Synchronization and collective motion of globally coupled Brownian particles

Sevilla, Francisco J.; Dossetti, V.; Heiblum-Robles, Alexandro

doi:10.1088/1742-5468/2014/12/p12025

Cited by 9 publications

(13 citation statements)

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“…It is interesting to notice, though, that the phase transition of our model takes place for finite values ofΓ even in the limit cases when ρ → ∞ or when global coupling is considered [16]. 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: 77%

“…In fact, as ρ → ∞ or if global coupling (R/L = 1) is considered, this feature allows for the analytical treatment of the model where the instability of the disordered close-to-equilibrium state can be demonstrated, and the relation of our model to the Kuramoto model of synchronization is revealed. This case is discussed in details in [16]. Another feature displayed by ordered far-fromequilibrium phases, whenever the interactions depend on the distance, is the strong coupling between local density and local order [5,6].…”

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confidence: 97%

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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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confidence: 97%

Emergence of Collective Motion in a Model of Interacting Brownian Particles

Dossetti

Sevilla

2015

Phys. Rev. Lett.

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“…Although the results are derived in a specific model system, we argue that the scaling behaviors should be valid for general nonequilibrium systems.As a nonequilibrium model, we adopt the particle system in two dimensions introduced in Ref. [15]. This model describes a flocking phenomenon of passive particles.…”

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“…As a nonequilibrium model, we adopt the particle system in two dimensions introduced in Ref. [15]. This model describes a flocking phenomenon of passive particles.…”

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Macroscopic time-reversal symmetry breaking at a nonequilibrium phase transition

2016

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We study the entropy production in a macroscopic nonequilibrium system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. It is found that the entropy production rate per particle vanishes in the disordered phase and becomes positive in the ordered phase following critical scaling laws. We derive the scaling relations for associated critical exponents. Our study reveals that a nonequilibrium ordered state is sustained at the expense of macroscopic time-reversal symmetry breaking with an extensive entropy production while a disordered state costs only a subextensive entropy production.PACS numbers: 05.70.Fh, 05.70.Ln, 64.60.Cn Detailed balance is the hallmark of the thermal equilibrium state. A system is said to obey detailed balance if the probability current along any microscopic trajectory in the phase space is balanced by that along the timereversed one [1]. Consequently, time-reversal symmetry is preserved in thermal equilibrium.Thermodynamics of nonequilibrium systems, where detailed balance and time-reversal symmetry are broken with a positive entropy production, has been attracting a lot of interests [2][3][4][5][6][7][8]. Recent studies have been focused on microscopic systems with a few degrees of freedom where the effect of thermal fluctuations are strong. Under the framework of stochastic thermodynamics, various fluctuation theorems are discovered, which provide useful insights on the nature of nonequilibrium fluctuations. Theoretical works foster experimental studies of microscopic systems such as molecular motors, nano heat engines, biomolecules, and so on [9][10][11][12][13][14].Macroscopic systems pose an intriguing question on the level of irreversibility. Consider a many-particle system displaying an order-disorder phase transition whose microscopic dynamics does not obey detailed balance. Does the broken detailed balance result in time-reversal symmetry breaking at the macroscopic level? On the one hand, one may expect that entropy productions of each particle add up to a macroscopic amount irrespective of a macroscopic state. On the other hand, if the system is in a disordered phase so that all configurations are almost equally likely, then irreversibility may not show up on a macroscopic level producing only a subextensive amount of entropy. A system in an ordered state has a lower entropy than in a disordered state. Then, which phase produces more total entropy including the system entropy and the environmental entropy? These questions lead us to the study of the entropy production in a model system undergoing nonequilibrium phase transition.In this paper, we investigate the emergence of macroscopic irreversibility out of microscopic dynamics with broken detailed balance. We find that the total entropy production changes its character from being subextensive to being extensive as the system undergoes an orderdisorder phase transition. The entropy production rate per particle exhibits c...

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Theory of the Spread of Epidemics and Movement Ecology of Animals

Kenkre¹,

Giuggioli

2021

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Exploiting powerful techniques from physics and mathematics, this book studies animal movement in ecology, with a focus on epidemic spread. Pulmonary syndrome is not only feared in epidemics of recent times, such as COVID-19, but is also characteristic of epidemics studied earlier such as Hantavirus. The Hantavirus is one of the book's central topics. Correlations between epidemic outbreaks and precipitation events like El Niño are analyzed and spatial reservoirs of infection in off-period of the epidemic, known as refugia, are studied. Predicted traveling waves of infection are successfully compared to field observations. Territoriality in scent-marking animals is presented, with parallels drawn with the theory of melting. The flocking and herding of birds and mammals are described in terms of collective excitations. For scientists interested in movement ecology and epidemic spread, this book provides effective solutions to long-standing problems.

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Synchronization and collective motion of globally coupled Brownian particles

Cited by 9 publications

References 44 publications

Emergence of Collective Motion in a Model of Interacting Brownian Particles

Emergence of Collective Motion in a Model of Interacting Brownian Particles

Macroscopic time-reversal symmetry breaking at a nonequilibrium phase transition

Theory of the Spread of Epidemics and Movement Ecology of Animals

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