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Nestler M, Praetorius S, Huang ZF, Löwen H, Voigt A. Active smectics on a sphere. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:185001. [PMID: 38262063 DOI: 10.1088/1361-648x/ad21a7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 01/23/2024] [Indexed: 01/25/2024]
Abstract
The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.
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Affiliation(s)
- Michael Nestler
- Institute of Scientific Computing, Technische Universität Dresden, 01062 Dresden, Germany
| | - Simon Praetorius
- Institute of Scientific Computing, Technische Universität Dresden, 01062 Dresden, Germany
| | - Zhi-Feng Huang
- Department of Physics and Astronomy, Wayne State University, Detroit, MI 48201, United States of America
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, 40225 Düsseldorf, Germany
| | - Axel Voigt
- Institute of Scientific Computing, Technische Universität Dresden, 01062 Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstr. 108, 01307 Dresden, Germany
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2
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Valdés Gómez A, Sevilla FJ. Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies. Phys Rev E 2023; 108:054117. [PMID: 38115432 DOI: 10.1103/physreve.108.054117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Accepted: 10/04/2023] [Indexed: 12/21/2023]
Abstract
We analyze fractional Brownian motion and scaled Brownian motion on the two-dimensional sphere S^{2}. We find that the intrinsic long-time correlations that characterize fractional Brownian motion collude with the specific dynamics (navigation strategies) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for S^{2} (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, nonequilibrium stationary distributions are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger et al. New J. Phys. 21, 022002 (2019)1367-263010.1088/1367-2630/ab075f; Vojta et al. Phys. Rev. E 102, 032108 (2020)2470-004510.1103/PhysRevE.102.032108]; however, in the case analyzed here, there are no boundaries that affect the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the equilibrium distribution on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times toward the stationary distribution depend on the particular value of the Hurst parameter. We also show that on S^{2}, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on S^{2}, and the numerical results obtained from our numerical method to generate ensemble of trajectories.
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Affiliation(s)
- Adriano Valdés Gómez
- Facultad de Ciencias, Universidad Nacional Autónoma de México, Alcaldía Coyoacán, C.P. 04510 Ciudad Universitaria, Ciudad de México, México
- BBVA AI Factory México
| | - Francisco J Sevilla
- Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, 01000, Ciudad de México, México
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3
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Caprini L, Marini Bettolo Marconi U, Löwen H. Entropy production and collective excitations of crystals out of equilibrium: The concept of entropons. Phys Rev E 2023; 108:044603. [PMID: 37978682 DOI: 10.1103/physreve.108.044603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2023] [Accepted: 09/21/2023] [Indexed: 11/19/2023]
Abstract
We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.
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Affiliation(s)
- L Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
| | - U Marini Bettolo Marconi
- Physics Department, Scuola di Scienze e Tecnologie, Università di Camerino - via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy
| | - H Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II: Weiche Materie, Universitätsstrasse, 40225 Düsseldorf, Germany
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4
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Caprini L, Marini Bettolo Marconi U, Puglisi A, Löwen H. Entropons as collective excitations in active solids. J Chem Phys 2023; 159:041102. [PMID: 37486049 DOI: 10.1063/5.0156312] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2023] [Accepted: 07/05/2023] [Indexed: 07/25/2023] Open
Abstract
The vibrational dynamics of solids is described by phonons constituting basic collective excitations in equilibrium crystals. Here, we consider a non-equilibrium active solid, formed by self-propelled particles, which bring the system into a non-equilibrium steady-state. We identify novel vibrational collective excitations of non-equilibrium (active) origin, which coexist with phonons and dominate over them when the system is far from equilibrium. These vibrational excitations are interpreted in the framework of non-equilibrium physics, in particular, stochastic thermodynamics. We call them "entropons" because they are the modes of spectral entropy production (at a given frequency and wave vector). The existence of entropons could be verified in future experiments on dense self-propelled colloidal Janus particles and granular active matter, as well as in living systems, such as dense cell monolayers.
