Structure and stability of graphene nanoribbons in oxygen, carbon dioxide, water, and ammonia

We determine, by means of density functional theory, the stability and the structure of graphene nanoribbon (GNR) edges in presence of molecules such as oxygen, water, ammonia, and carbon dioxide. As in the case of hydrogen-terminated nanoribbons, we find that the most stable armchair and zigzag configurations are characterized by a non-metallic/non-magnetic nature, and are compatible with Clar's sextet rules, well known in organic chemistry. In particular, we predict that, at thermodynamic equilibrium, neutral GNRs in oxygen-rich atmosphere should preferentially be along the armchair direction, while water-saturated GNRs should present zigzag edges. Our results promise to be particularly useful to GNRs synthesis, since the most recent and advanced experimental routes are most effective in water and/or ammonia-containing solutions.Comment: accepted for publication in PR

Structure, Stability, Edge States and Aromaticity of Graphene Ribbons

We determine the stability, the geometry, the electronic and magnetic structure of hydrogen-terminated graphene-nanoribbons edges as a function of the hydrogen content of the environment by means of density functional theory. Antiferromagnetic zigzag ribbons are stable only at extremely-low ultra-vacuum pressures. Under more standard conditions, the most stable structures are the mono- and di-hydrogenated armchair edges and a zigzag edge reconstruction with one di- and two mono-hydrogenated sites. At high hydrogen-concentration ``bulk'' graphene is not stable and spontaneously breaks to form ribbons, in analogy to the spontaneous breaking of graphene into small-width nanoribbons observed experimentally in solution. The stability and the existence of exotic edge electronic-states and/or magnetism is rationalized in terms of simple concepts from organic chemistry (Clar's rule)Comment: 4 pages, 3 figures, accepted for publication by Physical Review Letter

The self-organized critical forest-fire model on large scales

We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively different types of fires that superimpose to give the effective exponents typically measured in simulations. We show that this explains not only why the exponent characterizing the fire-size distribution changes with increasing correlation length, but allows also to predict its asymptotic value. We support our arguments by computer simulations of a coarse-grained model, by scaling arguments and by analyzing states that are created artificially by superimposing the two types of fires.Comment: 26 pages, 7 figure

Synchronization and Coarsening (without SOC) in a Forest-Fire Model

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

Phase Transitions in a Forest-Fire Model

We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only one side and hysteresis. The critical behavior is found to be that of the self-organized critical forest-fire model [B. Drossel and F. Schwabl, Phys. Rev. Lett. 69, 1629 (1992)], whereas in the adjacent phase one finds the spiral waves of the Bak et al. forest-fire model [P. Bak, K. Chen and C. Tang, Phys. Lett. A 147, 297 (1990)]. In the third phase one observes clustering of trees with the fire burning at the edges of the clusters. The relation between the density distribution in the spiral state and the percolation threshold is explained and the implications for stationary states with spiral waves in arbitrary excitable systems are discussed. Furthermore, we comment on the possibility of mapping self-organized critical systems onto 'ordinary' critical systems.Comment: 30 pages RevTeX, 9 PostScript figures (Figs. 1,2,4 are of reduced quality), to appear in Phys. Rev.

Phase Transition in a Stochastic Forest Fire Model and Effects of the Definition of Neighbourhood

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits a surprisingly sharp phase transition which can be shifted by redefinition of neighbourhood. The results can also be interpreted in terms of disease-spreading and are quite unsettling from the epidemologist's point of view, since variation of one crucial parameter only by a few percent can result in the change from endemic to epidemic behaviour.Comment: 23 pages, 13 figure

Broken scaling in the Forest Fire Model

We investigate the scaling behavior of the cluster size distribution in the Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical simulations, partly on (massively) parallel machines. It turns out that simple scaling is clearly violated, as already pointed out by Grassberger [P. Grassberger, J. Phys. A: Math. Gen. 26, 2081 (1993)], but largely ignored in the literature. Most surprisingly the statistics not seems to be described by a universal scaling function, and the scale of the physically relevant region seems to be a constant. Our results strongly suggest that the DS-FFM is not critical in the sense of being free of characteristic scales.Comment: 9 pages in RevTEX4 format (9 figures), submitted to PR

Corrections to scaling in the forest-fire model

We present a systematic study of corrections to scaling in the self-organized critical forest-fire model. The analysis of the steady-state condition for the density of trees allows us to pinpoint the presence of these corrections, which take the form of subdominant exponents modifying the standard finite-size scaling form. Applying an extended version of the moment analysis technique, we find the scaling region of the model and compute the first non-trivial corrections to scaling.Comment: RevTeX, 7 pages, 7 eps figure

Forest fires and other examples of self-organized criticality

We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of the initial conditions and without fine-tuning of the parameters. After an introduction, we define the rules of the model and discuss various large-scale structures which may appear in this system. The origin of the critical behavior is explained, critical exponents are introduced, and scaling relations between the exponents are derived. Results of computer simulations and analytical calculations are summarized. The existence of an upper critical dimension and the universality of the critical behavior under changes of lattice symmetry or the introduction of immunity are discussed. A survey of interesting modifications of the forest-fire model is given. Finally, several other important SOC models are briefly described.Comment: 37 pages RevTeX, 13 PostScript figures (Figs 1, 4, 13 are of reduced quality to keep download times small