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Bassu G, Laurati M, Fratini E. Transition from active motion to anomalous diffusion for Bacillus subtilis confined in hydrogel matrices. Colloids Surf B Biointerfaces 2024; 236:113797. [PMID: 38431996 DOI: 10.1016/j.colsurfb.2024.113797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2023] [Revised: 12/06/2023] [Accepted: 02/11/2024] [Indexed: 03/05/2024]
Abstract
We investigate the motility of B. subtilis under different degrees of confinement induced by transparent porous hydrogels. The dynamical behavior of the bacteria at short times is linked to characteristic parameters describing the hydrogel porosity. Mean squared displacements (MSDs) reveal that the run-and-tumble dynamics of unconfined B. subtilis progressively turns into sub-diffusive motion with increasing confinement. Correspondingly, the median instantaneous velocity of bacteria decreases and becomes more narrowly distributed, while the reorientation rate increases and reaches a plateau value. Analyzing single-trajectories, we show that the average dynamical behavior is the result of complex displacements, in which active, diffusive and sub-diffusive segments coexist. For small and moderate confinements, the number of active segments reduces, while the diffusive and sub-diffusive segments increase. The alternation of sub-diffusion, diffusion and active motion along the same trajectory can be described as a hopping ad trapping motion, in which hopping events correspond to displacements with an instantaneous velocity exceeding the corresponding mean value along a trajectory. Different from previous observations, escape from local trapping occurs for B. subtilis through active runs but also diffusion. Interestingly, the contribution of diffusion is maximum at intermediate confinements. At sufficiently long times transport coefficients estimated from the experimental MSDs under different degrees of confinement can be reproduced using a recently proposed hopping and trapping model. Finally, we propose a quantitative relationship linking the median velocity of confined and unconfined bacteria through the characteristic confinement length of the hydrogel matrix. Our work provides new insights for the bacterial motility in complex media that mimic natural environments and are relevant to important problems like sterilization, water purification, biofilm formation, membrane permeation and bacteria separation.
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Affiliation(s)
- Gavino Bassu
- Department of Chemistry "Ugo Schiff", Via della Lastruccia 3, Sesto Fiorentino 50019, Italy; Consorzio per lo Sviluppo dei Sistemi a Grande Interfase (CSGI)), Via della Lastruccia 3, Sesto Fiorentino 50019, Italy
| | - Marco Laurati
- Department of Chemistry "Ugo Schiff", Via della Lastruccia 3, Sesto Fiorentino 50019, Italy; Consorzio per lo Sviluppo dei Sistemi a Grande Interfase (CSGI)), Via della Lastruccia 3, Sesto Fiorentino 50019, Italy.
| | - Emiliano Fratini
- Department of Chemistry "Ugo Schiff", Via della Lastruccia 3, Sesto Fiorentino 50019, Italy; Consorzio per lo Sviluppo dei Sistemi a Grande Interfase (CSGI)), Via della Lastruccia 3, Sesto Fiorentino 50019, Italy
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Loewe B, Kozhukhov T, Shendruk TN. Anisotropic run-and-tumble-turn dynamics. SOFT MATTER 2024; 20:1133-1150. [PMID: 38226730 PMCID: PMC10828927 DOI: 10.1039/d3sm00589e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 12/12/2023] [Indexed: 01/17/2024]
Abstract
Run-and-tumble processes successfully model several living systems. While studies have typically focused on particles with isotropic tumbles, recent examples exhibit "tumble-turns", in which particles undergo 90° tumbles and so possess explicitly anisotropic dynamics. We study the consequences of such tumble-turn anisotropicity at both short and long-time scales. We model run-and-tumble-turn particles as self-propelled particles subjected to an angular potential that favors directions of movement parallel to Cartesian axes. Using agent-based simulations, we study the effects of the interplay between rotational diffusion and an aligning potential on the particles' trajectories, which leads to the right-angled turns. We demonstrate that the long-time effect is to alter the tumble-turn time, which governs the long-time dynamics. In particular, when normalized by this timescale, trajectories become independent of the underlying details of the potential. As such, we develop a simplified continuum theory, which quantitatively agrees with agent-based simulations. We find that the purely diffusive hydrodynamic limit still exhibits anisotropic features at intermediate times and conclude that the transition to diffusive dynamics precedes the transition to isotropic dynamics. By considering short-range repulsive and alignment particle-particle interactions, we show how the anisotropic features of a single particle are inherited by the global order of the system. We hope this work will shed light on how active systems can extend local anisotropic properties to macroscopic scales, which might be important in biological processes occurring in anisotropic environments.
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Affiliation(s)
- Benjamin Loewe
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Timofey Kozhukhov
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
| | - Tyler N Shendruk
- SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
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Rojas-Vega M, de Castro P, Soto R. Mixtures of self-propelled particles interacting with asymmetric obstacles. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:95. [PMID: 37819444 DOI: 10.1140/epje/s10189-023-00354-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 09/22/2023] [Indexed: 10/13/2023]
Abstract
In the presence of an obstacle, active particles condensate into a surface "wetting" layer due to persistent motion. If the obstacle is asymmetric, a rectification current arises in addition to wetting. Asymmetric geometries are therefore commonly used to concentrate microorganisms like bacteria and sperms. However, most studies neglect the fact that biological active matter is diverse, composed of individuals with distinct self-propulsions. Using simulations, we study a mixture of "fast" and "slow" active Brownian disks in two dimensions interacting with large half-disk obstacles. With this prototypical obstacle geometry, we analyze how the stationary collective behavior depends on the degree of self-propulsion "diversity," defined as proportional to the difference between the self-propulsion speeds, while keeping the average self-propulsion speed fixed. A wetting layer rich in fast particles arises. The rectification current is amplified by speed diversity due to a superlinear dependence of rectification on self-propulsion speed, which arises from cooperative effects. Thus, the total rectification current cannot be obtained from an effective one-component active fluid with the same average self-propulsion speed, highlighting the importance of considering diversity in active matter.
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Affiliation(s)
- Mauricio Rojas-Vega
- Institute of Science and Technology Austria, Am Campus 1, 3400, Klosterneuburg, Austria
| | - Pablo de Castro
- ICTP South American Institute for Fundamental Research and Instituto de Física Teórica, Universidade Estadual Paulista - UNESP, São Paulo, 01140-070, Brazil.
| | - Rodrigo Soto
- Departamento de Física, FCFM, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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de Castro P, Urbina F, Norambuena A, Guzmán-Lastra F. Sequential epidemic-like spread between agglomerates of self-propelled agents in one dimension. Phys Rev E 2023; 108:044104. [PMID: 37978653 DOI: 10.1103/physreve.108.044104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate between them, and disease recovery rate. While the emergence of agglomerates permits early interventions, it also explains longer real epidemics. In this work, we study the spread of susceptible-infected-recovered (SIR) epidemics (or any sort of information exchange by contact) in one-dimensional spatially structured systems. By working in one dimension, we establish a necessary foundation for future investigation in higher dimensions and mimic micro-organisms in narrow channels. We employ a model of self-propelled particles which spontaneously form multiple clusters. For a lower rate of stochastic reorientation, particles have a higher tendency to agglomerate and therefore the clusters become larger and less numerous. We examine the time evolution averaged over many epidemics and how it is affected by the existence of clusters through the eventual recovery of infected particles before reaching new clusters. New terms appear in the SIR differential equations in the last epidemic stages. We show how the final number of ever-infected individuals depends nontrivially on single-individual parameters. In particular, the number of ever-infected individuals first increases with the reorientation rate since particles escape sooner from clusters and spread the disease. For higher reorientation rate, travel between clusters becomes too diffusive and the clusters too small, decreasing the number of ever-infected individuals.
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Affiliation(s)
- Pablo de Castro
- ICTP-South American Institute for Fundamental Research - Instituto de Física Teórica da UNESP, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 São Paulo, Brazil
| | - Felipe Urbina
- Centro Multidisciplinario de Física, Universidad Mayor, Huechuraba, 8580745 Santiago, Chile
| | - Ariel Norambuena
- Centro Multidisciplinario de Física, Universidad Mayor, Huechuraba, 8580745 Santiago, Chile
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Villa-Torrealba A, Navia S, Soto R. Kinetic modeling of the chemotactic process in run-and-tumble bacteria. Phys Rev E 2023; 107:034605. [PMID: 37072994 DOI: 10.1103/physreve.107.034605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 03/14/2023] [Indexed: 04/20/2023]
Abstract
The chemotactic process of run-and-tumble bacteria results from modulating the tumbling rate in response to changes in chemoattractant gradients felt by the bacteria. The response has a characteristic memory time and is subject to important fluctuations. These ingredients are considered in a kinetic description of chemotaxis, allowing the computation of the stationary mobility and the relaxation times needed to reach the steady state. For large memory times, these relaxation times become large, implying that finite-time measurements give rise to nonmonotonic currents as a function of the imposed chemoattractant gradient, contrary to the stationary regime where the response is monotonic. The case of an inhomogeneous signal is analyzed. Contrary to the usual Keller-Segel model, the response is nonlocal, and the bacterial profile is smoothed with a characteristic length that grows with the memory time. Finally, the case of traveling signals is considered, where appreciable differences appear compared to memoryless chemotactic descriptions.
