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

Causal Quantum Theory and the Collapse Locality Loophole

Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no non-local correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise theory of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it obvious that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments -- the {\it collapse locality loophole} -- which exists because of the possible time lag between a particle entering a measuring device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\approx 0.1$ light seconds.Comment: Discussion expanded; typos corrected; references adde

Further Evidence that the Redshifts of AGN Galaxies May Contain Intrinsic Components

In the decreasing intrinsic redshift (DIR) model galaxies are assumed to be born as compact objects that have been ejected with large intrinsic redshift components, z_(i), out of the nuclei of mature AGN galaxies. As young AGN (quasars) they are initially several magnitudes sub-luminous to mature galaxies but their luminosity gradually increases over 10^8 yrs, as z_(i) decreases and they evolve into mature AGN (Seyferts and radio galaxies). Evidence presented here that low- and intermediate-redshift AGN are unquestionably sub-luminous to radio galaxies is then strong support for this model and makes it likely that the high-redshift AGN (quasars) are also sub-luminous, having simply been pushed above the radio galaxies on a logz-m_(v) plot by the presence of a large intrinsic component in their redshifts. An increase in luminosity below z = 0.06 is also seen. It is associated in the DIR model with an increase in luminosity as the sources mature but, if real, is difficult to interpret in the cosmological redshift (CR) model since at this low redshift it is unlikely to be associated with a higher star formation rate or an increase in the material used to build galaxies. Whether it might be possible in the CR model to explain these results by selection effects is also examined.Comment: 12 pages, 2 figures. Contains response to referees suggestions. (Accepted for ApJL

Sensitivity of the structure of untripped mixing layers to small changes in initial conditions

An experimental study was conducted concerning the influence of small changes in initial conditions on the near- and far-field evolution of the three-dimensional structure of a plan mixing layer. A two-stream mixing layer with a velocity ratio of 0.6 was generated with the initial boundary layers on the splitter plate laminar and was nominally two-dimensional. The initial conditions were changed slightly by interchanging the high- and low-speed sides of the wind tunnel, while maintaining the same velocities, and hence velocity ratio. This resulted in small changes in the initial boundary layer properties, and the perturbations present in the boundary layers were interchanged between the high- and low-speed sides for the two cases. The results indicate that, even with this relatively minor change in initial conditions, the near-field regions of the two cases differ significantly. The peak Reynolds stress levels in the near-field differ by up to 100 percent, and this is attributed to a difference in the location of the initial spanwise vortex roll-up. In addition, the positions and shapes of the individual streamwise vortical structures differ for the two cases, although the overall structures differ for the two cases, although the overall qualitative description of these structures is comparable. The subsequent reorganization and decay of the streamwise vortical structures is very similar for the two cases. As a result, in the far field, both mixing layers achieve similar structure, yielding comparable growth rates, Reynolds stress, distribution, and spectral content

A 3-component laser-Doppler velocimeter data acquisition and reduction system

A laser doppler velocimeter capable of measuring all three components of velocity simultaneously in low-speed flows is described. All the mean velocities, Reynolds stresses, and higher-order products can be evaluated. The approach followed is to split one of the two colors used in a 2-D system, thus creating a third set of beams which is then focused in the flow from an off-axis direction. The third velocity component is computed from the known geometry of the system. The laser optical hardware and the data acquisition electronics are described in detail. In addition, full operating procedures and listings of the software (written in BASIC and ASSEMBLY languages) are also included. Some typical measurements obtained with this system in a vortex/mixing layer interaction are presented and compared directly to those obtained with a cross-wire system

Cosmic ray acceleration to ultrahigh energy in radio galaxies

The origin of ultrahigh energy cosmic rays (UHECRs) is an open question. In this proceeding, we first review the general physical requirements that a source must meet for acceleration to 10-100 EeV, including the consideration that the shock is not highly relativistic. We show that shocks in the backflows of radio galaxies can meet these requirements. We discuss a model in which giant-lobed radio galaxies such as Centaurus A and Fornax A act as slowly-leaking UHECR reservoirs, with the UHECRs being accelerated during a more powerful past episode. We also show that Centaurus A, Fornax A and other radio galaxies may explain the observed anisotropies in data from the Pierre Auger Observatory, before examining some of the difficulties in associating UHECR anisotropies with astrophysical sources.Comment: 6 pages, 4 figures. Proceedings of UHECR 2018, 8-12 October 2018, Paris, Franc

Light to Mass Variations with Environment

Large and well defined variations exist between the distribution of mass and the light of stars on extragalactic scales. Mass concentrations in the range 10^12 - 10^13 M_sun manifest the most light per unit mass. Group halos in this range are typically the hosts of spiral and irregular galaxies with ongoing star formation. On average M/L_B ~ 90 M_sun/L_sun in these groups . More massive halos have less light per unit mass. Within a given mass range, halos that are dynamically old as measured by crossing times and galaxy morphologies have distinctly less light per unit mass. At the other end of the mass spectrum, below 10^12 M_sun, there is a cutoff in the manifestation of light. Group halos in the range 10^11 - 10^12 M_sun can host dwarf galaxies but with such low luminosities that M/L_B values can range from several hundred to several thousand. It is suspected that there must be completely dark halos at lower masses. Given the form of the halo mass function, it is the low relative luminosities of the high mass halos that has the greatest cosmological implications. Of order half the clustered mass may reside in halos with greater than 10^14 M_sun. By contrast, only 5-10% of clustered mass would lie in entities with less than 10^12 M_sun.Comment: 15 pages, 9 figures, 2 tables, Accepted Astrophysical Journal 619, 000, 2005 (Jan 1