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Affiliation(s)
- Lorenzo Caprini
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
| | - Umberto Marini Bettolo Marconi
- Scuola di Scienze e Tecnologie, Università di Camerino, via Madonna delle Carceri, 62032 Camerino, Italy
- Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, Via A. Pascoli, I-06123 Perugia, Italy
| | - Andrea Puglisi
- Istituto dei Sistemi Complessi-CNR and Università di Roma Sapienza, P.le Aldo Moro 2, 00185 Rome, Italy
- INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - Hartmut Löwen
- Heinrich-Heine-Universität Düsseldorf, Institut für Theoretische Physik II-Weiche Materie, D-40225 Düsseldorf, Germany
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5
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Schönhöfer PWA, Glotzer SC. Curvature-controlled geometrical lensing behavior in self-propelled colloidal particle systems. SOFT MATTER 2022; 18:8561-8571. [PMID: 36200373 DOI: 10.1039/d2sm01012g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
In many biological systems, the curvature of the surfaces cells live on influences their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) how curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, which we explain theoretically by the nature of parallel lines in spherical and hyperbolic space. Curvature also fluidizes dense MIPS clusters due to the emergence of defect patterns disrupting the crystalline order inside the clusters. Using our findings, we engineer three confining surfaces that strategically combine regions of different curvature to produce a host of novel dynamical behaviors, including cyclic MIPS on spherocylinders, directionally biased cyclic MIPS on spherocones, and position dependent cluster fluctuations on metaballs.
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Affiliation(s)
| | - Sharon C Glotzer
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA.
- Biointerfaces Institute, University of Michigan, Ann Arbor, MI 48109, USA
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Voß J, Wittkowski R. Acoustic Propulsion of Nano- and Microcones: Dependence on the Viscosity of the Surrounding Fluid. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:10736-10748. [PMID: 35998334 DOI: 10.1021/acs.langmuir.2c00603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
This article investigates how the acoustic propulsion of cone-shaped colloidal particles that are exposed to a traveling ultrasound wave depends on the viscosity of the fluid surrounding the particles. Using acoustofluidic computer simulations, we found that the propulsion of such nano- and microcones decreases strongly and even changes sign for increasing shear viscosity. In contrast, we found only a weak dependence of the propulsion on the bulk viscosity. The obtained results are in line with the findings of previous theoretical and experimental studies.
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Affiliation(s)
- Johannes Voß
- Institute of Theoretical Physics, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
| | - Raphael Wittkowski
- Institute of Theoretical Physics, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, 48149 Münster, Germany
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7
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Activity-induced polar patterns of filaments gliding on a sphere. Nat Commun 2022; 13:2579. [PMID: 35546549 PMCID: PMC9095588 DOI: 10.1038/s41467-022-30128-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2022] [Accepted: 04/19/2022] [Indexed: 11/16/2022] Open
Abstract
Active matter systems feature the ability to form collective patterns as observed in a plethora of living systems, from schools of fish to swimming bacteria. While many of these systems move in a wide, three-dimensional environment, several biological systems are confined by a curved topology. The role played by a non-Euclidean geometry on the self-organization of active systems is not yet fully understood, and few experimental systems are available to study it. Here, we introduce an experimental setup in which actin filaments glide on the inner surface of a spherical lipid vesicle, thus embedding them in a curved geometry. We show that filaments self-assemble into polar, elongated structures and that, when these match the size of the spherical geometry, both confinement and topological constraints become relevant for the emergent patterns, leading to the formation of polar vortices and jammed states. These results experimentally demonstrate that activity-induced complex patterns can be shaped by spherical confinement and topology. Active matter exhibits a range of collective behaviors offering insights into how complex patterns can emerge at different length scales. Here, Hsu et al. confine active filaments on the spherical surface of a lipid vesicle and observe the formation of off-equator polar vortices and jammed patterns.
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8
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Bickmann J, Bröker S, Jeggle J, Wittkowski R. Analytical approach to chiral active systems: suppressed phase separation of interacting Brownian circle swimmers. J Chem Phys 2022; 156:194904. [DOI: 10.1063/5.0085122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider chirality in active systems by exemplarily studying the phase behavior of planar systems of interacting Brownian circle swimmers with a spherical shape. For this purpose, we derive a predictive field theory that is able to describe the collective dynamics of circle swimmers. The theory yields a mapping between circle swimmers and noncircling active Brownian particles and predicts that the angular propulsion of the particles leads to a suppression of their motility-induced phase separation, being in line with recent simulation results. In addition, the theory provides analytical expressions for the spinodal corresponding to the onset of motility-induced phase separation and the associated critical point as well as for their dependence on the angular propulsion of the circle swimmers. We confirm our findings by Brownian dynamics simulations. The agreement between results from theory and simulations is found to be good.
