In our ongoing multi-wavelength study of cluster AGN, we find ~75% of the spectroscopically identified cluster X-ray point sources (XPS) with L(0.3-8.0keV)>10^{42} erg s^{-1} and cluster radio galaxies with P(1.4 GHz) > 3x10^{23} W Hz^{-1} in 11 moderate redshift clusters (0.2<z<0.4) are located within 500 kpc from the cluster center. In addition, these sources are much more centrally concentrated than luminous cluster red sequence (CRS) galaxies. With the exception of one luminous X-ray source, we find that cluster XPSs are hosted by passive red sequence galaxies, have X-ray colors consistent with an AGN power-law spectrum, and have little intrinsic obscuring columns in the X-ray (in agreement with previous studies). Our cluster radio sources have properties similar to FR1s, but are not detected in X-ray probably because their predicted X-ray emission falls below our sensitivity limits. Based on the observational properties of our XPS population, we suggest that the cluster XPSs are low-luminosity BL Lac objects, and thus are beamed low-power FR 1s. Extrapolating the X-ray luminosity function of BL Lacs and the Radio luminosity function of FR 1s down to fainter radio and X-ray limits, we estimate that a large fraction, perhaps all CRSs with L>L* possess relativistic jets which can inject energy into the ICM, potentially solving the uniform heating problem in the central region of clusters.

Quyen N. Hart John T. Stocke Eric J. Hallman

Using Chandra imaging spectroscopy and Very Large Array (VLA) L-band radio maps, we have identified radio sources at P_{1.4GHz} >=5x10^{23} W Hz^{-1} and X-ray point sources (XPSs) at L_{0.3-8keV}>=5x10^{42} erg s^{-1} in L>L* galaxies in 12 high-redshift (0.4<z<1.2) clusters of galaxies. The radio galaxies and XPSs in this cluster sample, chosen to be consistent with Coma Cluster progenitors at these redshifts, are compared to those found at low-z analyzed in Hart et al. (2009). Within a projected radius of 1 Mpc of the cluster cores, we find 17 cluster radio galaxies (11 with secure redshifts, including one luminous FR II radio source at z=0.826, and 6 more with host galaxy colors similar to cluster ellipticals). The radio luminosity function (RLF) of the cluster radio galaxies as a fraction of the cluster red sequence (CRS) galaxies reveals significant evolution of this population from high-z to low-z, with higher power radio galaxies situated in lower temperature clusters at earlier epochs. Additionally, there is some evidence that cluster radio galaxies become more centrally concentrated than CRS galaxies with cosmic time. Within this same projected radius, we identify 7 spectroscopically-confirmed cluster XPSs, all with CRS host galaxy colors. Consistent with the results from Martini et al. (2009), we estimate a minimum X-ray active fraction of 1.4+/-0.8% for CRS galaxies in high-z clusters, corresponding to an approximate 10-fold increase from 0.15+/-0.15% at low-z. Although complete redshift information is lacking for several XPSs in z>0.4 cluster fields, the increased numbers and luminosities of the CRS radio galaxies and XPSs suggest a substantial (9-10 fold) increase in the heat injected into high redshift clusters by AGN compared to the present epoch.

Quyen N. Hart John T. Stocke August E. Evrard Erica E. Ellingson Wayne A. Barkhouse

A 1.8 T dipole magnet using thin grain oriented silicon steel laminations has been constructed as a prototype for a muon synchrotron ramping at 400 Hz. Following the practice in large 3 phase transformers and our own Opera-2d simulations, joints are mitred to take advantage of the magnetic properties of the steel which are much better in the direction in which the steel was rolled. Measurements with a Hysteresigraph 5500 and Epstein frame show a high magnetic permeability which minimizes stored energy in the yoke allowing the magnet to ramp quickly with modest voltage. Coercivity is low which minimizes hysteresis losses. A power supply with a fast Insulated Gate Bipolar Transistor (IGBT) switch and a capacitor was constructed. Coils are wound with 12 gauge copper wire. Thin wire and laminations minimize eddy current losses. The magnetic field was measured with a peak sensing Hall probe.

