1
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Yu H, Jack RL. Competition between lanes and transient jammed clusters in driven binary mixtures. Phys Rev E 2024; 109:024123. [PMID: 38491710 DOI: 10.1103/physreve.109.024123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
We consider mixtures of oppositely driven particles, showing that their nonequilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilized. We analyze the interplay between these two types of nonequilibrium pattern formation, including their implications for macroscopic demixing perpendicular to the drive. Finite-size scaling analysis indicates that there is no critical driving force associated with demixing, which appears as a crossover in finite systems. We attribute this effect to the disruption of long-ranged order by the transient jammed clusters.
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Affiliation(s)
- Honghao Yu
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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2
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Benois A, Jardat M, Dahirel V, Démery V, Agudo-Canalejo J, Golestanian R, Illien P. Enhanced diffusion of tracer particles in nonreciprocal mixtures. Phys Rev E 2023; 108:054606. [PMID: 38115513 DOI: 10.1103/physreve.108.054606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 10/19/2023] [Indexed: 12/21/2023]
Abstract
We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.
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Affiliation(s)
- Anthony Benois
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 75005 Paris, France
| | - Marie Jardat
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 75005 Paris, France
| | - Vincent Dahirel
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 75005 Paris, France
| | - Vincent Démery
- Gulliver, UMR CNRS 7083, ESPCI Paris PSL, 75005 Paris, France
- Université Lyon, ENS de Lyon, Université Claude Bernard, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Jaime Agudo-Canalejo
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany
| | - Ramin Golestanian
- Department of Living Matter Physics, Max Planck Institute for Dynamics and Self-Organization, D-37077 Göttingen, Germany
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OX1 3PU Oxford, United Kingdom
| | - Pierre Illien
- Sorbonne Université, CNRS, Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux (PHENIX), 75005 Paris, France
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3
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Bernard O, Jardat M, Rotenberg B, Illien P. On analytical theories for conductivity and self-diffusion in concentrated electrolytes. J Chem Phys 2023; 159:164105. [PMID: 37873957 DOI: 10.1063/5.0165533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 09/19/2023] [Indexed: 10/25/2023] Open
Abstract
Describing analytically the transport properties of electrolytes, such as their conductivity or the self-diffusion of the ions, has been a central challenge of chemical physics for almost a century. In recent years, this question has regained some interest in light of Stochastic Density Field Theory (SDFT) - an analytical framework that allows the approximate determination of density correlations in fluctuating systems. In spite of the success of this theory to describe dilute electrolytes, its extension to concentrated solutions raises a number of technical difficulties, and requires simplified descriptions of the short-range repulsion between the ions. In this article, we discuss recent approximations that were proposed to compute the conductivity of electrolytes, in particular truncations of Coulomb interactions at short distances. We extend them to another observable (the self-diffusion coefficient of the ions) and compare them to earlier analytical approaches, such as the mean spherical approximation and mode-coupling theory. We show how the treatment of hydrodynamic effects in SDFT can be improved, that the choice of the modified Coulomb interactions significantly affects the determination of the properties of the electrolytes, and that comparison with other theories provides a guide to extend SDFT approaches in this context.
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Affiliation(s)
- Olivier Bernard
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Marie Jardat
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Benjamin Rotenberg
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux), 4 Place Jussieu, 75005 Paris, France
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Abstract
Laning is a paradigmatic example of spontaneous organization in active two-component flows that has been observed in diverse contexts, including pedestrian traffic, driven colloids, complex plasmas, and molecular transport. We introduce a kinetic theory that elucidates the physical origins of laning and quantifies the propensity for lane nucleation in a given physical system. Our theory is valid in the low-density regime, and it makes different predictions about situations in which lanes may form that are not parallel with the direction of flow. We report on experiments with human crowds that verify two notable consequences of this phenomenon: tilting lanes under broken chiral symmetry and lane nucleation along elliptic, parabolic, and hyperbolic curves in the presence of sources or sinks.
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Affiliation(s)
- Karol A Bacik
- Centre for Networks and Collective Behaviour, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
| | - Bogdan S Bacik
- Department of Human Motor Behavior, Institute of Sport Sciences, Academy of Physical Education in Katowice, ul. Mikołowska 72c, 40-065 Katowice, Poland
| | - Tim Rogers
- Centre for Networks and Collective Behaviour, Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK
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5
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Jardat M, Dahirel V, Illien P. Diffusion of a tracer in a dense mixture of soft particles connected to different thermostats. Phys Rev E 2022; 106:064608. [PMID: 36671123 DOI: 10.1103/physreve.106.064608] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 11/28/2022] [Indexed: 12/23/2022]
Abstract
We study the dynamics of a tracer in a dense mixture of particles connected to different thermostats. Starting from the overdamped Langevin equations that describe the evolution of the system, we derive the expression of the self-diffusion coefficient of a tagged particle in the suspension, in the limit of soft interactions between the particles. Our derivation, which relies on the linearization of the Dean-Kawasaki equations obeyed by the density fields and on a path-integral representation of the dynamics of the tracer, extends previous derivations that held for tracers in contact with a single bath. Our analytical result is confronted to results from Brownian dynamics simulations. The agreement with numerical simulations is very good even for high densities. We show how the diffusivity of tracers can be affected by the activity of a dense environment of soft particles that may represent polymer coils-a result that could be of relevance in the interpretation of measurements of diffusivity in biological media. Finally, our analytical result is general and can be applied to the diffusion of tracers coupled to different types of fluctuating environments, provided that their evolution equations are linear and that the coupling between the tracer and the bath is weak.
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Affiliation(s)
- Marie Jardat
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Vincent Dahirel
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX), 4 Place Jussieu, 75005 Paris, France
| | - Pierre Illien
- Sorbonne Université, CNRS, Laboratoire PHENIX (Physico-Chimie des Électrolytes et Nanosystèmes Interfaciaux, PHENIX), 4 Place Jussieu, 75005 Paris, France
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6
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Casiulis M, Levine D. Emergent synchronization and flocking in purely repulsive self-navigating particles. Phys Rev E 2022; 106:044611. [PMID: 36397598 DOI: 10.1103/physreve.106.044611] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 10/10/2022] [Indexed: 06/16/2023]
Abstract
Inspired by groups of animals and robots, we study the collective dynamics of large numbers of active particles, each one trying to get to its own randomly placed target, while avoiding collisions with each other. The particles we study are repulsive homing active Brownian particles, self-propelled particles whose orientation relaxes at a finite rate towards an absorbing target in two-dimensional continuous space. For a wide range of parameters, these particles form synchronized system-wide chiral flocks, in spite of the absence of explicit alignment interactions. We show that this dramatic behavior obtains for different system sizes and density, that it is robust against the addition of noise, polydispersity, and bounding walls, and that it can exhibit dynamical topological defects. We develop an analogy to an off-lattice, ferromagnetic XY model, which allows us to interpret the different phases, as well as the topological defects.
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Affiliation(s)
- Mathias Casiulis
- Department of Physics, Technion-IIT, 32000 Haifa, Israel
- Department of Chemistry, New York University, New York, New York 10003, USA
- Center for Soft Matter Research, Department of Physics, New York University, New York, New York 10003, USA
| | - Dov Levine
- Department of Physics, Technion-IIT, 32000 Haifa, Israel
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7
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Bagchi D. Macroscopic charge segregation in driven polyelectrolyte solutions. SOFT MATTER 2022; 18:5676-5686. [PMID: 35861507 DOI: 10.1039/d2sm00448h] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Understanding the behavior of charged complex fluids is crucial for a plethora of important industrial, technological, and medical applications. Here, using coarse-grained molecular dynamics simulations, we investigate the properties of a polyelectrolyte solution with explicit counterions and implicit solvent that is driven by a steady electric field. By properly tuning the interplay between interparticle electrostatics and the applied electric field, we uncover two non-equilibrium continuous phase transitions as a function of the driving field. The first transition occurs from a homogeneous mixed phase to a macroscopic charge-segregated phase in which the polyelectrolyte solution self-organizes to form two lanes of like-charges, parallel to the applied field. We show that the fundamental underlying factor responsible for the emergence of this charge segregation in the presence of an electric field is the excluded volume interactions of the drifting polyelectrolyte chains. As the driving field is increased further, a re-entrant transition is observed from a charge-segregated phase to a homogeneous phase. The re-entrance is signaled by a decrease in the mobility of the monomers and counterions as the electric field is increased. Furthermore, with multivalent counterions, a counterintuitive regime of negative differential mobility is observed in which the charges move progressively more slowly as the driving field is increased. We show that all these features can be consistently explained using an intuitive trapping mechanism that operates between the oppositely moving charges, and present numerical evidence to support our claims. Parameter dependencies and phase diagrams are studied to better understand charge segregation in such driven polyelectrolyte solutions.
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Affiliation(s)
- Debarshee Bagchi
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru, India.
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8
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Yu H, Thijssen K, Jack RL. Perpendicular and parallel phase separation in two-species driven diffusive lattice gases. Phys Rev E 2022; 106:024129. [PMID: 36110007 DOI: 10.1103/physreve.106.024129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating.
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Affiliation(s)
- Honghao Yu
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Kristian Thijssen
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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9
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Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation. ENTROPY 2022; 24:e24040500. [PMID: 35455163 PMCID: PMC9028018 DOI: 10.3390/e24040500] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/28/2022] [Accepted: 03/28/2022] [Indexed: 12/04/2022]
Abstract
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.
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10
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Khelfa B, Korbmacher R, Schadschneider A, Tordeux A. Heterogeneity-induced lane and band formation in self-driven particle systems. Sci Rep 2022; 12:4768. [PMID: 35306506 PMCID: PMC8934355 DOI: 10.1038/s41598-022-08649-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 03/08/2022] [Indexed: 01/23/2023] Open
Abstract
The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and nonuniform patterns. In this article, we investigate the effects of different types of heterogeneity in a two-species self-driven particle system. We show that heterogeneity can generically initiate segregation in the motion and identify two heterogeneity mechanisms. Longitudinal lanes parallel to the direction of motion emerge when the heterogeneity statically lies in the agent characteristics (quenched disorder). While transverse bands orthogonal to the motion direction arise from dynamic heterogeneity in the interactions (annealed disorder). In both cases, non-linear transitions occur as the heterogeneity increases, from disorder to ordered states with lane or band patterns. These generic features are observed for a first and a second order motion model and different characteristic parameters related to particle speed and size. Simulation results show that the collective dynamics occur in relatively short time intervals, persist stationary, and are partly robust against random perturbations.
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Affiliation(s)
- Basma Khelfa
- School for Mechanical Engineering and Safety Engineering, University of Wuppertal, Wuppertal, Germany
| | - Raphael Korbmacher
- School for Mechanical Engineering and Safety Engineering, University of Wuppertal, Wuppertal, Germany
| | | | - Antoine Tordeux
- School for Mechanical Engineering and Safety Engineering, University of Wuppertal, Wuppertal, Germany.
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11
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Samsuzzaman M, Sayeed A, Saha A. Reentrant melting of lanes of rough circular disks. Phys Rev E 2022; 105:024608. [PMID: 35291112 DOI: 10.1103/physreve.105.024608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.