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Affiliation(s)
- Jens Bickmann
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Stephan Bröker
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Julian Jeggle
- Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
| | - Raphael Wittkowski
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster Fachbereich 11 Physik, Germany
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9
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Krause V, Voigt A. Deformable active nematic particles and emerging edge currents in circular confinements. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:14. [PMID: 35175445 PMCID: PMC8854302 DOI: 10.1140/epje/s10189-022-00162-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 01/08/2022] [Indexed: 06/14/2023]
Abstract
We consider a microscopic field theoretical approach for interacting active nematic particles. With only steric interactions the self-propulsion strength in such systems can lead to different collective behaviour, e.g. synchronized self-spinning and collective translation. The different behaviour results from the delicate interplay between internal nematic structure, particle shape deformation and particle-particle interaction. For intermediate active strength an asymmetric particle shape emerges and leads to chirality and self-spinning crystals. For larger active strength the shape is symmetric and translational collective motion emerges. Within circular confinements, depending on the packing fraction, the self-spinning regime either stabilizes positional and orientational order or can lead to edge currents and global rotation which destroys the synchronized self-spinning crystalline structure.
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Affiliation(s)
- Veit Krause
- Institut für Wissenschaftliches Rechnen, TU Dresden, 01062, Dresden, Germany
| | - Axel Voigt
- Institut für Wissenschaftliches Rechnen, TU Dresden, 01062, Dresden, Germany.
- Center for Systems Biology Dresden (CSBD), Pfotenhauerstr. 108, 01307, Dresden, Germany.
- Cluster of Excellence, Physics of Life, TU Dresden, 01062, Dresden, Germany.
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10
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James M, Suchla DA, Dunkel J, Wilczek M. Emergence and melting of active vortex crystals. Nat Commun 2021; 12:5630. [PMID: 34561437 PMCID: PMC8463610 DOI: 10.1038/s41467-021-25545-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/18/2021] [Indexed: 11/09/2022] Open
Abstract
Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.
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Affiliation(s)
- Martin James
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany
| | - Dominik Anton Suchla
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany.,Faculty of Physics, University of Göttingen, Göttingen, Germany
| | - Jörn Dunkel
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Michael Wilczek
- Max Planck Institute for Dynamics and Self-Organization (MPI DS), Göttingen, Germany. .,Faculty of Physics, University of Göttingen, Göttingen, Germany.
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11
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Gnidovec A, Čopar S. Long-range order in quadrupolar systems on spherical surfaces. SOFT MATTER 2021; 17:4874-4883. [PMID: 33890591 DOI: 10.1039/d1sm00228g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The interplay between curvature, confinement and ordering on curved manifolds, with anisotropic interactions between building blocks, takes a central role in many fields of physics. In this paper, we investigate the effects of lattice symmetry and local positional order on orientational ordering in systems of long-range interacting point quadrupoles on a sphere in the zero temperature limit. Locally triangular spherical lattices show long-range ordered quadrupolar configurations only for specific symmetric lattices as strong geometric frustration prevents general global ordering. Conversely, the ground states on Caspar-Klug lattices are more diverse, with many different symmetries depending on the position of quadrupoles within the fundamental domain. We also show that by constraining the quadrupole tilts with respect to the surface normal, which models interactions with the substrate, and by considering general quadrupole tensors, we can manipulate the ground state configuration symmetry.
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Affiliation(s)
- AndraŽ Gnidovec
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000 Ljubljana, Slovenia.
| | - Simon Čopar
- University of Ljubljana, Faculty of Mathematics and Physics, SI-1000 Ljubljana, Slovenia.