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Affiliation(s)
- Andrea Villa-Torrealba
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Simón Navia
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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Rojas-Vega M, de Castro P, Soto R. Wetting dynamics by mixtures of fast and slow self-propelled particles. Phys Rev E 2023; 107:014608. [PMID: 36797971 DOI: 10.1103/physreve.107.014608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Accepted: 01/06/2023] [Indexed: 01/26/2023]
Abstract
We study active surface wetting using a minimal model of bacteria that takes into account the intrinsic motility diversity of living matter. A mixture of "fast" and "slow" self-propelled Brownian particles is considered in the presence of a wall. The evolution of the wetting layer thickness shows an overshoot before stationarity and its composition evolves in two stages, equilibrating after a slow elimination of excess particles. Nonmonotonic evolutions are shown to arise from delayed avalanches towards the dilute phase combined with the emergence of a transient particle front.
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Affiliation(s)
| | - Pablo de Castro
- ICTP South American Institute for Fundamental Research & Instituto de Física Teórica, Universidade Estadual Paulista - UNESP, 01140-070 São Paulo, Brazil
| | - Rodrigo Soto
- Departamento de Física, FCFM, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile
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Shaebani MR, Rieger H, Sadjadi Z. Kinematics of persistent random walkers with two distinct modes of motion. Phys Rev E 2022; 106:034105. [PMID: 36266824 DOI: 10.1103/physreve.106.034105] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti)persistence. We present an analytical formalism to provide a quantitative link between these two microscopic statistical properties of the trajectory and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain an exact expression for the time evolution of the mean square displacement over all timescales and provide a recipe to obtain higher displacement moments. Our approach enables us to disentangle the combined effects of velocity, persistence, and switching probabilities between the two states on the kinematics of particles in a wide range of stochastic active or passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.
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Affiliation(s)
- M Reza Shaebani
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Heiko Rieger
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Zeinab Sadjadi
- Department of Theoretical Physics and Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
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Menzel AM. Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions. J Chem Phys 2022; 157:011102. [DOI: 10.1063/5.0093598] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.
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Affiliation(s)
- Andreas M. Menzel
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
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9
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Scagliarini A, Pagonabarraga I. Hydrodynamic and geometric effects in the sedimentation of model run-and-tumble microswimmers. SOFT MATTER 2022; 18:2407-2413. [PMID: 35266484 PMCID: PMC9904398 DOI: 10.1039/d1sm01594j] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/08/2021] [Accepted: 02/15/2022] [Indexed: 06/14/2023]
Abstract
The sedimentation process in an active suspension is the result of the competition between gravity and the autonomous motion of particles. We carry out simulations of run-and-tumble squirmers that move in a fluid medium, focusing on the dependence of the non-equilibrium steady state on the swimming properties. We find that for large enough activity, the density profiles are no longer simple exponentials; we recover the numerical results through the introduction of a local effective temperature, suggesting that the breakdown of the Perrin-like exponential form is a collective effect due to fluid-mediated dynamic correlations among particles. We show that analogous concepts can also fit the case of active non-motile particles, for which we report the first study of this kind. Moreover, we provide evidence of scenarios where the solvent hydrodynamics induces non-local effects which require the full three-dimensional dynamics to be taken into account in order to understand sedimentation in active suspensions. Finally, analyzing the statistics of the orientations of microswimmers, the emergence of a height-dependent polar order in the system is discussed.
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Affiliation(s)
- Andrea Scagliarini
- IAC-CNR, Istituto per le Applicazioni del Calcolo "Mauro Picone", Via dei Taurini 19, 00185 Rome, Italy.
- INFN, Sezione Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Ignacio Pagonabarraga
- CECAM, Centre Européen de Calcul Atomique et Moléculaire, Ecole Polytechnique Fédérale de Lausanne, Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, Carrer de Martí i Franquès 1, 08028 Barcelona, Spain
- Universitat de Barcelona, Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
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de Castro P, M Rocha F, Diles S, Soto R, Sollich P. Diversity of self-propulsion speeds reduces motility-induced clustering in confined active matter. SOFT MATTER 2021; 17:9926-9936. [PMID: 34676388 DOI: 10.1039/d1sm01009c] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Self-propelled swimmers such as bacteria agglomerate into clusters as a result of their persistent motion. In 1D, those clusters do not coalesce macroscopically and the stationary cluster size distribution (CSD) takes an exponential form. We develop a minimal lattice model for active particles in narrow channels to study how clustering is affected by the interplay between self-propulsion speed diversity and confinement. A mixture of run-and-tumble particles with a distribution of self-propulsion speeds is simulated in 1D. Particles can swap positions at rates proportional to their relative self-propulsion speed. Without swapping, we find that the average cluster size Lc decreases with diversity and follows a non-arithmetic power mean of the single-component Lc's, unlike the case of tumbling-rate diversity previously studied. Effectively, the mixture is thus equivalent to a system of identical particles whose self-propulsion speed is the harmonic mean self-propulsion speed of the mixture. With swapping, particles escape more quickly from clusters. As a consequence, Lc decreases with swapping rates and depends less strongly on diversity. We derive a dynamical equilibrium theory for the CSDs of binary and fully polydisperse systems. Similarly to the clustering behaviour of one-component models, our qualitative results for mixtures are expected to be universal across active matter. Using literature experimental values for the self-propulsion speed diversity of unicellular swimmers known as choanoflagellates, which naturally differentiate into slower and faster cells, we predict that the error in estimating their Lcvia one-component models which use the conventional arithmetic mean self-propulsion speed is around 30%.
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Affiliation(s)
- Pablo de Castro
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
| | | | - Saulo Diles
- Faculdade de Física, Universidade Federal do Pará, Campus Salinópolis, Rua Raimundo Santana Cruz S/N, 68721-000, Salinópolis, Pará, Brazil
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
| | - Peter Sollich
- Disordered Systems Group, Department of Mathematics, King's College London, London, UK
- Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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de Castro P, Diles S, Soto R, Sollich P. Active mixtures in a narrow channel: motility diversity changes cluster sizes. SOFT MATTER 2021; 17:2050-2061. [PMID: 33475129 DOI: 10.1039/d0sm02052d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The persistent motion of bacteria produces clusters with a stationary cluster size distribution (CSD). Here we develop a minimal model for bacteria in a narrow channel to assess the relative importance of motility diversity (i.e. polydispersity in motility parameters) and confinement. A mixture of run-and-tumble particles with a distribution of tumbling rates (denoted generically by α) is considered on a 1D lattice. Particles facing each other cross at constant rate, rendering the lattice quasi-1D. To isolate the role of diversity, the global average α stays fixed. For a binary mixture with no particle crossing, the average cluster size (Lc) increases with the diversity as lower-α particles trap higher-α ones for longer. At finite crossing rate, particles escape from the clusters sooner, making Lc smaller and the diversity less important, even though crossing can enhance demixing of particle types between the cluster and gas phases. If the crossing rate is increased further, the clusters become controlled by particle crossing. We also consider an experiment-based continuous distribution of tumbling rates, revealing similar physics. Using parameters fitted from experiments with Escherichia coli bacteria, we predict that the error in estimating Lc without accounting for polydispersity is around 60%. We discuss how to find a binary system with the same CSD as the fully polydisperse mixture. An effective theory is developed and shown to give accurate expressions for the CSD, the effective α, and the average fraction of mobile particles. We give reasons why our qualitative results are expected to be valid for other active matter models and discuss the changes that would result from polydispersity in the active speed rather than in the tumbling rate.
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Affiliation(s)
- Pablo de Castro
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
| | - Saulo Diles
- Faculdade de Física, Universidade Federal do Pará, Campus Salinópolis, Rua Raimundo Santana Cruz S/N, 68721-000, Salinópolis, Pará, Brazil
| | - Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile.
| | - Peter Sollich
- Disordered Systems Group, Department of Mathematics, King's College London, London, UK and Institut für Theoretische Physik, Georg-August-Universität Göttingen, 37077 Göttingen, Germany
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