D. J. Summers L. M. Cremaldi T. L. Hart L. P. Perera M. Reep H. Witte S. Hansen M. L. Lopes J. Reidy, Jr.

This paper discusses a paper by L. E. J. Brouwer on possible cardinalities of subsets of the continuum.

Klaas Pieter Hart

This article is a reflection on the mathematical legacy of Professor Petr Simon.

K. P. Hart M. Hrusak J. L. Verner

In this work, we present a bilinear Tb theorem for singular integral operators of Calder\'on-Zygmund type. We prove some new accretive type Littlewood-Paley theory and bilinear paraproduct for a para-accretive function setting. We also introduce a criterion for extending certain Lp Clader\'on reproducing formulas to convergence in H1.

Jarod Hart

We begin the study of categorical logic for continuous model theory. In particular, we 1. introduce the notions of metric logical categories and functors as categorical equivalents of a metric theory and interpretations, 2. prove a continuous version of conceptual completeness showing that $T^\eq$ is the maximal conservative expansion of $T$, and 3. define the concept of a metric pre-topos.

Jean-Martin Albert Bradd Hart

For the wave equation $\partial_t^2-\Delta+V$ on $\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\rightarrow 0$ for the relative trace of the wave group.

Hart F. Smith

The R-Matrix incorporating Time (RMT) method is a new method for solving the time-dependent Schroedinger equation for multi-electron atomic systems exposed to intense short-pulse laser light. We have employed the RMT method to investigate the time delay in the photoemission of an electron liberated from a 2p orbital in a neon atom with respect to one released from a 2s orbital following absorption of an attosecond XUV pulse. Time delays due to XUV pulses in the range 76-105 eV are presented. For an XUV pulse at the experimentally relevant 105.2 eV, we calculate the time delay to be 10.2 +/- 1.3 attoseconds, somewhat larger than estimated by other theoretical calculations, but still a factor two smaller than experiment. We repeated the calculation for a photon energy of 89.8 eV with a larger basis set capable of modelling correlated-electron dynamics within the neon atom and the residual Ne(+) ion. A time delay of 14.5 +/- 1.5 attoseconds was observed, compared to a 16.7 +/- 1.5 attosecond result using a single-configuration representation of the residual Ne(+) ion.

L. R. Moore M. A. Lysaght J. S. Parker H. W. van der Hart K. T. Taylor

The complexity and size of state-of-the-art cell models have significantly increased in part due to the requirement that these models possess complex cellular functions which are thought--but not necessarily proven--to be important. Modern cell models often involve hundreds of parameters; the values of these parameters come, more often than not, from animal experiments whose relationship to the human physiology is weak with very little information on the errors in these measurements. The concomitant uncertainties in parameter values result in uncertainties in the model outputs or Quantities of Interest (QoIs). Global Sensitivity Analysis (GSA) aims at apportioning to individual parameters (or sets of parameters) their relative contribution to output uncertainty thereby introducing a measure of influence or importance of said parameters. New GSA approaches are required to deal with increased model size and complexity; a three stage methodology consisting of screening (dimension reduction), surrogate modeling, and computing Sobol' indices, is presented. The methodology is used to analyze a physiologically validated numerical model of neurovascular coupling which possess 160 uncertain parameters. The sensitivity analysis investigates three quantities of interest (QoIs), the average value of $K^+$ in the extracellular space, the average volumetric flow rate through the perfusing vessel, and the minimum value of the actin/myosin complex in the smooth muscle cell. GSA provides a measure of the influence of each parameter, for each of the three QoIs, giving insight into areas of possible physiological dysfunction and areas of further investigation.

J. L. Hart P. A. Gremaud T. David