Scaling behavior of non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles

2016 ◽  
Vol 30 (24) ◽  
pp. 1650304 ◽  
Author(s):  
R. Bakir ◽  
I. Tarras ◽  
A. Hader ◽  
H. Sbiaai ◽  
M. Mazroui ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Collective Motion ◽  
Equilibrium Phase ◽  
Deposition Process ◽  
Scaling Behavior ◽  
Scaling Exponents ◽  
Vicsek Model ◽  
Self Similar ◽  
Ordered Motion ◽  
Non Equilibrium

Many animal groups, such as bird flocks, clearly present structural order and appear to move as a single coherent entity. In interest to understand the complex behavior of these systems, many models have been proposed and tested so far. The aim of this work is to study and discuss numerically the scaling behavior in the 2D non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles in the framework of Vicsek model. This model is an important tool to study the behavior of collective motion of live biological and physical organisms. The calculation of the scaling exponents is effected by using the scaling dynamic method. However, the time evolution of the particles velocity present two different regimes separated by a cross-over time which increases linearly with both applied noise and radius of repulsive zone, but it decreases exponentially with the radius of orientation zone. The results show that the obtained exponents are similar to the growth and roughness ones used in the interfaces growth and to the submonolayer deposition process. The obtained values of these exponents are not dependent on the noises value, which proves their universality characters. Hence the kinetic evolution of the spontaneously ordered motion of self-propelled particles is self-similar. Implications of these findings are discussed.

scholarly journals Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200688
Author(s):  
Valerio Lucarini ◽  
Grigorios A. Pavliotis ◽  
Niccolò Zagli
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Linear Response ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Transitions ◽  
Autocorrelation Time ◽  
The Common ◽  
Fokker Planck Equations ◽  
Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

Equilibrium and non-equilibrium phase transitions in copolymer polyelectrolyte hydrogels

1997 ◽  
Vol 107 (5) ◽  
pp. 1645-1654 ◽  
Author(s):  
Anthony E. English ◽  
Toyoichi Tanaka ◽  
Elazer R. Edelman
Keyword(s):  
Phase Transitions ◽  
Equilibrium Phase ◽  
Non Equilibrium

Non-Equilibrium Phase Transitions and Living Organisms

2016 ◽  
Author(s):  
Maria Pilar Buera ◽  
Yrjö Roos ◽  
Harry Levine ◽  
Louise Slade ◽  
Horacio R. Corti ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Equilibrium Phase ◽  
Living Organisms ◽  
Non Equilibrium

scholarly journals Non-Equilibrium Phase Transitions Induced by Social Temperature In Kinetic Exchange Opinion Models on Regular Lattices

2017 ◽  
Vol 01 (01) ◽  
pp. 1740001 ◽  
Author(s):  
Nuno Crokidakis
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Equilibrium Phase ◽  
Critical Dimension ◽  
Point Of View ◽  
Majority Opinion ◽  
Regular Lattices ◽  
Independent Behavior ◽  
Non Equilibrium

In this work, we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular [Formula: see text]-dimensional lattice has a probability [Formula: see text] to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability [Formula: see text], the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes non-equilibrium phase transitions at critical points [Formula: see text] that depend on the lattice dimension. These transitions are of order–disorder type, presenting the same critical exponents of the Ising model. The results also suggest that the upper critical dimension of the model is [Formula: see text], as for the Ising model. From the social point of view, with increasing number of social connections, it is easier to observe a majority opinion in the population.

Semiconductor models for first and second order non-equilibrium phase transitions

1979 ◽  
Vol 365 (1723) ◽  
pp. 495-510 ◽  
Keyword(s):  
Phase Transitions ◽  
General Principle ◽  
Impact Ionization ◽  
Equilibrium Phase ◽  
Steady States ◽  
Second Order ◽  
Far From Equilibrium ◽  
P Type ◽  
Non Equilibrium

Non-equilibrium phase transitions in semiconductors due to impact ionization from traps have been obtained theoretically, and are discussed in detail. They include first and second order phase transitions, and develop previous work, which was restricted to second order phase transitions involving band-band processes. The models include switching transitions from non-conducting to conducting states, and from n- to p-type states. They furnish simple illustrations of the general principle that a system which is driven far from equilibrium can exhibit new stable steady states.

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