Complex-space singularities of 2D Euler flow in Lagrangian coordinates

We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination of complex-space Lagrangian singularities. Lagrangian singularities are found to be closer to the real domain than Eulerian singularities and seem to correspond to fluid particles which escape to (complex) infinity by the current time. Various mathematical conjectures regarding Eulerian/Lagrangian singularities are presented.Comment: 5 pages, 2 figures, submitted to Physica

Singularities of Euler flow? Not out of the blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.(A version of the paper with higher-quality figures is available at http://www.obs-nice.fr/etc7/complex.pdf)Comment: RevTeX4, 10 pages, 9 figures. J.Stat.Phys. in press (updated version

Orbiting dynamic compression laboratory

In order to examine the feasibility of carrying out dynamic compression experiments on a space station, the possibility of using explosive gun launchers is studied. The question of whether powders of a refractory metal (molybdenum) and a metallic glass could be well considered by dynamic compression is examined. In both cases extremely good bonds are obtained between grains of metal and metallic glass at 180 and 80 kb, respectively. When the oxide surface is reduced and the dynamic consolidation is carried out in vacuum, in the case of molybdenum, tensile tests of the recovered samples demonstrated beneficial ultimate tensile strengths

Effect of helicity and rotation on the free decay of turbulent flows

The self-similar decay of energy in a turbulent flow is studied in direct numerical simulations with and without rotation. Two initial conditions are considered: one non-helical (mirror-symmetric), and one with maximal helicity. The results show that, while in the absence of rotation the energy in the helical and non-helical cases decays with the same rate, in rotating flows the helicity content has a major impact on the decay rate. These differences are associated with differences in the energy and helicity cascades when rotation is present. Properties of the structures that arise in the flow at late times in each time are also discussed.Comment: 4 pages, 4 figure

Orientation dependence of the elastic instability on strained SiGe films

At low strain, SiGe films on Si substrates undergo a continuous nucleationless morphological evolution known as the Asaro-Tiller-Grinfeld instability. We demonstrate experimentally that this instability develops on Si(001) but not on Si(111) even after long annealing. Using a continuum description of this instability, we determine the origin of this difference. When modeling surface diffusion in presence of wetting, elasticity and surface energy anisotropy, we find a retardation of the instability on Si(111) due to a strong dependence of the instability onset as function of the surface stiffness. This retardation is at the origin of the inhibition of the instability on experimental time scales even after long annealing.Comment: 3 pages, 4 figure

On Making Good Games - Using Player Virtue Ethics and Gameplay Design Patterns to Identify Generally Desirable Gameplay Features

This paper uses a framework of player virtues to perform a theoretical exploration of what is required to make a game good. The choice of player virtues is based upon the view that games can be seen as implements, and that these are good if they support an intended use, and the intended use of games is to support people to be good players. A collection of gameplay design patterns, identified through their relation to the virtues, is presented to provide specific starting points for considering design options for this type of good games. 24 patterns are identified supporting the virtues, including RISK/REWARD, DYNAMIC ALLIANCES, GAME MASTERS, and PLAYER DECIDED RESULTS, as are 7 countering three or more virtues, including ANALYSIS PARALYSIS, EARLY ELIMINATION, and GRINDING. The paper concludes by identifying limitations of the approach as well as by showing how it can be applied using other views of what are preferable features in games

Soliton turbulences in the complex Ginzburg-Landau equation

We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger equation. We find that the distributions of amplitude and wavenumber of pulses depend only on the ratio of the two parameters of the amplification and the viscosity. This implies that a one-parameter family of soliton turbulence states characterized by different distributions of the soliton parameters exists continuously around the completely integrable system.Comment: 5 figure

Haughton Astrobleme: A Mid-Cenozoic Impact Crater Devon Island, Canadian Arctic Archipelago

Haughton Astrobleme is a nearly circular impact crater with a diameter of about 16 km and a central uplift in Devon Island. Bedrock exposed in the crater comprised the following mainly carbonate Lower Ordovician to Upper Silurian formations in order upward: Eleanor River, Bay Fiord, Thumb Mountain, Irene Bay and Allen Bay. The Eleanor River Formation in the centre of the crater is raised about 480 m above its normal stratigraphic position outside the crater. The much shattered and faulted lower Paleozoic rocks within the crater contrast markedly with the subhorizontal surrounding strata. The Allen Bay Formation constitutes surface exposure around all but the easternmost part of the crater's border where the Thumb Mountain and Irene Bay Formations are exposed. Also exposed in the crater are two newly recognized, and as yet unnamed, formations: a polymict impact breccia that overlies the lower Paleozoic rocks, with marked angular unconformity and crops out over about a quarter of the area of the crater; and a unit of lake sediments near the western border of the crater that lies disconformably on the impact breccia and with angular unconformity on the lower Paleozoic rocks. The impact breccia is composed chiefly of carbonate rocks, but locally contains clasts of Precambrian crystalline basement from a depth estimated to be at least 1700 m. The basement clasts show varying degrees of shock metamorphism, the highest being that displayed by rocks with vesicular, flow-banded feldspar or quartz glass. Coesite has been identified in a sample of gneiss. The lake sediments are interpreted as an infilling of the crater that occurred shortly after impact. On the basis of fossils these sediments are dated as Miocene or, possibly, Pliocene. From this and other evidence, it is concluded that the impact took place in the Miocene or Pliocene

Multifractality of the Feigenbaum attractor and fractional derivatives

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities $f(\alpha)$. This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions (Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1, 1984)) and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres