Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

More Evidence for an Oscillation Superimposed on the Hubble Flow

In a recent investigation evidence was presented for a low-level sinusoidal oscillation superimposed on top of the Hubble flow. This oscillation was in V$_{CMB}$, in a sample of type Ia Supernovae sources with accurate distances, and it was found to have a wavelength close to 40 Mpc. It became easily visible after the removal of several previously identified discrete velocity components. Its amplitude like that of the Hubble velocity showed an increase with distance, as would be expected for a constant-amplitude space oscillation. Here we report that this oscillation is also present in distance clumping in these sources, with the same wavelength, but in phase quadrature. The discrete velocity components do not play a role in detecting the distance clumping wavelength. Assuming that time proceeds from high cosmological redshift to low, the blue-shifted velocity peaks, which represent the contraction stage of the velocity oscillation, then lead the density peaks. With the discrete velocity components removed we also find evidence for at least one other, weaker velocity oscillation. It is found to have a wavelength similar to one reported in density clumping by previous investigators. In those cases the source samples were much larger.Comment: 7 pages, with 6 figures, accepted for publication in Astrophysics and Space Scienc

On The Depolarization Asymmetry Seen in Giant Radio Lobes

The depolarization asymmetry seen in double-lobed radio sources, referred to as the Laing-Garrington (L-G) effect where more rapid depolarization is seen in the lobe with no visible jet as the wavelength increases, can be explained either by internal differences between the two lobes, or by an external Faraday screen that lies in front of only the depolarized lobe. If the jet one-sidedness is due to relativistic beaming the depolarization asymmetry must be due to an intervening Faraday screen. If it is intrinsic the depolarization asymmetry must be related to internal differences in the lobes. We assume in this paper that the speed in the outer jet of several Fanaroff-Riley Class 1 (FRI) sources exhibiting the L-G effect is close to the 0.1c reported by several other investigators. For these sources we find that the jet one-sidedness cannot be explained by beaming and therefore must be intrinsic. In these FRI sources the L-G effect must be due to differences that originate inside the lobes themselves. Although it is not known if the flow in the outer jets of FRII sources also slows to this speed it is suggested that the explanation of the L-G effect is likely to be the same in both types. This argument is strengthened by the recent evidence that FRII galaxies have very large viewing angles, which in turn implies that the L-G model cannot work regardless of the jet velocity. It may therefore be too soon to completely rule out internal depolarization in the lobes as the true explanation for the L-G effect.Comment: 8 pages with 4 figures. Accepted for publication in Ap&S

Towards the Distributed Burning Regime in Turbulent Premixed Flames

Three-dimensional numerical simulations of canonical statistically-steady statistically-planar turbulent flames have been used in an attempt to produce distributed burning in lean methane and hydrogen flames. Dilatation across the flame means that extremely large Karlovitz numbers are required; even at the extreme levels of turbulence studied (up to a Karlovitz number of 8767) distributed burning was only achieved in the hydrogen case. In this case, turbulence was found to broaden the reaction zone visually by around an order of magnitude, and thermodiffusive effects (typically present for lean hydrogen flames) were not observed. In the preheat zone, the species compositions differ considerably from those of one-dimensional flames based a number of different transport models (mixture-averaged, unity Lewis number, and a turbulent eddy viscosity model). The behaviour is a characteristic of turbulence dominating non-unity Lewis number species transport, and the distinct limit is again attributed to dilatation and its effect on the turbulence. Peak local reaction rates are found to be lower in the distributed case than in the lower Karlovitz cases but higher than in the laminar flame, which is attributed to effects that arise from the modified fuel-temperature distribution that results from turbulent mixing dominating low Lewis number thermodiffusive effects. Finally, approaches to achieve distributed burning at realisable conditions are discussed; factors that increase the likelihood of realising distributed burning are higher pressure, lower equivalence ratio, higher Lewis number, and lower reactant temperature

Picking pockets on the lawn: the development of tactics and strategies in a mobile game

This paper presents Treasure, an outdoor mobile multiplayer game inspired by Weiser’s notion of seams, gaps and breaks in different media. Playing Treasure involves movement in and out of a wi-fi network, using PDAs to pick up virtual ’coins’ that may be scattered outside network coverage. Coins have to be uploaded to a server to gain game points, and players can collaborate with teammates to double the points given for an upload. Players can also steal coins from opponents. As they move around, players’ PDAs sample network signal strength and update coverage maps. Reporting on a study of players taking part in multiple games, we discuss how their tactics and strategies developed as their experience grew with successive games. We suggest that meaningful play arises in just this way, and that repeated play is vital when evaluating such games

Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory

We use polarization-entangled photon pairs to demonstrate quantum nonlocality in an experiment suitable for advanced undergraduates. The photons are produced by spontaneous parametric downconversion using a violet diode laser and two nonlinear crystals. The polarization state of the photons is tunable. Using an entangled state analogous to that described in the Einstein-Podolsky-Rosen ``paradox,'' we demonstrate strong polarization correlations of the entanged photons. Bell's idea of a hidden variable theory is presented by way of an example and compared to the quantum prediction. A test of the Clauser, Horne, Shimony and Holt version of the Bell inequality finds $S = 2.307 \pm 0.035$, in clear contradiciton of hidden variable theories. The experiments described can be performed in an afternoon.Comment: 10 pages, 6 figure

Reality in quantum mechanics, Extended Everett Concept, and consciousness

Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer's consciousness into quantum theory of measurements. Most naturally this is achieved in the framework of Everett's "many-worlds interpretation" of quantum mechanics. According to this interpretation, various classical alternatives are perceived by consciousness separately from each other. In the Extended Everett Concept (EEC) proposed by the present author, the separation of the alternatives is identified with the phenomenon of consciousness. This explains classical character of the alternatives and unusual manifestations of consciousness arising "at the edge of consciousness" (i.e. in sleep or trance) when its access to "other alternative classical realities" (other Everett's worlds) becomes feasible. Because of reversibility of quantum evolution in EEC, all time moments in the quantum world are equivalent while the impression of flow of time appears only in consciousness. If it is assumed that consciousness may influence onto probabilities of alternatives (which is consistent in case of infinitely many Everett's worlds), EEC explains free will, "probabilistic miracles" (observing low-probability events) and decreasing entropy in the sphere of life.Comment: 17 pages, 2 figures in EP