1
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Chan CW, Wu D, Qiao K, Fong KL, Yang Z, Han Y, Zhang R. Chiral active particles are sensitive reporters to environmental geometry. Nat Commun 2024; 15:1406. [PMID: 38365770 PMCID: PMC10873462 DOI: 10.1038/s41467-024-45531-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 01/24/2024] [Indexed: 02/18/2024] Open
Abstract
Chiral active particles (CAPs) are self-propelling particles that break time-reversal symmetry by orbiting or spinning, leading to intriguing behaviors. Here, we examined the dynamics of CAPs moving in 2D lattices of disk obstacles through active Brownian dynamics simulations and granular experiments with grass seeds. We find that the effective diffusivity of the CAPs is sensitive to the structure of the obstacle lattice, a feature absent in achiral active particles. We further studied the transport of CAPs in obstacle arrays under an external field and found a reentrant directional locking effect, which can be used to sort CAPs with different activities. Finally, we demonstrated that parallelogram lattices of obstacles without mirror symmetry can separate clockwise and counter-clockwise CAPs. The mechanisms of the above three novel phenomena are qualitatively explained. As such, our work provides a basis for designing chirality-based tools for single-cell diagnosis and separation, and active particle-based environmental sensors.
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Affiliation(s)
- Chung Wing Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Daihui Wu
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Kaiyao Qiao
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Kin Long Fong
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
- Physik-Department, Technische Universität München, James-Franck-Straße 1, 85748, Garching, Germany
| | - Zhiyu Yang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Yilong Han
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR
| | - Rui Zhang
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR.
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2
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Marchello R, Colombi A, Preziosi L, Giverso C. A non local model for cell migration in response to mechanical stimuli. Math Biosci 2024; 368:109124. [PMID: 38072125 DOI: 10.1016/j.mbs.2023.109124] [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: 04/07/2023] [Revised: 11/17/2023] [Accepted: 12/05/2023] [Indexed: 12/22/2023]
Abstract
Cell migration is one of the most studied phenomena in biology since it plays a fundamental role in many physiological and pathological processes such as morphogenesis, wound healing and tumorigenesis. In recent years, researchers have performed experiments showing that cells can migrate in response to mechanical stimuli of the substrate they adhere to. Motion towards regions of the substrate with higher stiffness is called durotaxis, while motion guided by the stress or the deformation of the substrate itself is called tensotaxis. Unlike chemotaxis (i.e. the motion in response to a chemical stimulus), these migratory processes are not yet fully understood from a biological point of view. In this respect, we present a mathematical model of single-cell migration in response to mechanical stimuli, in order to simulate these two processes. Specifically, the cell moves by changing its direction of polarization and its motility according to material properties of the substrate (e.g., stiffness) or in response to proper scalar measures of the substrate strain or stress. The equations of motion of the cell are non-local integro-differential equations, with the addition of a stochastic term to account for random Brownian motion. The mechanical stimulus to be integrated in the equations of motion is defined according to experimental measurements found in literature, in the case of durotaxis. Conversely, in the case of tensotaxis, substrate strain and stress are given by the solution of the mechanical problem, assuming that the extracellular matrix behaves as a hyperelastic Yeoh's solid. In both cases, the proposed model is validated through numerical simulations that qualitatively reproduce different experimental scenarios.
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Affiliation(s)
- Roberto Marchello
- Mathematics Area, SISSA (International School for Advanced Studies), Via Bonomea 265, Trieste, 34136, Italy
| | - Annachiara Colombi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Luigi Preziosi
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy
| | - Chiara Giverso
- Department of Mathematical Sciences G. L. Lagrange, Politecnico di Torino, C.so Duca degli Abruzzi 24, Torino, 10129, Italy.
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3
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Stuhlmüller NCX, Farrokhzad F, Kuświk P, Stobiecki F, Urbaniak M, Akhundzada S, Ehresmann A, Fischer TM, de Las Heras D. Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes. Nat Commun 2023; 14:7517. [PMID: 37980403 PMCID: PMC10657436 DOI: 10.1038/s41467-023-43390-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 11/07/2023] [Indexed: 11/20/2023] Open
Abstract
Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.
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Affiliation(s)
- Nico C X Stuhlmüller
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - Farzaneh Farrokhzad
- Experimatalphysik X, Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - Piotr Kuświk
- Institute of Molecular Physics, Polish Academy of Sciences, 60-179, Poznań, Poland
| | - Feliks Stobiecki
- Institute of Molecular Physics, Polish Academy of Sciences, 60-179, Poznań, Poland
| | - Maciej Urbaniak
- Institute of Molecular Physics, Polish Academy of Sciences, 60-179, Poznań, Poland
| | - Sapida Akhundzada
- Institute of Physics and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, D-34132, Kassel, Germany
| | - Arno Ehresmann
- Institute of Physics and Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), University of Kassel, D-34132, Kassel, Germany
| | - Thomas M Fischer
- Experimatalphysik X, Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany
| | - Daniel de Las Heras
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440, Bayreuth, Germany.
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4
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Moore F, Russo J, Liverpool TB, Royall CP. Active Brownian particles in random and porous environments. J Chem Phys 2023; 158:104907. [PMID: 36922118 DOI: 10.1063/5.0131340] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/23/2023] Open
Abstract
The transport of active particles may occur in complex environments, in which it emerges from the interplay between the mobility of the active components and the quenched disorder of the environment. Here, we explore the structural and dynamical properties of active Brownian particles (ABPs) in random environments composed of fixed obstacles in three dimensions. We consider different arrangements of the obstacles. In particular, we consider two particular situations corresponding to experimentally realizable settings. First, we model pinning particles in (non-overlapping) random positions and, second, in a percolating gel structure and provide an extensive characterization of the structure and dynamics of ABPs in these complex environments. We find that the confinement increases the heterogeneity of the dynamics, with new populations of absorbed and localized particles appearing close to the obstacles. This heterogeneity has a profound impact on the motility induced phase separation exhibited by the particles at high activity, ranging from nucleation and growth in random disorder to a complex phase separation in porous environments.
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Affiliation(s)
- Fergus Moore
- Bristol Centre for Functional Nanomaterials, University of Bristol, Bristol BS8 1FD, United Kingdom
| | - John Russo
- Department of Physics, Sapienza University of Rome, P.le Aldo Moro 5, 00185 Rome, Italy
| | | | - C Patrick Royall
- H. H. Wills Physics Laboratory, Tyndall Ave., Bristol BS8 1TL, United Kingdom
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5
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Chepizhko O, Franosch T. Resonant Diffusion of a Gravitactic Circle Swimmer. PHYSICAL REVIEW LETTERS 2022; 129:228003. [PMID: 36493425 DOI: 10.1103/physrevlett.129.228003] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Revised: 08/16/2022] [Accepted: 10/07/2022] [Indexed: 06/17/2023]
Abstract
We investigate the dynamics of a single chiral active particle subject to an external torque due to the presence of a gravitational field. Our computer simulations reveal an arbitrarily strong increase of the long-time diffusivity of the gravitactic agent when the external torque approaches the intrinsic angular drift. We provide analytic expressions for the mean-square displacement in terms of eigenfunctions and eigenvalues of the noisy-driven-pendulum problem. The pronounced maximum in the diffusivity is then rationalized by the vanishing of the lowest eigenvalues of the Fokker-Planck equation for the angular motion as the rotational diffusion decreases and the underlying classical bifurcation is approached. A simple harmonic-oscillator picture for the barrier-dominated motion provides a quantitative description for the onset of the resonance while its range of validity is determined by the crossover to a critical-fluctuation-dominated regime.
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Affiliation(s)
- Oleksandr Chepizhko
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
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6
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Li W, Li L, Shi Q, Yang M, Zheng N. Chiral separation of rotating robots through obstacle arrays. POWDER TECHNOL 2022. [DOI: 10.1016/j.powtec.2022.117671] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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7
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Park S, Kim H, Wang Y, Eom DS, Allard J. Zebrafish airinemes optimize their shape between ballistic and diffusive search. eLife 2022; 11:75690. [PMID: 35467525 PMCID: PMC9098217 DOI: 10.7554/elife.75690] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 04/25/2022] [Indexed: 11/13/2022] Open
Abstract
In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing communication, cellular protrusions must find their target cell. Here we demonstrate that the shapes of airinemes in zebrafish are consistent with a finite persistent random walk model. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive search (highly curved, random). We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme's source, finding that there is a theoretical trade-off between search optimality and directional information. This provides a framework to characterize the shape, and performance objectives, of non-canonical cellular protrusions in general.
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Affiliation(s)
- Sohyeon Park
- Center for Complex Biological Systems, University of California, Irvine, Irvine, United States
| | - Hyunjoong Kim
- Department of Mathematics, University of Pennsylvania, Pennsylvania, United States
| | - Yi Wang
- Center for Complex Biological Systems, University of California, Irvine, Irvine, United States
| | - Dae Seok Eom
- Center for Complex Biological Systems, University of California, Irvine, Irvine, United States
| | - Jun Allard
- dDepartment of Physics and Astronomy, University of California, Irvine, Irvine, United States
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Forgács P, Libál A, Reichhardt C, Reichhardt CJO. Active matter shepherding and clustering in inhomogeneous environments. Phys Rev E 2021; 104:044613. [PMID: 34781504 DOI: 10.1103/physreve.104.044613] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2021] [Accepted: 10/08/2021] [Indexed: 11/07/2022]
Abstract
We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.
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Affiliation(s)
- P Forgács
- Mathematics and Computer Science Department, Babeş-Bolya University, Cluj 400084, Romania
| | - A Libál
- Mathematics and Computer Science Department, Babeş-Bolya University, Cluj 400084, Romania
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, 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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9
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Submersed micropatterned structures control active nematic flow, topology, and concentration. Proc Natl Acad Sci U S A 2021; 118:2106038118. [PMID: 34535551 DOI: 10.1073/pnas.2106038118] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/24/2021] [Indexed: 01/10/2023] Open
Abstract
Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.