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12
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Ophaus L, Knobloch E, Gurevich SV, Thiele U. Two-dimensional localized states in an active phase-field-crystal model. Phys Rev E 2021; 103:032601. [PMID: 33862772 DOI: 10.1103/physreve.103.032601] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Accepted: 02/08/2021] [Indexed: 11/07/2022]
Abstract
The active phase-field-crystal (active PFC) model provides a simple microscopic mean field description of crystallization in active systems. It combines the PFC model (or conserved Swift-Hohenberg equation) of colloidal crystallization and aspects of the Toner-Tu theory for self-propelled particles. We employ the active PFC model to study the occurrence of localized and periodic active crystals in two spatial dimensions. Due to the activity, crystalline states can undergo a drift instability and start to travel while keeping their spatial structure. Based on linear stability analyses, time simulations, and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of resting and traveling states. We explore, for instance, how the slanted homoclinic snaking of steady localized states found for the passive PFC model is modified by activity. Morphological phase diagrams showing the regions of existence of various solution types are presented merging the results from all the analysis tools employed. We also study how activity influences the crystal structure with transitions from hexagons to rhombic and stripe patterns. This in-depth analysis of a simple PFC model for active crystals and swarm formation provides a clear general understanding of the observed multistability and associated hysteresis effects, and identifies thresholds for qualitative changes in behavior.
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Affiliation(s)
- Lukas Ophaus
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.,Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstrasse 2, 48149 Münster, Germany
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Svetlana V Gurevich
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.,Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstrasse 2, 48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.,Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstrasse 2, 48149 Münster, Germany
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13
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Hoffmann KB, Sbalzarini IF. Robustness of topological defects in discrete domains. Phys Rev E 2021; 103:012602. [PMID: 33601629 DOI: 10.1103/physreve.103.012602] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2020] [Accepted: 12/02/2020] [Indexed: 11/07/2022]
Abstract
Topological defects are singular points in vector fields, important in applications ranging from fingerprint detection to liquid crystals to biomedical imaging. In discretized vector fields, topological defects and their topological charge are identified by finite differences or finite-step paths around the tentative defect. As the topological charge is (half) integer, it cannot depend continuously on each input vector in a discrete domain. Instead, it switches discontinuously when vectors change beyond a certain amount, making the analysis of topological defects error prone in noisy data. We improve existing methods for the identification of topological defects by proposing a robustness measure for (i) the location of a defect, (ii) the existence of topological defects and the total topological charge within a given area, (iii) the annihilation of a defect pair, and (iv) the formation of a defect pair. Based on the proposed robustness measure, we show that topological defects in discrete domains can be identified with optimal trade-off between localization precision and robustness. The proposed robustness measure enables uncertainty quantification for topological defects in noisy discretized nematic fields (orientation fields) and polar fields (vector fields).
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Affiliation(s)
- Karl B Hoffmann
- Technische Universität Dresden, Faculty of Computer Science, Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany; Center for Systems Biology Dresden, Dresden, Germany; and Cluster of Excellence Physics of Life, TU Dresden, Germany
| | - Ivo F Sbalzarini
- Technische Universität Dresden, Faculty of Computer Science, Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany; Center for Systems Biology Dresden, Dresden, Germany; and Cluster of Excellence Physics of Life, TU Dresden, Germany
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14
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Ophaus L, Kirchner J, Gurevich SV, Thiele U. Phase-field-crystal description of active crystallites: Elastic and inelastic collisions. CHAOS (WOODBURY, N.Y.) 2020; 30:123149. [PMID: 33380045 DOI: 10.1063/5.0019426] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2020] [Accepted: 12/07/2020] [Indexed: 06/12/2023]
Abstract
The active Phase-Field-Crystal (aPFC) model combines elements of the Toner-Tu theory for self-propelled particles and the classical Phase-Field-Crystal (PFC) model that describes the transition between liquid and crystalline phases. In the liquid-crystal coexistence region of the PFC model, crystalline clusters exist in the form of localized states that coexist with a homogeneous background. At sufficiently strong activity (related to self-propulsion strength), they start to travel. We employ numerical path continuation and direct time simulations to first investigate the existence regions of different types of localized states in one spatial dimension. The results are summarized in morphological phase diagrams in the parameter plane spanned by activity and mean density. Then we focus on the interaction of traveling localized states, studying their collision behavior. As a result, we distinguish "elastic" and "inelastic" collisions. In the former, localized states recover their properties after a collision, while in the latter, they may completely or partially annihilate, forming resting bound states or various traveling states.
