Boltzmann and hydrodynamic description for self-propelled particles

Bertin, Éric; Droz, Michel; Grégoire, Guillaume

doi:10.1103/physreve.74.022101

Cited by 353 publications

(656 citation statements)

References 27 publications

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“…These methods aim at investigating possibly universal features of collective motion over diffusion, long-range order or presence of high-order and high-density regions at the onset of collective motion [87], named travelling bands. They may be analytical, through translations of agent-based models to Eulerian descriptions (in terms of continuous velocity and density fields), either phenomenologically [88] or analytically derived [89]. This approach aims at the understanding of the general mechanisms by which local rules lead to large-scale synchronization, those mechanisms being thought to be rather independent of the detailed nature of the systems' components.…”

Section: Statistical Physics Of Collective Motionmentioning

confidence: 99%

From behavioural analyses to models of collective motion in fish schools

et al. 2012

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Fish schooling is a phenomenon of long-lasting interest in ethology and ecology, widely spread across taxa and ecological contexts, and has attracted much interest from statistical physics and theoretical biology as a case of self-organized behaviour. One topic of intense interest is the search of specific behavioural mechanisms at stake at the individual level and from which the school properties emerges. This is fundamental for understanding how selective pressure acting at the individual level promotes adaptive properties of schools and in trying to disambiguate functional properties from non-adaptive epiphenomena. Decades of studies on collective motion by means of individual-based modelling have allowed a qualitative understanding of the self-organization processes leading to collective properties at school level, and provided an insight into the behavioural mechanisms that result in coordinated motion. Here, we emphasize a set of paradigmatic modelling assumptions whose validity remains unclear, both from a behavioural point of view and in terms of quantitative agreement between model outcome and empirical data. We advocate for a specific and biologically oriented re-examination of these assumptions through experimental-based behavioural analysis and modelling.

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Section: Statistical Physics Of Collective Motionmentioning

confidence: 99%

From behavioural analyses to models of collective motion in fish schools

et al. 2012

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“…Bertin et al 2002;Bertin 2006) packages to produce images with cosmic rays and other image defects removed, and to produce final calibrated and aligned images; these newly acquired data have then been combined with the previously reduced data. Descriptions of the MissFits, SCAMP and SWarp software are given in http://www.astromatic.net.…”

Section: Toolsmentioning

confidence: 99%

The DAFT/FADA survey

Guennou

Adami

Ulmer

et al. 2010

A&A

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Context. As a contribution to the understanding of the dark energy concept, the Dark energy American French Team (DAFT, in French FADA) has started a large project to characterize statistically high redshift galaxy clusters, infer cosmological constraints from weak lensing tomography, and understand biases relevant for constraining dark energy and cluster physics in future cluster and cosmological experiments. Aims. The purpose of this paper is to establish the basis of reference for the photo-z determination used in all our subsequent papers, including weak lensing tomography studies. Methods. This project is based on a sample of 91 high redshift (z ≥ 0.4), massive ( > ∼ 3 × 10 14 M ) clusters with existing HST imaging, for which we are presently performing complementary multi-wavelength imaging. This allows us in particular to estimate spectral types and determine accurate photometric redshifts for galaxies along the lines of sight to the first ten clusters for which all the required data are available down to a limit of I AB = 24./24.5 with the LePhare software. The accuracy in redshift is of the order of 0.05 for the range 0.2 ≤ z ≤ 1.5. Results. We verified that the technique applied to obtain photometric redshifts works well by comparing our results to with previous works. In clusters, photo-z accuracy is degraded for bright absolute magnitudes and for the latest and earliest type galaxies. The photo-z accuracy also only slightly varies as a function of the spectral type for field galaxies. As a consequence, we find evidence for an environmental dependence of the photo-z accuracy, interpreted as the standard used spectral energy distributions being not very well suited to cluster galaxies. Finally, we modeled the LCDCS 0504 mass with the strong arcs detected along this line of sight.

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“…The connection between the Vicsek model and the Toner-Tu continuum equations was missing until the equations were derived from a microscopic model of particles with binary collisions using a Boltzmann approach [45][46][47][48]. The method was generalized later by considering multiple collisions using an Enskog-type kinetic theory [49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

Gaussian theory for spatially distributed self-propelled particles

2016

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Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting selfpropelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

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Boltzmann and hydrodynamic description for self-propelled particles

Cited by 353 publications

References 27 publications

From behavioural analyses to models of collective motion in fish schools

From behavioural analyses to models of collective motion in fish schools

The DAFT/FADA survey

Gaussian theory for spatially distributed self-propelled particles

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