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Affiliation(s)
- Md Samsuzzaman
- Department of Physics, Savitribai Phule Pune University, Pune 411007, India
| | - Ahmed Sayeed
- Department of Physics, Savitribai Phule Pune University, Pune 411007, India
| | - Arnab Saha
- Department of Physics, University Of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata-700009, India
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12
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Dhont JKG, Park GW, Briels WJ. Motility-induced inter-particle correlations and dynamics: a microscopic approach for active Brownian particles. SOFT MATTER 2021; 17:5613-5632. [PMID: 33998621 DOI: 10.1039/d1sm00426c] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Amongst the theoretical approaches towards the dynamics and phase behaviour of suspensions of active Brownian particles (ABPs), no attempt has been made to specify the motility-induced inter-particle correlations as quantified by the pair-correlation function. Here, we derive expressions for the pair-correlation function for ABPs with very short-ranged direct interactions for small and large swimming velocities and low concentrations. The pair-correlation function is the solution of a differential equation that is obtained from the Fokker-Planck equation for the probability density function of the positions and orientations of the ABPs. For large swimming Peclet numbers, λ, the pair-correlation function is highly asymmetric. The pair-correlation function attains a large value, ∼λ, within a small region of spatial extent, ∼1/λ, near contact of the ABPs when the ABPs approach each other. The pair-correlation function is small within a large region of spatial extent, ∼λ1/3, when the ABPs move apart, with a contact value that is essentially zero. From the explicit expressions for the pair-correlation function, Fick's diffusion equation is generalized to include motility. It is shown that mass transport, in case of large swimming velocities, is dominated by a preferred swimming direction that is induced by concentration gradients. The expression for the pair-correlation function derived in this paper could serve as a starting point to obtain approximate results for high concentrations, which could then be employed in a first-principles analysis of the dynamics and phase behaviour of ABPs at higher concentrations.
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Affiliation(s)
- J K G Dhont
- Institute of Biological Information Processing, IBI-4, Biomacromolecular Systems and Processes, Forschungszentrum Jülich GmbH, D-52428 Jülich, Germany. and Heinrich Heine Universität, 40225 Düsseldorf, Germany
| | - G W Park
- Institute of Biological Information Processing, IBI-4, Biomacromolecular Systems and Processes, Forschungszentrum Jülich GmbH, D-52428 Jülich, Germany.
| | - W J Briels
- Institute of Biological Information Processing, IBI-4, Biomacromolecular Systems and Processes, Forschungszentrum Jülich GmbH, D-52428 Jülich, Germany. and MESA+ Institute for Nanotechnology, University of Twente, P. O. Box 217, 7500 AE Enschede, The Netherlands.
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13
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Mahdisoltani S, Golestanian R. Long-Range Fluctuation-Induced Forces in Driven Electrolytes. PHYSICAL REVIEW LETTERS 2021; 126:158002. [PMID: 33929248 DOI: 10.1103/physrevlett.126.158002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Revised: 01/20/2021] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.
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Affiliation(s)
- Saeed Mahdisoltani
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
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14
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Poncet A, Bénichou O, Démery V, Nishiguchi D. Pair correlation of dilute active Brownian particles: From low-activity dipolar correction to high-activity algebraic depletion wings. Phys Rev E 2021; 103:012605. [PMID: 33601595 DOI: 10.1103/physreve.103.012605] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 12/16/2020] [Indexed: 11/07/2022]
Abstract
We study the pair correlation of active Brownian particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: While particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity, where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.
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Affiliation(s)
- Alexis Poncet
- LPTMC, CNRS/Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France.,Department of Physics, The University of Tokyo, Hongo 7-3-1, Tokyo, 113-0033, Japan
| | - Olivier Bénichou
- LPTMC, CNRS/Sorbonne Université, 4 Place Jussieu, F-75005 Paris, France
| | - Vincent Démery
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, Paris, France.,Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Daiki Nishiguchi
- Department of Physics, The University of Tokyo, Hongo 7-3-1, Tokyo, 113-0033, Japan
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15
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Emergence of scale-free smectic rivers and critical depinning in emulsions driven through disorder. Proc Natl Acad Sci U S A 2020; 117:13914-13920. [PMID: 32513726 DOI: 10.1073/pnas.2000681117] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
During the past 60 min, oil companies have extracted 6 trillion liters of oil from the ground, thereby giving a striking illustration of the impact of multiphase flows on the world economy. From a fundamental perspective, we largely understand the dynamics of interfaces separating immiscible fluids driven through heterogeneous environments. In stark contrast, the basic mechanisms ruling the transport of fragmented fluids, such as foams and emulsions, remain elusive with studies mostly limited to isolated droplets and bubbles. Here, we demonstrate that the mobilization of emulsion driven through model disordered media is a critical plastic depinning transition. To elucidate this collective dynamics, we track the trajectories of hundreds of thousands of microfluidic droplets advected through random lattices of pinning sites. Their dynamics reveals that macroscopic mobilization only requires the coordinated motion of small groups of particles and does not involve any large-scale avalanches. Criticality arises from the interplay between contact and hydrodynamic interaction, which channel seemingly erratic depinning events along smectic river networks correlated over system spanning scales. Beyond the specifics of emulsion transport, we close our article discussing the similarities and profound differences with the plastic depinning transitions of driven flux lines in high-T c superconductors, charged colloids, and grain transport in eroded sand beds.
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16
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Frusawa H. Transverse Density Fluctuations around the Ground State Distribution of Counterions near One Charged Plate: Stochastic Density Functional View. ENTROPY 2019; 22:e22010034. [PMID: 33285809 PMCID: PMC7516456 DOI: 10.3390/e22010034] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/10/2019] [Revised: 12/17/2019] [Accepted: 12/23/2019] [Indexed: 01/22/2023]
Abstract
We consider the Dean–Kawasaki (DK) equation of overdamped Brownian particles that forms the basis of the stochastic density functional theory. Recently, the linearized DK equation has successfully reproduced the full Onsager theory of symmetric electrolyte conductivity. In this paper, the linear DK equation is applied to investigate density fluctuations around the ground state distribution of strongly coupled counterions near a charged plate, focusing especially on the transverse dynamics along the plate surface. Consequently, we find a crossover scale above which the transverse density dynamics appears frozen and below which diffusive behavior of counterions can be observed on the charged plate. The linear DK equation provides a characteristic length of the dynamical crossover that is similar to the Wigner–Seitz radius used in equilibrium theory for the 2D one-component plasma, which is our main result. Incidentally, general representations of longitudinal dynamics vertical to the plate further suggest the existence of advective and electrical reverse-flows; these effects remain to be quantitatively investigated.
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Affiliation(s)
- Hiroshi Frusawa
- Laboratory of Statistical Physics, Kochi University of Technology, Tosa-Yamada, Kochi 782-8502, Japan
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17
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Reichhardt CJO, Reichhardt C. Disordering, clustering, and laning transitions in particle systems with dispersion in the Magnus term. Phys Rev E 2019; 99:012606. [PMID: 30780381 DOI: 10.1103/physreve.99.012606] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2018] [Indexed: 11/07/2022]
Abstract
We numerically examine a two-dimensional system of repulsively interacting particles with dynamics that are governed by both a damping term and a Magnus term. The magnitude of the Magnus term has one value for half of the particles and a different value for the other half of the particles. In the absence of a driving force, the particles form a triangular lattice, while when a driving force is applied, we find that there is a critical drive above which a Magnus-induced disordering transition can occur even if the difference in the Magnus term between the two particle species is as small as one percent. The transition arises due to the different Hall angles of the two species, which causes their motion to decouple at the critical drive. At higher drives, the disordered state can undergo both species and density phase separation into a density-modulated stripe that is oriented perpendicular to the driving direction. We observe several additional phases that occur as a function of drive and Magnus force disparity, including a variety of density-modulated diagonal-laned phases. In general, we find a much richer variety of states compared to systems of oppositely driven overdamped Yukawa particles. We discuss the implications of our work for skyrmion systems, where we predict that even for small skyrmion dispersities, a drive-induced disordering transition can occur along with clustering phases and pattern-forming states.