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Affiliation(s)
- Lukas Ophaus
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| | - Johannes Kirchner
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| | - Svetlana V Gurevich
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
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15
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Huang ZF, Menzel AM, Löwen H. Dynamical Crystallites of Active Chiral Particles. PHYSICAL REVIEW LETTERS 2020; 125:218002. [PMID: 33274968 DOI: 10.1103/physrevlett.125.218002] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 10/02/2020] [Indexed: 06/12/2023]
Abstract
One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.
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Affiliation(s)
- Zhi-Feng Huang
- Department of Physics and Astronomy, Wayne State University, Detroit, Michigan 48201, USA
| | - Andreas M Menzel
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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16
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Hindes J, Edwards V, Kamimoto S, Stantchev G, Schwartz IB. Stability of milling patterns in self-propelled swarms on surfaces. Phys Rev E 2020; 102:022212. [PMID: 32942377 DOI: 10.1103/physreve.102.022212] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 07/31/2020] [Indexed: 06/11/2023]
Abstract
In some physical and biological swarms, agents effectively move and interact along curved surfaces. The associated constraints and symmetries can affect collective-motion patterns, but little is known about pattern stability in the presence of surface curvature. To make progress, we construct a general model for self-propelled swarms moving on surfaces using Lagrangian mechanics. We find that the combination of self-propulsion, friction, mutual attraction, and surface curvature produce milling patterns where each agent in a swarm oscillates on a limit cycle with different agents splayed along the cycle such that the swarm's center-of-mass remains stationary. In general, such patterns loose stability when mutual attraction is insufficient to overcome the constraint of curvature, and we uncover two broad classes of stationary milling-state bifurcations. In the first, a spatially periodic mode undergoes a Hopf bifurcation as curvature is increased, which results in unstable spatiotemporal oscillations. This generic bifurcation is analyzed for the sphere and demonstrated numerically for several surfaces. In the second, a saddle-node-of-periodic orbits occurs in which stable and unstable milling states collide and annihilate. The latter is analyzed for milling states on cylindrical surfaces. Our results contribute to the general understanding of swarm pattern formation and stability in the presence of surface curvature and may aid in designing robotic swarms that can be controlled to move over complex surfaces and terrains.
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Affiliation(s)
- Jason Hindes
- U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
| | | | - Sayomi Kamimoto
- Department of Mathematics, George Mason University, Fairfax, Virginia 22030, USA
| | | | - Ira B Schwartz
- U.S. Naval Research Laboratory, Washington, D.C. 20375, USA
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Popescu MN. Chemically Active Particles: From One to Few on the Way to Many. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:6861-6870. [PMID: 32233489 PMCID: PMC7331135 DOI: 10.1021/acs.langmuir.9b03973] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2019] [Revised: 04/01/2020] [Indexed: 06/01/2023]
Abstract
Chemically active particles suspended in a liquid solution can achieve self-motility by locally changing the chemical composition of the solution via catalytic reactions at their surfaces. They operate intrinsically out of equilibrium, continuously extracting free energy from the environment to power the dissipative self-motility. The effective interactions involving active particles are, in general, nonreciprocal and anisotropic, even if the particles have simple shapes (e.g., Janus spheres). Accordingly, for chemically active particles a very rich behavior of collective motion and self-assembly may be expected to emerge, including phenomena such as microphase separation in the form of kinetically stable, finite-sized aggregates. Here, I succinctly review a number of recent experimental studies that demonstrate the self-assembly of structures, involving chemically active Janus particles, which exhibit various patterns of motion. These examples illustrate concepts such as "motors made out of motors" (as suggestively named by Fischer [Fischer, P. Nat. Phys. 2018, 14, 1072]). The dynamics of assembly and structure formation observed in these systems can provide benchmark, in-depth testing of the current understanding of motion and effective interactions produced by chemical activity. Finally, one notes that these significant achievements are likely just the beginning of the field. Recently reported particles endowed with time-dependent chemical activity or switchable reaction mechanisms open the way for exciting developments, such as periodic reshaping of self-assembled structures based on man-made internal clocks.
