Pattern formation in active particle systems due to competing alignment interactions

Großmann, Robert; Romanczuk, Pawel; Bär, Markus; Schimansky‐Geier, Lutz

doi:10.1140/epjst/e2015-02462-3

Cited by 32 publications

(60 citation statements)

References 51 publications

(127 reference statements)

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“…When the collective properties of many interacting agents are investigated, such statistical approaches become important [60][61][62][63][64][65][66]. Recently, we have derived and evaluated a microscopic statistical description for straight-propelling microswimmers in terms of a classical dynamical density functional theory (DDFT) [66].…”

Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

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Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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“…">IntroductionActive matter systems-ensembles of self-driven particles-are a central subject of non-equilibrium statistical physics [1-4]:examples include micron-sized active colloids and rods driven by chemical reactions [5,6] or by the Quincke effect [7,8] as well as macroscopic collective motion patterns in bird flocks or sheep herds [9][10][11]. In particular, the study of bacterial systems as well as their theoretical analysis within simple self-propelled particle models has lead to interesting insights into the physics of active matter-consider, for example, the clustering of myxobacteria [12,13] or the dynamic vortex formation in dense suspensions of swimming bacteria [14][15][16][17].In order to understand the cooperative behavior of active particles as well as the associated pattern formation processes, reliable knowledge of the dynamics of individual entities is crucial. In this work, we therefore focus on the dynamics of individual active particles.…”

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confidence: 99%

Diffusion properties of active particles with directional reversal

2016

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The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is modeled by a stochastic clock. The velocity correlation function as well as the mean squared displacement is investigated and, furthermore, a general expression for the diffusion coefficient for self-propelled particles with directional reversal is derived. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the diffusion coefficient. We comment on the relevance of these results with regard to biological systems and suggest further experiments in this context. IntroductionActive matter systems-ensembles of self-driven particles-are a central subject of non-equilibrium statistical physics [1-4]:examples include micron-sized active colloids and rods driven by chemical reactions [5,6] or by the Quincke effect [7,8] as well as macroscopic collective motion patterns in bird flocks or sheep herds [9][10][11]. In particular, the study of bacterial systems as well as their theoretical analysis within simple self-propelled particle models has lead to interesting insights into the physics of active matter-consider, for example, the clustering of myxobacteria [12,13] or the dynamic vortex formation in dense suspensions of swimming bacteria [14][15][16][17].In order to understand the cooperative behavior of active particles as well as the associated pattern formation processes, reliable knowledge of the dynamics of individual entities is crucial. In this work, we therefore focus on the dynamics of individual active particles. We particularly consider particles that are able to reverse their direction of motion repeatedly. More precisely, particles follow an alternating motion pattern where rather persistent motion is interrupted by sudden reversals of the direction of motion.This type of motion has been reported in a variety of bacterial systems [18][19][20][21][22][23][24][25][26]. For instance, the soil bacterium Myxococcus xanthus constitutes a paradigmatic example of a bacterium exhibiting periodic reversals in the direction of motion:internal oscillations of the protein dynamics cause switches in cell polarity and, correspondingly, in the direction of motion [18,19,27,28]. Under certain conditions, the reversals of several, densely packed bacteria appear synchronously leading to remarkable accordion wave patterns [29,30]. Apart from myxobacteria, a variety of marine microorganisms exhibit run-and-reverse motion [20], such as Pseudoalteromonas haloplanktis and Shewanella putrefaciens [21]. Similar motion patterns were reported for Pseudomonas citronellolis [31], Paenibacillus dendritiformis [22] and Pseudomonas putida [23][24][25][26].More complex, three-step (run-reverse-flick) motion patterns, composed of rather straight runs, directional reversals and 90°turns, were found in the marine bacterium Vibrio alginolyticus [32,33]. In this con...

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“…This energy can be transformed into active motion of the system elements, which is the most studied case [11,33]. But also complex interactions such as chemotaxis [10,35,46], clustering [20,57] or chiral pattern formation [15] have been investigated.…”

Section: Introductionmentioning

confidence: 99%

An agent-based framework of active matter with applications in biological and social systems

Schweitzer

2018

Eur. J. Phys.

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Active matter, as other types of self-organizing systems, relies on the take-up of energy that can be used for different activities, such as active motion or structure formation. Here we provide an agent-based framework to model these processes at different levels of organization, physical, biological and social, using the same dynamic approach. Driving variables describe the take-up, storage and conversion of energy, whereas driven variables describe the energy consuming activities. The stochastic dynamics of both types of variables follow a modified Langevin equation. Additional non-linear functions allow to encode system-specific hypotheses about the relation between driving and driven variables. To demonstrate the applicability of this framework, we recast a number of existing models of Brownian agents and Active Brownian Particles. Specifically, active motion, clustering and self-wiring of networks based on chemotactic interactions, online communication and polarization of opinions based on emotional influence are discussed. The framework allows to obtain critical parameters for active motion and the emergence of collective phenomena. This highlights the role of energy take-up and dissipation in obtaining different dynamic regimes. An agent-based framework of active matter with applications in biological and social systems European Journal of Physics (Revised submission) Some historical remarks. To put the recent research about active matter into perspective, it is useful to remind on some relations to existing scientific paradigms. The systemic capabilities of active matter to develop and to maintain coherent structures, or collective states, based on the input and the conversion of energy were previously described using the term self-organization. It was heuristically defined as the "spontaneous formation, evolution and differentiation of complex order structures forming in non-linear dynamic systems by way of feedback mechanisms involving the elements of the systems, when these systems have passed a critical distance from the statical equilibrium as a result of the influx of unspecific energy, matter or information." [40]. The physics of self-organization and evolution [13] has made fundamental contributions to the scientific understanding of self-organizing systems -the thermodynamics of irreversible processes, deterministic and stochastic models of nonlinear dynamics, the theory of reaction-diffusion processes, information-theoretical approaches to sequences, to name just a few.While self-organization could be seen as the leading paradigm of the 1970th and 1980th, it was gradually replaced by complex systems as the leading paradigm after the year 1990. This development came along with a shifting focus. Self-organization and pattern formation could be well described on the macroscopic or systemic level, for example by coupled partial differential equations. With complex systems, i.e. systems composed of a large number of (strongly) interacting elements, the focus was more on the emergence of systemic pro...

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Pattern formation in active particle systems due to competing alignment interactions

Cited by 32 publications

References 51 publications

Dynamical density functional theory for circle swimmers

Dynamical density functional theory for circle swimmers

Diffusion properties of active particles with directional reversal

An agent-based framework of active matter with applications in biological and social systems

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