PACS 64.60.Ht -Dynamic critical phenomena PACS 05.10.Ln -Monte Carlo methods PACS 75.60.Ch -Domain walls and domain structure Abstract -With Monte Carlo simulations, we study the creep motion of a domain wall in the twodimensional random-field Ising model with a driving field. We observe the nonlinear field-velocity relation, and determine the creep exponent µ. To further investigate the universality class of the creep motion, we also measure the roughness exponent ζ and energy barrier exponent ψ from the zero-field relaxation process. For strong disorder, the exponents are consistent with those of the Edwards-Wilkinson equation; for weak disorder, a different universality class is detected.
A long-standing problem in biology, economics, and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. This paper investigates how to promote the evolution of cooperation in the Prisoner’s Dilemma game (PDG). Differing from previous approaches, we not only propose a tag-based control (TBC) mechanism but also look at how the evolution of cooperation by TBC can be successfully promoted. The effect of TBC on the evolutionary process of cooperation shows that it can both reduce the payoff of defectors and inhibit defection; although when the cooperation rate is high, TBC will also reduce the payoff of cooperators unless the identified rate of the TBC is large enough. An optimal timing control (OTC) of switched replicator dynamics is designed to consider the control costs, the cooperation rate at terminal time, and the cooperator’s payoff. The results show that the switching control (SC) between an optimal identified rate control of the TBC and no TBC can properly not only maintain a high cooperation rate but also greatly enhance the payoff of the cooperators. Our results provide valuable insights for some clusters, for example, logistics parks and government, to regard the decision to promote cooperation.
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