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Affiliation(s)
- C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Tracer diffusion in crowded narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:443001. [PMID: 30211693 DOI: 10.1088/1361-648x/aae13a] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.
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Affiliation(s)
- O Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 4 Place Jussieu, 75252 Paris Cedex 05, France
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Reichhardt C, Thibault J, Papanikolaou S, Reichhardt CJO. Laning and clustering transitions in driven binary active matter systems. Phys Rev E 2018; 98:022603. [PMID: 30253470 DOI: 10.1103/physreve.98.022603] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2018] [Indexed: 06/08/2023]
Abstract
It is well known that a binary system of nonactive disks that experience driving in opposite directions exhibits jammed, phase separated, disordered, and laning states. In active matter systems, such as a crowd of pedestrians, driving in opposite directions is common and relevant, especially in conditions which are characterized by high pedestrian density and emergency. In such cases, the transition from laning to disordered states may be associated with the onset of a panic state. We simulate a laning system containing active disks that obey run-and-tumble dynamics, and we measure the drift mobility and structure as a function of run length, disk density, and drift force. The activity of each disk can be quantified based on the correlation timescale of the velocity vector. We find that in some cases, increasing the activity can increase the system mobility by breaking up jammed configurations; however, an activity level that is too high can reduce the mobility by increasing the probability of disk-disk collisions. In the laning state, the increase of activity induces a sharp transition to a disordered strongly fluctuating state with reduced mobility. We identify a novel drive-induced clustered laning state that remains stable even at densities below the activity-induced clustering transition of the undriven system. We map out the dynamic phase diagrams highlighting transitions between the different phases as a function of activity, drive, and density.
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Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J Thibault
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Department of Mechanical and Aerospace Engineering, Western Virginia University, Morgantown, West Virginia 26506, USA
| | - S Papanikolaou
- Department of Mechanical and Aerospace Engineering, Western Virginia University, Morgantown, West Virginia 26506, USA
- Department of Physics, Western Virginia University, Morgantown, West Virginia 26506, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Kliushnychenko OV, Lukyanets SP. Effects of collectively induced scattering of gas stream by impurity ensembles: Shock-wave enhancement and disorder-stimulated nonlinear screening. Phys Rev E 2018; 98:020101. [PMID: 30253471 DOI: 10.1103/physreve.98.020101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2017] [Indexed: 06/08/2023]
Abstract
We report on specific effects of collective scattering for a cloud of heavy impurities exposed to a gas stream. Formation is presented of a common density perturbation and shock waves, both generated collectively by a system of scatterers at sudden application of the stream-inducing external field. Our results demonstrate that (i) the scattering of gas stream can be essentially amplified, due to nonlinear collective effects, upon fragmentation of a solid obstacle into a cluster of impurities (heterogeneously fractured obstacle); (ii) a cluster of disordered impurities can produce considerably stronger scattering accompanied by enhanced and accelerated shock wave, as compared to a regularly ordered cluster. We also show that the final steady-state density distribution is formed as a residual perturbation left after the shock front passage. In particular, a kinklike steady distribution profile can be formed as a result of shock front stopping effect. The possibility of the onset of solitary diffusive density waves, reminiscent of precursor solitons, is shown and briefly discussed.
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Affiliation(s)
- O V Kliushnychenko
- Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kiev, Ukraine
| | - S P Lukyanets
- Institute of Physics, NAS of Ukraine, Prospect Nauky 46, 03028 Kiev, Ukraine
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Dutta S, Chakrabarti J. Transient dynamical responses of a charged binary colloid in an electric field. SOFT MATTER 2018; 14:4477-4482. [PMID: 29808207 DOI: 10.1039/c7sm02552a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
In a model system of oppositely charged colloids we study via Brownian dynamics simulation the dynamical response as the system approaches steady states upon application of a constant electric field. The system is known to form patterns of like charges in the transverse plane to the field that are elongated along the field as lanes. We show that an increase in structural heterogeneity leads to non-Gaussian tails in the probability distribution of particle displacements [self van Hove functions (self-vHfs)]. The self-diffusion coefficient depends upon the time of the observations and consequently indicates aging in the system. However, the anomalies in the self-vHfs and diffusion do not appear during the melting of the structures.
