scholarly journals PHASE TRANSITION IN EVOLUTIONARY GAMES

1999 ◽  
Vol 14 (10) ◽  
pp. 1551-1559 ◽  
Author(s):  
ZHEN CAO ◽  
RUDOLPH C. HWA
Keyword(s):  
Phase Transition ◽  
Critical Region ◽  
Nuclear Physics ◽  
Cooperative Behavior ◽  
Evolutionary Games ◽  
Scaling Exponent ◽  
Factorial Moments ◽  
Physical Systems ◽  
Prisoners Dilemma ◽  
Evolution Dynamics

The evolution of cooperative behavior is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region 1.8<b<2.0, where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behavior of the moments a scaling exponent is determined and is found to lie in the range where phase transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behavior is thus extended to include also this particular model of evolution dynamics.

DYNAMICS OF FRACTALITY AND PHASE TRANSITION IN MULTIPARTICLE PRODUCTION IN RELATIVISTIC NUCLEUS–NUCLEUS COLLISIONS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350033 ◽  
Author(s):  
ARSHAD KAMAL ◽  
N. AHMAD ◽  
M. M. KHAN ◽  
M. I. HAQUE ◽  
M. ZAFAR ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Value ◽  
Data Sets ◽  
Scaling Exponent ◽  
Factorial Moments ◽  
Universal Scaling ◽  
Average Value ◽  
Thermal Phase ◽  
Scaled Factorial Moments ◽  
Second Order Phase Transition

This paper reports the results of an investigation regarding occurrence of second-order phase transition in 14.5A GeV /c28 Si -nucleus interactions using the method of scaled factorial moments. Incidentally, the value of the universal scaling exponent, ν, for our experimental data is found to be 1.224±0.068, which is quite close to its critical value 1.304. An attempt is also made to search for the evidence of phase transition in terms of Levy index, μ, using scaled factorial moments as well as Takagi moments for both experimental and FRITIOF generated data sets. Average value of μ, calculated from Fq moments, turns out to be more than unity but is less than unity when estimated in terms of Takagi moments for both the data sets. Thus the analyses carried out in terms of Fq and Takagi moments reveal the occurrence of nonthermal and thermal phase transitions, respectively.

scholarly journals A Brief Review of Generalized Entropies

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 813 ◽  
Author(s):  
José Amigó ◽  
Sámuel Balogh ◽  
Sergio Hernández
Keyword(s):  
Diffusion Processes ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Point Of View ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Physical Systems ◽  
New Phenomena ◽  
Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

scholarly journals Multimessenger approaches to exploring dense matter in neutron stars

2021 ◽  
Author(s):  
◽  
Lukas Weih
Keyword(s):  
Phase Transition ◽  
Neutron Star ◽  
Nuclear Physics ◽  
Computational Cost ◽  
Dense Matter ◽  
High Energy ◽  
Radiative Transport ◽  
Binary Neutron Star ◽  
Starting Point ◽  
Numerical Astrophysics

High-energy astrophysics plays an increasingly important role in the understanding of our universe. On one hand, this is due to ground-breaking observations, like the gravitational-wave detections of the LIGO and Virgo network or the black-hole shadow observations of the EHT collaboration. On the other hand, the field of numerical relativity has reached a level of sophistication that allows for realistic simulations that include all four fundamental forces of nature. A prime example of how observations and theory complement each other can be seen in the studies following GW170817, the first detection of gravitational waves from a binary neutron-star merger. The same detection is also the chronological starting point of this Thesis. The plethora of information and constraints on nuclear physics derived from GW170817 in conjunction with theoretical computations will be presented in the first part of this Thesis. The second part goes beyond this detection and prepares for future observations when also the high-frequency postmerger signal will become detectable. Specifically, signatures of a quark-hadron phase transition are discussed and the specific case of a delayed phase transition is analyzed in detail. Finally, the third part of this Thesis focuses on the inclusion of radiative transport in numerical astrophysics. In the context of binary neutron-star mergers, radiation in the form of neutrinos is crucial for realistic long-term simulations. Two methods are introduced for treating radiation: the approximate state-of-the-art two-moment method (M1) and the recently developed radiative Lattice-Boltzmann method. The latter promises to be more accurate than M1 at a comparable computational cost. Given that most methods for radiative transport or either inaccurate or unfeasible, the derivation of this new method represents a novel and possibly paradigm-changing contribution to an accurate inclusion of radiation in numerical astrophysics.

scholarly journals Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 780
Author(s):  
Liang-Jun Zhai ◽  
Guang-Yao Huang ◽  
Huai-Yu Wang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Behavior ◽  
Critical Region ◽  
Numerical Study ◽  
Transverse Field ◽  
Scaling Theory ◽  
New Order ◽  
Edge Singularity ◽  
Transverse Field Ising Model

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

scholarly journals Scaling Properties of Multiplicity Fluctuations in the AMPT Model

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Rohni Sharma ◽  
Ramni Gupta
Keyword(s):  
Phase Transition ◽  
Charged Particles ◽  
Scaling Behavior ◽  
Spatial Distributions ◽  
Scaling Exponents ◽  
Ginzburg Landau ◽  
Multiphase Transport ◽  
Factorial Moments ◽  
Scaling Properties ◽  
Second Order Phase Transition

From the events generated from the MC code of a multiphase transport (AMPT) model with string melting, the properties of multiplicity fluctuations of charged particles in Pb–Pb collisions at sNN = 2.76 TeV are studied. Normalized factorial moments, Fq, of spatial distributions of the particles have been determined in the framework of intermittency. Those moments are found in some kinematic regions to exhibit scaling behavior at small bin sizes, but not in most regions. However, in relating Fq to F2 scaling behavior is found in nearly all regions. The corresponding scaling exponents, ν, determined in the low transverse momentum (pT) region ≤ 1.0 GeV/c are observed to be independent of the pT bin position and width. The value of ν is found to be larger than 1.304, which is the value that characterizes the Ginzburg-Landau type second-order phase transition. Thus there is no known signature for phase transition in the AMPT model. This study demonstrates that, for the system under investigation, the method of analysis is effective in extracting features that are relevant to the question of whether the dynamical processes leading phase transition are there or not.

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