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Ai BQ, Zhou BY, Zhang XM. Binary mixtures of active and passive particles on a sphere. SOFT MATTER 2020; 16:4710-4717. [PMID: 32367106 DOI: 10.1039/d0sm00281j] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
We study the cooperation and segregation dynamics of binary mixtures of active and passive particles on a sphere. According to the competition between rotational diffusion and polar alignment, we find three distinct phases: a mixed phase and two different demixed phases. When rotational diffusion dominates the dynamics, the demixing is due to the aggregation of passive particles, where active and passive particles respectively occupy two hemispheres. When polar alignment is dominated, the demixing is caused by the aggregation of active particles, where active particles occupy the equator of the sphere and passive particles occupy the two poles of the sphere. In this case, there exist a circulating band cluster and two cambered surface clusters, which is a purely curvature-driven effect with no equivalent in the planar model. When rotational diffusion and polar alignment are comparable, particles are completely mixed. Our findings are relevant to the experimental pursuit of segregation dynamics of binary mixtures on curved surfaces.
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Affiliation(s)
- Bao-Quan Ai
- Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China.
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Bickmann J, Wittkowski R. Predictive local field theory for interacting active Brownian spheres in two spatial dimensions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:214001. [PMID: 31791019 DOI: 10.1088/1361-648x/ab5e0e] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For high accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B+ as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Andersen potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.
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Affiliation(s)
- Jens Bickmann
- Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany
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Napoli G, Turzi S. Spontaneous helical flows in active nematics lying on a cylindrical surface. Phys Rev E 2020; 101:022701. [PMID: 32168710 DOI: 10.1103/physreve.101.022701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 01/17/2020] [Indexed: 06/10/2023]
Abstract
Within the framework of the two-dimensional Ericksen-Leslie model, we explore the effect of geometric confinement on the spontaneous flow of active nematic gels. The nematic particles are assumed to flow on a cylindrical surface, while a degenerate tangential anchoring is enforced. Using the linear approximation of the motion equations, we show that there is a close interplay among extrinsic curvature, flow, director alignment, and activity. We find that the extrinsic curvature promotes the director alignment parallel to the cylindrical axis and is responsible for raising the critical threshold with respect to the flat case. Our analysis reveals a very rich scenario where the key quantities are the activity coefficient, the tumbling parameter, and the anisotropic viscosity ratio. Thus, solutions can exhibit a double periodicity in both the azimuthal and axial variables. As a consequence, the velocity field can make a finite angle with the cylinder axis and the active flow winds on the surface with a helical pattern, while the director oscillates around the cylinder generators. Our results can be validated on thin layers of nematic gels placed between two concentric cylinders and suggest which material properties are most suited for the design of active microfluidic devices.
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Affiliation(s)
- Gaetano Napoli
- Dipartimento di Matematica e Fisica "E. De Giorgi," Università del Salento, Lecce 73100, Italy
| | - Stefano Turzi
- Dipartimento di Matematica, Politecnico di Milano, Milan 20133, Italy
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Hoell C, Löwen H, Menzel AM. Multi-species dynamical density functional theory for microswimmers: Derivation, orientational ordering, trapping potentials, and shear cells. J Chem Phys 2019. [DOI: 10.1063/1.5099554] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Christian Hoell
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Andreas M. Menzel
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
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Ophaus L, Gurevich SV, Thiele U. Resting and traveling localized states in an active phase-field-crystal model. Phys Rev E 2018; 98:022608. [PMID: 30253633 DOI: 10.1103/physreve.98.022608] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2018] [Indexed: 06/08/2023]
Abstract
The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Löwen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.
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Affiliation(s)
- Lukas Ophaus
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany, and Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster Corrensstrasse 2, 48149 Münster, Germany
| | - Svetlana V Gurevich
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany, and Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster Corrensstrasse 2, 48149 Münster, Germany
| | - Uwe Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany, and Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster Corrensstrasse 2, 48149 Münster, Germany
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