Sports are spontaneous generators of stories. Through skill and chance, the script of each game is dynamically written in real time by players acting out possible trajectories allowed by a sports rules. By properly characterizing a given sports ecolo
gy of `game stories, we are able to capture the sports capacity for unfolding interesting narratives, in part by contrasting them with random walks. Here, we explore the game story space afforded by a data set of 1,310 Australian Football League (AFL) score lines. We find that AFL games exhibit a continuous spectrum of stories rather than distinct clusters. We show how coarse-graining reveals identifiable motifs ranging from last minute comeback wins to one-sided blowouts. Through an extensive comparison with biased random walks, we show that real AFL games deliver a broader array of motifs than null models, and we provide consequent insights into the narrative appeal of real games.
We show that by changing a single non-dimensional number, the thermal Rossby number, global atmospheric simulations with only axisymmetric forcing pass from an Earth-like atmosphere to a superrotating atmosphere that more resembles the atmospheres of
Venus or Titan. The transition to superrotation occurs under conditions in which equatorward-propagating Rossby waves generated by baroclinic instability at intermediate and high latitudes are suppressed, which will occur when the deformation radius exceeds the planetary radius. At large thermal Rossby numbers following an initial, nearly axisymmetric phase, a global baroclinic wave of zonal wavenumber one generated by mixed barotropic-baroclinic instability dominates the eddy flux of zonal momentum. The global wave converges eastward zonal momentum to the equator and deposits westward momentum at intermediate latitudes during spinup and before superrotation emerges, and the baroclinic instability ceases once superrotation is established. A global barotropic mode of zonal wavenumber one generated by a mix of high- and low-latitude barotropic instability is responsible for maintaining superrotation in the statistically steady state. At intermediate thermal Rossby numbers, momentum flux by the global baroclinic mode is subdominant relative to smaller baroclinic modes, and thus strong superrotation does not develop.
(Abridged) The thermal state of the intracluster medium results from a competition between gas cooling and heating. The heating comes from two distinct sources: gravitational heating from the collapse of the dark matter halo and thermal input from ga
laxy/black hole formation. However, a long standing problem has been that cosmological simulations based on smoothed particle hydrodynamics (SPH) and Eulerian mesh codes predict different results even when cooling and galaxy/black hole heating are switched off. Clusters formed in SPH simulations show near powerlaw entropy profiles, while those formed in mesh simulations develop a core and do not allow gas to reach such low entropies. Since the cooling rate is closely connected to the minimum entropy of the gas, the differences are of potentially key importance. In this paper, we investigate the origin of this discrepancy. By comparing simulations run using the GADGET-2 SPH code and the FLASH adaptive Eulerian mesh code, we show that the discrepancy arises during the idealised merger of two clusters. The difference is not sensitive to the resolution of our simulations, nor is it is due differences in the gravity solvers, Galilean non-invariance of the mesh code, or an effect of unsuitable artificial viscosity in the SPH code. Instead, we find that the difference is inherent to the treatment of eddies and fluid instabilities. These are suppressed in the SPH simulations, while the cluster mergers generate strong vortices in the mesh simulations that efficiently mix the fluid and erase the low entropy gas. Consequently, particles in the SPH simulations retain a close connection to their initial entropy, while this connection is much weaker in the mesh simulations. We discuss the potentially profound implications of these results.
We test four commonly used astrophysical simulation codes; Enzo, Flash, Gadget and Hydra, using a suite of numerical problems with analytic initial and final states. Situations similar to the conditions of these tests, a Sod shock, a Sedov blast and
both a static and translating King sphere occur commonly in astrophysics, where the accurate treatment of shocks, sound waves, supernovae explosions and collapsed haloes is a key condition for obtaining reliable validated simulations. We demonstrate that comparable results can be obtained for Lagrangian and Eulerian codes by requiring that approximately one particle exists per grid cell in the region of interest. We conclude that adaptive Eulerian codes, with their ability to place refinements in regions of rapidly changing density, are well suited to problems where physical processes are related to such changes. Lagrangian methods, on the other hand, are well suited to problems where large density contrasts occur and the physics is related to the local density itself rather than the local density gradient.
