We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an "always-move" rule, when compared with the strongly viscous ("never-move") case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the problem of the onset of cooperation.

We study the distribution of domain areas, areas enclosed by domain boundaries ͑"hulls"͒, and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, n h ͑A , t͒dA, with enclosed area in the interval ͑A , A + dA͒, is described, for a disordered initial condition, by the scaling function n h ͑A , t͒ =2c h / ͑A + h t͒ 2 , where c h =1/ 8 ͱ 3 Ϸ 0.023 is a universal constant and h is a material parameter. For a critical initial condition, the same form is obtained, with the same h but with c h replaced by c h / 2. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form . These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.

We consider the statistics of the areas enclosed by domain boundaries (''hulls'') during the curvaturedriven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form N h A; t 2c=A t, demonstrating the validity of dynamical scaling in this system, where c 1=8 3 p is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A=t. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c=2. DOI: 10.1103/PhysRevLett.98.145701 PACS numbers: 64.60.Cn, 64.60.Ht Coarsening dynamics has attracted enormous interest over the last 40 years. The classic scenario concerns a system that in equilibrium exhibits a phase transition from a disordered high-temperature phase to an ordered low-temperature phase with a broken symmetry of the high-temperature phase. The simplest example is, perhaps, the Ising ferromagnet. When the system is cooled rapidly through the transition temperature, domains of the two ordered phases form and grow (''coarsen'') with time under the influence of the interfacial surface tension, which acts as a driving force for the domain growth [1][2][3].While phase transitions provide the traditional arena for coarsening dynamics, there are many other examples, including soap froths [4], breath figures [5], granular media [6], and interfacial fluctuations [7]. A common feature of nearly all such coarsening systems is that they are well described by a dynamical scaling phenomenology in which there is a single characteristic length scale, Rt, which grows with time. If dynamical scaling holds, the domain morphology is statistically the same at all times when all lengths are measured in units of Rt. The assumption of dynamical scaling also makes possible the determination of the length scale Rt for a large class of coarsening systems [3,8].Despite the success of the scaling hypothesis in describing experimental and simulation data, its validity has only been proved for very simple models, including the 1d Glauber-Ising model [9] and the nonconserved On model in the limit n ! 1 [10]. Another noteworthy exact result is the Lifshitz-Slyozov derivation of the domain-size distribution for a conserved scalar field in the limit where the minority phase occupies a vanishingly small volume fraction [11]. The only other exact results, to our knowledge, for domain-size distributions in coarsening dynamics are for the zero-temperature Glauber-Potts [12] and timedependent Ginzburg-Landau [13] models in 1d.In this work we obtain some exact results for the coarsening dynamics of a nonconserved scalar field in 2d, demonstrating, en passant, the validity of the scaling hypothesis. To do this, we use a continuum model in which the velocity, v, of each element of a domain boundary is proportional to the local interfacial curvature, :where is a material constant with the...

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, λ (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class -contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.

PACS. 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc. - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling,