Self-Propelled Interacting Particle Systems With Roosting Force

Carrillo, José A.; Klar, Axel; Martin, Stephan; Tiwari, Sudarshan

doi:10.1142/s0218202510004684

Cited by 95 publications

(91 citation statements)

References 42 publications

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“…These models include short-range repulsion, long-range attraction, self-propelling and friction forces, reorientation or alignment see [4,65,58,66,60,53,37,57,7,6]. We consider self-propelled particles with Rayleigh friction [35,34,27,32,8,3,30,31], and alignment, introduced through the Cucker-Smale reorientation procedure [38,39], see also [56,54,28,29,61,62] for further details and [59] for a survey. If we denote by f = f (t, x, v) ≥ 0 the particle density in the phase space (x, v) ∈ R d × R d , with d ∈ {2, 3}, the self-propulsion/friction mechanism is given by the term div v {f (α − β|v| 2 )v}.…”

Section: Introductionmentioning

confidence: 99%

Reduced fluid models for self-propelled particles interacting through alignment

Bostan

Carrillo

2017

Math. Models Methods Appl. Sci.

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The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are dominated by the selfpropulsion and friction forces. The former hypothesis leads to a macroscopic fluid model due to the fast averaging in velocity, while the second one imposes a fixed speed in the limit, and thus a reduction of the dynamics to a sphere in the velocity space. The analysis relies on averaging techniques successfully used in the magnetic confinement of charged particles. The limiting particle distribution is supported on a sphere, and therefore we are forced to work with measures in velocity. As for the Euler-type equations, the fluid model comes by integrating the kinetic equation against the collision invariants and its generalizations in the velocity space. The main difficulty is their identification for the averaged alignment kernel in our functional setting of measures in velocity.

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Section: Introductionmentioning

confidence: 99%

Reduced fluid models for self-propelled particles interacting through alignment

Bostan

Carrillo

2017

Math. Models Methods Appl. Sci.

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“…The case j = 1 refers to the interaction of the individuals, the interaction of individuals with external agents is denoted by j = 2. Inspired by [13], we use the values A 1 = 20, R 1 = 50, a 1 = 100, r 1 = 2, A 2 = 5, R 2 = 100, a 2 = 1000, r 2 = 50.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Remark 4.2. The variational inequalities (13) and (16) may be equivalently expressed as fixed point problems in terms of a projection operator Proj U : U → U ad which is defined by (see [29])…”

Section: 1mentioning

confidence: 99%

Instantaneous control of interacting particle systems in the mean-field limit

Burger

Pinnau

Totzeck

et al. 2020

Journal of Computational Physics

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Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit,i.e., for an increasing number of particles.

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“…In these works experimental studies as well as numerical experiments are presented In this work, we closely follow a procedure for interacting particle systems used, for example, in the description of coherent motion of animal groups such as schools of fish, flocks of birds or swarms of insects, see Ref. [9,10]. It has been applied to pedestrian flow modelling in Ref.…”

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confidence: 99%

Particle methods for multi-group pedestrian flow

Mahato

Klar

Tiwari

2018

Applied Mathematical Modelling

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Abstract. We consider a multi-group microscopic model for pedestrian flow describing the behaviour of large groups. It is based on an interacting particle system coupled to an eikonal equation. Hydrodynamic multi-group models are derived from the underlying particle system as well as scalar multi-group models. The eikonal equation is used to compute optimal paths for the pedestrians. Particle methods are used to solve the equations on all levels of the hierarchy. Numerical test cases are investigated and the models and, in particular, the resulting evacuation times are compared for a wide range of different parameters.

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Self-Propelled Interacting Particle Systems With Roosting Force

Cited by 95 publications

References 42 publications

Reduced fluid models for self-propelled particles interacting through alignment

Reduced fluid models for self-propelled particles interacting through alignment

Instantaneous control of interacting particle systems in the mean-field limit

Particle methods for multi-group pedestrian flow

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