Phase transitions induced by complex nonlinear noise in a system of self-propelled agents

Dossetti, V.; Sevilla, Francisco J.; Kenkre, V. M.

doi:10.1103/physreve.79.051115

Cited by 32 publications

(34 citation statements)

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“…This is a consequence of the long-range character of the centering interaction that we have chosen, and resembles the properties of some other models with this kind of interactions (see, e.g., [19,24]) -in particular, the Mikhailov and Zanette model that inspired ours.…”

Section: Different Sources Of Stochasticity and Free Flocksmentioning

confidence: 96%

“…The formulations to study the flocking phenomenon can be succinctly classified in rule-based [10,11,12,13,14,15,16,17,18], Lagrangian (trajectory-based) [19,20,21,22,23,24,25,26] and Eulerian (continuum) models [27,28,29]. Regarding the dimensionality of the models developed, most of them have been defined in dimensions higher than one [10,11,12,13,14,15,20,21,22,23,24,25,27,28,29,30], since the velocity of the self-propelled particles (SPP) in these models can have continuous values. In contrast, only a few one-dimensional (1D) models have been studied [5,16,17,18,19,26,31].…”

Section: Introductionmentioning

confidence: 99%

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Cohesive motion in one-dimensional flocking

Dossetti¹

2011

J. Phys. A: Math. Theor.

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Abstract. A one-dimensional rule-based model for flocking, that combines velocity alignment and long-range centering interactions, is presented and studied. The induced cohesion in the collective motion of the self-propelled agents leads to a unique group behaviour that contrasts with previous studies. Our results show that the largest cluster of particles, in the condensed states, develops a mean velocity slower than the preferred one in the absence of noise. For strong noise, the system also develops a non-vanishing mean velocity, alternating its direction of motion stochastically. This allows us to address the directional switching phenomenon. The effects of different sources of stochasticity on the system are also discussed.

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Section: Different Sources Of Stochasticity and Free Flocksmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Cohesive motion in one-dimensional flocking

Dossetti¹

2011

J. Phys. A: Math. Theor.

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“…In contrast, in the Vicsek et al model and some of its generalizations, in the same limits, the disordered phase only occurs at maximum noise (or, equivalently, in the infinite temperature limit) [8].…”

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confidence: 99%

“…The alignment interaction considered here corresponds to a simple generalization, with a finite aligning rate, of the one introduced in [2]. We must mention that alignment interactions with finite aligning rates have been considered before in some other forms [8,10,12].…”

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confidence: 99%

“…This has led to the development of sophisticated nonlinear friction terms [7,8], a bias that may be justified arguing, on the one hand, that the concept of self-propelled (or active Brownian) particles captures the natural ability (seen in many biological systems) for the agents to develop motion by themselves [9,10] and, on the other, that it is an important ingredient for pattern formation in models of collective motion [11].…”

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Emergence of Collective Motion in a Model of Interacting Brownian Particles

Dossetti

Sevilla

2015

Phys. Rev. Lett.

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By studying a system of Brownian particles, interacting only through a local social-like force (velocity alignment), we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to farfrom-equilibrium ones exhibiting collective motion, long-range order and giant number fluctuations, features typically associated to ordered phases of models where self-propulsion is considered.PACS numbers: 05.70.Fh, 05.70.Ln Collective motion is an ubiquitous phenomenon in biological groups such as flocks of birds, schools of fishes, swarms of insects, etc. The study of these far-fromequilibrium systems has attracted great interest over the last few decades, as the spontaneous emergence of such ordered phases and coordinated behavior, arising from local interactions, cannot be accounted for by the standard theorems of statistical mechanics [1].Introduced almost twenty years ago, the seminal model by Vicsek et al.[2] provided a simple tool to study the transition to collective motion, in a non-equilibrium situation, taking into account two basic ingredients: the selfpropulsive character of the particles and a local velocityalignment interaction among them. Due to the discrete nature of the model, a given particle instantaneously orients its direction of motion along the average direction of motion of its neighbors within a radius R, while stochastic perturbations are considered by adding a random angle ("noise") to this direction. In two dimensions, the system displays an ordered phase characterized by collective motion with long-range order and giant number fluctuations [3], just below a critical value of the noise intensity that depends on the particle density. It is in this respect that this model can be considered as a paradigm of non-equilibrium phase transitions, since such ordered phases are forbidden in equilibrium (for Heisenberg-like models) by the Mermin-Wagner-Hohenberg theorem [4]. Above this value, the ordered phase breaks down into a stationary, disordered and out-of-equilibrium one.Over the years, many generalizations of the model have been developed, keeping self-propulsion as an essential ingredient for the phase transition to take place, in combination with interactions of the "social" type among the particles such as velocity-alignment [5,6]. This has led to the development of sophisticated nonlinear friction terms [7,8], a bias that may be justified arguing, on the one hand, that the concept of self-propelled (or active Brownian) particles captures the natural ability (seen in many biological systems) for the agents to develop motion by themselves [9,10] and, on the other, that it is an important ingredient for pattern formation in models of collective motion [11].In this Letter, we study the emergence of collective motion in a two-dimensional system of N passive Brownian (not-self-propelled) partic...

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Defining emergence: Learning from flock behavior

Berrondo

Sandoval

2015

Complexity

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The idea of emergence originates from the fact that global effects emerge from local interactions producing a collective coherent behavior. A particular instance of emergence is illustrated by a flocking model of interacting ''boids'' encompassing two antagonistic conducts-consensus and frustration-giving rise to highly complex, unpredictable, coherent behavior. The cohesive motion arising from consensus can be described in terms of three ordered dynamic phases. Once frustration is included in the model, local phases for specific groups of flockmates, and transitions among them, replace the global ordered phases. Following the evolution of boids in a single group, we discovered that the boids in this group will alternate among the three phases. When we compare two uncorrelated groups, the second group shows a similar behavior to the first one, but with a different sequence of phases. Besides the visual observation of our animations with marked boids, the result is evident plotting the local order parameters. Rather than adopting one of the consensus ordered phases, the flock motion resembles more an entangled dynamic sequence of phase transitions involving each group of flockmates. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

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Phase transitions induced by complex nonlinear noise in a system of self-propelled agents

Cited by 32 publications

References 30 publications

Cohesive motion in one-dimensional flocking

Cohesive motion in one-dimensional flocking

Emergence of Collective Motion in a Model of Interacting Brownian Particles

Defining emergence: Learning from flock behavior

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