Discontinuous and continuous transitions of collective behaviors in living systems

2021 ◽  
Author(s):  
Xu Li ◽  
Tingting Xue ◽  
Yu Sun ◽  
Jingfang Fan ◽  
Hui Li ◽  
...  
Keyword(s):  
Cognitive Abilities ◽  
Collective Motion ◽  
Finite Size ◽  
Continuous Phase ◽  
Living System ◽  
Living Systems ◽  
Finite Size Scaling ◽  
Continuous Transition ◽  
Collective Behaviors ◽  
Large Groups

Abstract Living systems are full of astonishing diversity and complexity of life. Despite differences in the length scales and cognitive abilities of these systems, collective motion of large groups of individuals can emerge. It is of great importance to seek for the fundamental principles of collective motion, such as phase transitions and their natures. Via an eigen microstate approach, we have found a discontinuous transition of density and a continuous transition of velocity in the Vicsek models of collective motion, which are identified by the finite-size scaling form of order-parameter. At strong noise, living systems behave like gas. With the decrease of noise, the interactions between the particles of a living system become stronger and make them come closer. The living system experiences then a discontinuous gas-liquid like transition of density. The even stronger interactions at smaller noise make the velocity directions of particles become ordered and there is a continuous phase transition of collective motion in addition.

On The Phase Structure of the Asymmetric Three-State Potts Model

1982 ◽  
Vol 21 ◽  
Author(s):  
G. v. Gehlen
Keyword(s):  
Phase Boundary ◽  
Potts Model ◽  
Phase Structure ◽  
Asymmetry Parameter ◽  
Finite Size ◽  
Critical Index ◽  
Incommensurate Phase ◽  
Finite Size Scaling ◽  
Lifshitz Point ◽  
The Asymmetry

ABSTRACTFinite-size scaling is applied to the Hamiltonian version of the asymmetric Z3-Potts model. Results for the phase boundary of the commensurate region and for the corresponding critical index ν are presented. It is argued that there is no Lifshitz point, the incommensurate phase extending down to small values of the asymmetry parameter.

THE CRITICAL BEHAVIOR OF THE 2D SPIN-1 ISING MODEL WITH THE BILINEAR AND POSITIVE BIQUADRATIC NEAREST NEIGHBOR INTERACTIONS ON A CELLULAR AUTOMATON

2004 ◽  
Vol 15 (10) ◽  
pp. 1425-1438 ◽  
Author(s):  
A. SOLAK ◽  
B. KUTLU
Keyword(s):  
Cellular Automaton ◽  
Phase Boundary ◽  
Critical Behavior ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Beg Model

The two-dimensional BEG model with nearest neighbor bilinear and positive biquadratic interaction is simulated on a cellular automaton, which is based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transitions of the model are presented for comparison with those obtained from other calculations. We confirm the existence of the tricritical points over the phase boundary for D/K>0. The values of static critical exponents (α, β, γ and ν) are estimated within the framework of the finite size scaling theory along D/K=-1 and 1 lines. The results are compatible with the universal Ising critical behavior except the points over phase boundary.

scholarly journals An Algorithm for Global Optimization Inspired by Collective Animal Behavior

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Erik Cuevas ◽  
Mauricio González ◽  
Daniel Zaldivar ◽  
Marco Pérez-Cisneros ◽  
Guillermo García
Keyword(s):  
Global Optimization ◽  
Animal Behavior ◽  
Food Source ◽  
Collective Motion ◽  
Global Optimum ◽  
Migration Routes ◽  
Collective Behaviors ◽  
Biological Laws ◽  
Harvesting Efficiency ◽  
Collective Animal Behavior

A metaheuristic algorithm for global optimization called the collective animal behavior (CAB) is introduced. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central locations, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency, to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, the searcher agents emulate a group of animals which interact with each other based on the biological laws of collective motion. The proposed method has been compared to other well-known optimization algorithms. The results show good performance of the proposed method when searching for a global optimum of several benchmark functions.

scholarly journals A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

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