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10
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Reichhardt C, Reichhardt CJO. Clogging, dynamics, and reentrant fluid for active matter on periodic substrates. Phys Rev E 2021; 103:062603. [PMID: 34271652 DOI: 10.1103/physreve.103.062603] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Accepted: 05/20/2021] [Indexed: 12/14/2022]
Abstract
We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity, while at higher activity, the density becomes increasingly heterogeneous and an active clogged state emerges in which the mobility is strongly reduced. For driving along nonsymmetry or incommensurate directions, there are two different clogging behaviors consisting of a drive-dependent clogged state in the low activity thermal limit and a drive-independent clogged state at high activity. These regimes are separated by a uniform flowing liquid at intermediate activity. There is a critical activity level above which the thermal clogged state does not occur, as well as an optimal activity level that maximizes the disk mobility. Thermal clogged states are dependent on the driving direction while active clogged states are not. In the low activity regime, diluting the obstacles produces a monotonic increase in the mobility; however, for large activities, the mobility is more robust against obstacle dilution. We also examine the velocity-force curves for driving along nonsymmetry directions and find that they are linear when the activity is low or intermediate but become nonlinear at high activity and show behavior similar to that found for the plastic depinning of solids. At higher drives, the active clustering is lost. For low activity, we also find a reentrant fluid phase, where the system transitions from a high mobility fluid at low drives to a clogged state at higher drives and then back into another fluid phase at very high drives. We map the regions in which the thermally clogged, partially clogged, active uniform fluid, clustered fluid, active clogged, and directionally locked states occur as a function of disk density, drift force, and activity.
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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
| | - 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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11
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Vesperini D, Montalvo G, Qu B, Lautenschläger F. Characterization of immune cell migration using microfabrication. Biophys Rev 2021; 13:185-202. [PMID: 34290841 PMCID: PMC8285443 DOI: 10.1007/s12551-021-00787-9] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 01/24/2021] [Indexed: 12/14/2022] Open
Abstract
The immune system provides our defense against pathogens and aberrant cells, including tumorigenic and infected cells. Motility is one of the fundamental characteristics that enable immune cells to find invading pathogens, control tissue damage, and eliminate primary developing tumors, even in the absence of external treatments. These processes are termed "immune surveillance." Migration disorders of immune cells are related to autoimmune diseases, chronic inflammation, and tumor evasion. It is therefore essential to characterize immune cell motility in different physiologically and pathologically relevant scenarios to understand the regulatory mechanisms of functionality of immune responses. This review is focused on immune cell migration, to define the underlying mechanisms and the corresponding investigative approaches. We highlight the challenges that immune cells encounter in vivo, and the microfabrication methods to mimic particular aspects of their microenvironment. We discuss the advantages and disadvantages of the proposed tools, and provide information on how to access them. Furthermore, we summarize the directional cues that regulate individual immune cell migration, and discuss the behavior of immune cells in a complex environment composed of multiple directional cues.
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Affiliation(s)
- Doriane Vesperini
- Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
| | - Galia Montalvo
- Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
- Biophysics, Center for Integrative Physiology and Molecular Medicine (CIPMM), School of Medicine, Saarland University, 66421 Homburg, Germany
| | - Bin Qu
- Biophysics, Center for Integrative Physiology and Molecular Medicine (CIPMM), School of Medicine, Saarland University, 66421 Homburg, Germany
- Leibniz Institute for New Materials, 66123 Saarbrücken, Germany
| | - Franziska Lautenschläger
- Department of Experimental Physics, Saarland University, 66123 Saarbrücken, Germany
- Center for Biophysics, Saarland University, 66123 Saarbrücken, Germany
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12
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Abstract
We study the behaviour of the green alga Chlamydomonas reinhardtii (CR) in the presence of neighbouring regions of different viscosity. We show that the velocity and angular diffusion of the algae decreases when the viscosity of the surrounding medium is increased. We report on a phenomenon occurring when the algae try to cross from a region of low viscosity to a highly viscous one, which causes CR to re-orient and scatter away from the interface if it is approached at a sufficiently small angle. We highlight that the effect does not occur for CR crossing from high to low viscosity regions. Lastly we show that algae do not concentrate in the region of high viscosity despite them swimming slower there. On the contrary, they concentrate in the region of low viscosity or maintain a uniform concentration profile, depending on the viscosity ratio between the two regions.
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13
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Reichhardt C, Reichhardt CJO. Directional locking effects for active matter particles coupled to a periodic substrate. Phys Rev E 2020; 102:042616. [PMID: 33212736 DOI: 10.1103/physreve.102.042616] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Accepted: 10/12/2020] [Indexed: 06/11/2023]
Abstract
Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.
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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
| | - 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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