Mean-field theory of active electrolytes: Dynamic adsorption and overscreening

Frydel, Derek; Podgornik, Rudolf

doi:10.1103/physreve.97.052609

Cited by 8 publications

(2 citation statements)

References 59 publications

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“…The second term, represented by the modified Bessel function I 0 (x), is the contribution due to propelled motion. This term diverges far away from the center of the trap as I 0 (x) ≈ e x / √ 2πx and gives rise to particle deposition at the border of a trap [12].…”

Section: Theoretical Frameworkmentioning

confidence: 99%

Stationary distributions of propelled particles as a system with quenched disorder

Frydel

2021

Phys. Rev. E

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This article is the exploration of the viewpoint within which propelled particles in a steady state are regarded as a system with quenched disorder. The analogy is exact when the rate of the drift orientation vanishes and the linear potential, representing the drift, becomes part of an external potential, resulting in the effective potential u e f f . The stationary distribution is then calculated as a disorder-averaged quantity by considering all contributing drift orientations. To extend this viewpoint to the case when a drift orientation evolves in time, we reformulate the relevant Fokker-Planck equation as a self-consistent relation. One interesting aspect of this formulation is that it is represented in terms of the Boltzmann factor e −β u e f f . In the case of a run-and-tumble model, the formulation reveals an effective interaction between particles.

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Section: Theoretical Frameworkmentioning

confidence: 99%

Stationary distributions of propelled particles as a system with quenched disorder

Frydel

2021

Phys. Rev. E

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“…The non-equilibrium aspect of self-propelled particles makes those systems both a difficult and fascinating subject of study. It gives rise to new interesting behaviors, such as non-Boltzmann accumulation of particles near the system borders even without the presence of potential forces [1][2][3][4][5], or new types of phase transitions without participation of attractive interactions [6][7][8][9][10]. The treatment of self-propelled particles is also theoretically challenging.…”

Section: Introductionmentioning

confidence: 99%

Generalized run-and-tumble model in 1D geometry for an arbitrary distribution of drift velocities

Frydel¹

2021

J. Stat. Mech.

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In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = ±v 0 and the model is exactly solvable. Extension of the model to three drifts v = 0, ±v 0 yields the exact solution but the complexity of the expressions indicates that analytical treatment of higher-state models under the same procedure is impractical. Consequently, we modify our goal and consider a generalized version of the model for an arbitrary distribution of states P(v). To analyze such a system, we reformulate the Fokker–Planck equation as a self-consistent relation. The self-consistent relation is then analyzed by means of Laplace transform techniques.

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The run-and-tumble particle model with four-states: Exact solution at zero temperature

Frydel

2022

Physics of Fluids

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This paper considers the four-state run-and-tumble particle model (RTP) at zero temperature. The model is an extension of the RTP model in one-dimension for two drift velocities, v=±v0. This model is exactly solvable and imparts valuable insights for systems with finite temperature. However, at zero temperature, it yields uniform distributions for all parameter values and fails to provide any information about the structure of stationary distributions. To arrive at the model that more completely describes a zero temperature case, it is necessary to increase the number of discrete velocities. The four-state model with drifts v=±v0,±γv0 (where 0≤γ≤1) is the simplest such an extension. In this paper, the four-state model at zero temperature is solved exactly and analyzed. The resulting stationary distributions indicate that fast particles accumulate at the walls and the slow particles are depleted. Taken all particles together, a dominant trend is accumulation, similar to what is observed for the two-state model for D > 0, however, reflecting a different physics behind it.

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Mean-field theory of active electrolytes: Dynamic adsorption and overscreening

Cited by 8 publications

References 59 publications

Stationary distributions of propelled particles as a system with quenched disorder

Stationary distributions of propelled particles as a system with quenched disorder

Generalized run-and-tumble model in 1D geometry for an arbitrary distribution of drift velocities

The run-and-tumble particle model with four-states: Exact solution at zero temperature

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