A microscopic field theoretical approach for active systems

Alaimo, Francesco; Praetorius, Simon; Voigt, Axel

doi:10.1088/1367-2630/18/8/083008

Cited by 41 publications

(65 citation statements)

References 49 publications

(115 reference statements)

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“…A similar behavior has been found in the case of a flat periodic domain in Refs. [13,15,33]. For the sphere radii R considered in this work, the activity threshold v th of a b the resting to motion transition is v th ≈ 0.3, which is smaller than the threshold given in Ref.…”

Section: Resultsmentioning

confidence: 58%

Active crystals on a sphere

et al. 2018

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Two-dimensional crystals on curved manifolds exhibit nontrivial defect structures. Here we consider "active crystals" on a sphere, which are composed of self-propelled colloidal particles. Our work is based on a phase-field-crystal-type model that involves a density and a polarization field on the sphere. Depending on the strength of the self-propulsion, three different types of crystals are found: a static crystal, a self-spinning "vortex-vortex" crystal containing two vortical poles of the local velocity, and a self-translating "source-sink" crystal with a source pole where crystallization occurs and a sink pole where the active crystal melts. These different crystalline states as well as their defects are studied theoretically here and can in principle be confirmed in experiments.

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Section: Resultsmentioning

confidence: 58%

Active crystals on a sphere

et al. 2018

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“…To describe not only the onset of structure formation like MIPS, but also the emerging patterns and their time evolution, a model of fourth order in derivatives is required [31,39,40]. When the model includes derivatives up to sixth order, it is even able to describe crystallization of ABPs and the particle-resolved lattice structures [54][55][56][57][58]. It is reasonable to truncate the derivatives at an even order, since otherwise terms that include only ∂ i and ρ but not P i or Q ij could not contribute to the dynamic equation of ρ at the highest considered order in derivatives.…”

Section: B Approximationsmentioning

confidence: 99%

“…(2)-(4) of Ref. [56], a phenomenologically modified version of the active PFC model is proposed, which uses additional contributions known from the vacancy PFC model [71][72][73] to penalize negative values of the order parameter ψ that describes the spatial density variation and thus to support an interpretation of density peaks as individual particles. Assuming ψ = 0 and performing a QSA for this model, we obtain the dimensionless density current 47) and the constitutive equation for the dimensionless polarization vector…”

Section: Th-order Low-density Modelmentioning

confidence: 99%

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Bickmann¹,

Wittkowski²

2020

J. Phys.: Condens. Matter

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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 maximal 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-Anderson 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. arXiv:1909.03369v1 [cond-mat.soft] 8 Sep 2019 2 The actual particle number density or number concentration of the ABPs is given by 2πρ( r, t).

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“…Another possibility to improve performance is to extend techniques with multiple phase fields that have been applied in modeling grain growth [109, 110], where the number of phase fields can be reduced by judiciously combining multiple fields into one. [111] have also recently developed a simplified model that solves a single phase field crystal equation to represent all of the cells; this may represent an interesting compromise between the full detail of phase field models and continuum models of many cells.…”

Section: What Is a Collective Cell Motility Model? Basic Elements mentioning

confidence: 99%

Physical models of collective cell motility: from cell to tissue

Camley

Rappel

2017

J. Phys. D: Appl. Phys.

177

147

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In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell’s shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

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A microscopic field theoretical approach for active systems

Cited by 41 publications

References 49 publications

Active crystals on a sphere

Active crystals on a sphere

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

Physical models of collective cell motility: from cell to tissue

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