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Affiliation(s)
- Suman Dutta
- Department of Chemical, Biological and Macro-Molecular Sciences, S. N. Bose National Centre for Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700106, India.
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Reichhardt C, Reichhardt CJO. Velocity force curves, laning, and jamming for oppositely driven disk systems. SOFT MATTER 2018; 14:490-498. [PMID: 29214253 DOI: 10.1039/c7sm02162c] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Using simulations we examine a two-dimensional disk system in which two disk species are driven in opposite directions. We measure the average velocity of one of the species versus the applied driving force and identify four phases as function of drive and disk density: a jammed state, a completely phase separated state, a continuously mixing phase, and a laning phase. The transitions between these phases are correlated with jumps in the velocity-force curves that are similar to the behavior observed at dynamical phase transitions in driven particle systems with quenched disorder such as vortices in type-II superconductors. In some cases the transitions between phases are associated with negative differential mobility in which the average absolute velocity of either species decreases with increasing drive. We also consider the situation where the drive is applied to only one species as well as systems in which both species are driven in the same direction with different drive amplitudes. We show that the phases are robust against the addition of thermal fluctuations. Finally, we discuss how the transitions we observe could be related to absorbing phase transitions where a system in a phase separated or laning regime organizes to a state in which contacts between the disks no longer occur and dynamical fluctuations are lost.
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Affiliation(s)
- C Reichhardt
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
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Vasilyev OA, Bénichou O, Mejía-Monasterio C, Weeks ER, Oshanin G. Cooperative behavior of biased probes in crowded interacting systems. SOFT MATTER 2017; 13:7617-7624. [PMID: 28976526 DOI: 10.1039/c7sm00865a] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We study, via extensive numerical simulations, dynamics of a crowded mixture of mutually interacting (with a short-range repulsive potential) colloidal particles immersed in a suspending solvent, acting as a heat bath. The mixture consists of a majority component - neutrally buoyant colloids subject to internal stimuli only, and a minority component - biased probes (BPs) also subject to a constant force. In such a system each of the BPs alters the distribution of the colloidal particles in its vicinity, driving their spatial distribution out of equilibrium. This induces effective long-range interactions and multi-tag correlations between the BPs, mediated by an out-of-equilibrium majority component, and prompts the BPs to move collectively assembling in clusters. We analyse the size-distribution of the self-assembling clusters in the steady-state, their specific force-velocity relations and also properties of the effective interactions emerging between the BPs.
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Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
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Critical mingling and universal correlations in model binary active liquids. Nat Commun 2017; 8:15969. [PMID: 28656963 PMCID: PMC5493750 DOI: 10.1038/ncomms15969] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 05/15/2017] [Indexed: 11/12/2022] Open
Abstract
Ensembles of driven or motile bodies moving along opposite directions are generically reported to self-organize into strongly anisotropic lanes. Here, building on a minimal model of self-propelled bodies targeting opposite directions, we first evidence a critical phase transition between a mingled state and a phase-separated lane state specific to active particles. We then demonstrate that the mingled state displays algebraic structural correlations also found in driven binary mixtures. Finally, constructing a hydrodynamic theory, we single out the physical mechanisms responsible for these universal long-range correlations typical of ensembles of oppositely moving bodies. Self-driven particles can drive the system out of equilibrium without the help of external forces. Here Bain et al. develop a model for two groups of motile bodies targeting opposite directions and show that the system exhibits critical behaviour as a function of particle density.
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