Collective motion of run-and-tumble repulsive and attractive particles in one-dimensional systems

Gutiérrez, Celia; Campos, Christian Vanhille; Alarcón, Francisco; Pagonabarraga, Ignacio; Brito, Ricardo; Valeriani, Chantal

doi:10.1039/d1sm01006a

Cited by 8 publications

(6 citation statements)

References 48 publications

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“…The Lennard-Jones (LJ) potential can qualitatively account for the inter-particle short-range attraction and the steric repulsion present in many colloidal systems to mimic soft spherical particles. [42][43][44][45][46][47][48][49][50] Therefore, the LJ potential has been widely used as a model potential for soft matters. Successful applications of the LJ potential to model soft matters include many studies on their self-assembly (dispersion or clustering), 42,46 hydrodynamic, 43,45 self-propelling, 49 elastic, 44 phase transition, 47 phase separation, 50 and interfacial 48 properties.…”

Section: Methodsmentioning

confidence: 99%

“…[42][43][44][45][46][47][48][49][50] Therefore, the LJ potential has been widely used as a model potential for soft matters. Successful applications of the LJ potential to model soft matters include many studies on their self-assembly (dispersion or clustering), 42,46 hydrodynamic, 43,45 self-propelling, 49 elastic, 44 phase transition, 47 phase separation, 50 and interfacial 48 properties. We are also able to control the phase state of our model colloidal system based on the well-established LJ phase diagram.…”

Section: Methodsmentioning

confidence: 99%

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Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

et al. 2023

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

et al. 2023

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“…Here, the bacterium can only switch between left-and right motion in a stochastic manner. One-dimensional RT-models have proven to be an extremely rich reservoir for analytic calculations -in some sense, they are like the analogue of Ising models in active systems [15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

A one-dimensional three-state run-and-tumble model with a `cell cycle'

Breoni¹,

Schwarzendahl²,

Blossey³

et al. 2022

Preprint

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We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between a non-proliferation mobile phase and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their probability densities, where mobility is allowed with different activities in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean squared displacement, which shows a surprising super-ballistic scaling at early times. Including interactions between the three states, we explore the stability of the system and then employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

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“…Since we observe numerically that the fluctuations decrease as γ increases the above discussion remains valid for γ > 0. Finally, the second result in (25) indicates that the variance of the number of particles in an interval grows linearly with its size. This is in contrast with the case of the standard DBM where a similar calculation leads to logarithmic growth (see [43]).…”

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confidence: 97%

Interacting, running and tumbling: The active Dyson Brownian motion

Touzo

Doussal

Schehr

2023

EPL

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We introduce and study a model in one dimension of $N$ run-and-tumble particles (RTP) which repel each other logarithmically in the presence of an external quadratic potential. This is an ``active'' version of the well-known Dyson Brownian motion (DBM) where the particles are subjected to a telegraphic noise, with two possible states $\pm$ with velocity $\pm v_0$. We study analytically and numerically two different versions of this model. In model I a particle only interacts with particles in the same state, while in model II all the particles interact with each other. In the large time limit, both models converge to a steady state where the stationary density has a finite support. For finite $N$, the stationary density exhibits singularities, which disappear when $N \to +\infty$. In that limit, for model I, using a Dean-Kawasaki approach, we show that the stationary density of $+$ (respectively $-$) particles deviates from the DBM Wigner semi-circular shape, and vanishes with an exponent $3/2$ at one of the edges. In model II, the Dean-Kawasaki approach fails but we obtain strong evidence that the density in the large $N$ limit still retains a Wigner semi-circular shape.

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Collective motion of run-and-tumble repulsive and attractive particles in one-dimensional systems

Abstract: Active matter deals with system whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures several models have...

Cited by 8 publications

References 48 publications

Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

Modeling the viscoelastic relaxation dynamics of soft particles via molecular dynamics simulation-informed multi-dimensional transition-state theory

A one-dimensional three-state run-and-tumble model with a `cell cycle'

Interacting, running and tumbling: The active Dyson Brownian motion

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