76 research outputs found

    On the equilibrium morphology of systems drawn from spherical collapse experiments

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    We present a purely theoretical study of the morphological evolution of self-gravitating systems formed through the dissipationless collapse of N-point sources. We explore the effects of resolution in mass and length on the growth of triaxial structures formed by an instability triggered by an excess of radial orbits. We point out that as resolution increases, the equilibria shift, from mildly prolate, to oblate. A number of particles N ~= 100000 or larger is required for convergence of axial aspect ratios. An upper bound for the softening, e ~ 1/256, is also identified. We then study the properties of a set of equilibria formed from scale-free cold initial mass distributions, ro ~ r^-g with 0 <= g <= 2. Oblateness is enhanced for initially more peaked structures (larger values of g). We map the run of density in space and find no evidence for a power-law inner structure when g <= 3/2 down to a mass fraction <~0.1 per cent of the total. However, when 3/2 < g <= 2, the mass profile in equilibrium is well matched by a power law of index ~g out to a mass fraction ~ 10 per cent. We interpret this in terms of less-effective violent relaxation for more peaked profiles when more phase mixing takes place at the centre. We map out the velocity field of the equilibria and note that at small radii the velocity coarse-grained distribution function (DF) is Maxwellian to a very good approximation.Comment: 16 page

    A spatially explicit model for tropical tree diversity patterns

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    A complex two-parameter model resembling the classical voter model is introduced to describe macroecological properties of tropical tree communities. Monte-Carlo type computer simulations are performed on the model, investigating species abundances and the spatial distribution of individuals and species. Simulation results are critically compared with the experimental data obtained from a tree census on a 50 hectares area of the Barro Colorado Island (BCI), Panama. The model parameters are optimized for reproducing quantitatively the experimental results from the BCI dataset.Comment: 8 pages, 12 figure

    Evolutionary games on graphs

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    Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

    Picture-Book Professors:Academia and Children's Literature

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