by a sigmoid function, a supercritical Hopf bifurcation occurs at the stability-instability transition. Perturbing the fixed point, the frequency and amplitude of the resulting limit cycles respond to parameter changes like the dominant eigenvalue. In particular, they show similar discontinuities along specific lines. These results are largely independent of the exact shape of the sigmoid function. Our findings match well with previously reported results on a feedback-induced instability of vortex diffusion in a rotationally driven Newtonian fluid (Zeitz et al 2015 Eur. Phys. J. E 38 22). Thus, our model captures the essential features of nonlocal delayed feedback control in spatially extended dissipative systems.

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Section: Stability-to-instability Transitionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

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Dissipative systems with nonlocal delayed feedback control

et al. 2018

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Traveling band formation in feedback-driven colloids

2019

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Using simulation and theory we study the dynamics of a colloidal suspension in two dimensions subject to a time-delayed repulsive feedback that depends on the positions of the colloidal particles. The colloidal particles experience an additional potential that is a superposition of repulsive potential energies centered around the positions of all the particles a delay time ago. Here we show that such a feedback leads to self-organization of the particles into traveling bands. The width of the bands and their propagation speed can be tuned by the delay time and the range of the imposed repulsive potential. The emerging traveling band behavior is observed in Brownian dynamics computer simulations as well as microscopic dynamic density functional theory (DDFT). Traveling band formation also persists in systems of finite size leading to rotating traveling waves in the case of circularly confined systems. arXiv:1904.08373v2 [cond-mat.soft]

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Diffusion and separation of binary mixtures of chiral active particles driven by time-delayed feedback

Liao¹,

Lin²

2020

Acta Phys. Sin.

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Considering the periodic boundary conditions, a new prescription for separating binary mixtures of chiral active particles by time-delayed feedback in a two-dimensional square box is proposed. We investigate the angular velocity, the feedback intensity, the delayed time, the rotational diffusion coefficient, the self-propelled speed and the packing fraction as functions of the effective diffusion coefficient and the separation coefficient numerically by the extensive Brownian dynamics simulations. It is found that mixed chiral active particles be separated without time-delayed feedback, but the dynamics of chiral active particles are different obviously and mixed chiral particles can be separated when the time-delayed feedback is introduced. The particle configuration (mixing or demixing) is determined by the dominant factor of particles’ diffusion. We can control the extent to which the diffusion of counterclockwise (CCW) active particles is affected by the diffusion of clockwise (CW) active particles adjusting the strength and the delayed time of the feedback. The response to the feedback for different chiral particles show different behaviors under different system parameters. When the feedback intensity is strong and the delayed time is long enough, the angular velocity of counterclockwise particles is accelerated and the diffusion of which is dominated by the interactions between particles completely. However, the angular speed of clockwise particles change little and the diffusion of which is determined by its parameters and particle interactions jointly. In this case, the counterclockwise particles aggregate to form clusters easily, and the clockwise particles diffuse quickly, therefore, the mixed chirality active particles are separated. When the feedback intensity is weak and the delayed time is short, the chirality difference between different chiral particles modulated by the feedback is smaller than the former case. The diffusions of counterclockwise particles and clockwise particles are both determined by their parameters and particle interactions, and the particles are mixed. Our findings provide novel strategies for the experimental pursuit of separating mixed chiral active particles and could be applied practically in many biological circle swimmers, such as autochemotactic particles, the bacteria in an external light field and sperm cells with vortex motion.

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Time-delayed feedback control of shear-driven micellar systems

Cited by 3 publications

References 55 publications

Dissipative systems with nonlocal delayed feedback control

Dissipative systems with nonlocal delayed feedback control

Traveling band formation in feedback-driven colloids

Diffusion and separation of binary mixtures of chiral active particles driven by time-delayed feedback

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