Hobby Lobby and the Pathology of Citizens United

Four years ago, Citizens United v. Federal Election Commission held that for-profit corporations possess a First Amendment right to make independent campaign expenditures. In so doing, the United States Supreme Court invited speculation that such corporations might possess other First Amendment rights as well. The petitioners in Conestoga Wood Specialties Corp. v. Sebelius are now arguing that for-profit corporations are among the intended beneficiaries of the Free Exercise Clause and, along with the respondents in Sebelius v. Hobby Lobby Stores, that they also qualify as “persons” under the Religious Freedom Restoration Act (RFRA). Neither suggestion follows inexorably from Citizens United, and the role of the case in the pending disputes remains to be seen. Still, it seems fair to say that the Court’s fidelity to the concept of corporate personhood espoused in Citizens United will shape how it evaluates the pending religious liberty cases

Equation of state from lattice QCD

Recent results on the equation of state from lattice QCD are reviewed. The lattice technique and previous results are shortly discussed. New results for physical quark masses and two sets of lattice spacings are presented. The pressure, energy density, entropy density, speed of sound and quark number susceptibilities are determined.Comment: 10 pages, 11figures. Plenary talk presented at the Quark Matter 2005 conferenc

The Bar--Halo Interaction--I. From Fundamental Dynamics to Revised N-body Requirements

Only through resonances can non-axisymmetric features such as spiral arms and bars exert torques over large scales and change the overall structure of a near-equilibrium galaxy. We describe the resonant interaction mechanism in detail and derive explicit criteria for the particle number required to simulate these dynamical processes accurately using N-body simulations and illustrate them with numerical experiments. To do this, we perform direct numerical solution of perturbation theory and make detailed comparisons with N-body simulations. The criteria include: sufficient particle coverage in phase space near the resonance and enough particles to minimize gravitational potential fluctuations that will change the dynamics of the resonant encounter. Some of our more surprising findings are as follows. First, the Inner-Lindblad-like resonance (ILR), responsible for coupling the bar to the central halo cusp, requires almost 10^9 equal mass particles within the virial radius for a Milky-Way-like bar in an NFW profile. Second, orbits that linger near the resonance receive more angular momentum than orbits that move through the resonance quickly. Small-scale fluctuations present in state-of-the-art particle-particle simulations can knock orbits out of resonance, preventing them from lingering and, thereby, decrease the torque. The required particle numbers are sufficiently high for scenarios of interest that apparent convergence in particle number is misleading: the convergence is in the noise-dominated regime. State-of-the-art simulations are not adequate to follow all aspects of secular evolution driven by the bar-halo interaction. We present a procedure to test the requirements for individual N-body codes for the actual problem of interest. [abridged]Comment: 30 pages, 19 figures, submitted to Monthly Notices. For paper with figures at full resolution: http://www.astro.umass.edu/~weinberg/weinberg_katz_1.ps.g

Finite temperature and chemical potential in lattice QCD and its critical point

We propose a method to study lattice QCD at finite temperature (T) and chemical potential (\mu). We compare the method with direct results and with the Glasgow method by using n_f=4 QCD at Im(\mu)\neq0. We locate the critical endpoint (E) of QCD on the Re(\mu)-T plane. We use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices. Our results are based on {\cal{O}}(10^3-10^4) configurations.Comment: 8 pages, 4 figures. Talk given at the XXX. Hirschegg Workshop on Ultrarelativistic Heavy-Ion Collisions, January 13-19, 200

Lattice QCD results at finite T and \mu

We propose a method to study lattice QCD at finite temperature (T) and chemical potential (\mu). We test the method and compare it with the Glasgow method using n_f=4 staggered QCD with imaginary \mu. The critical endpoint (E) of QCD on the Re(\mu)-T plane is located. We use n_f=2+1 dynamical staggered quarks with semi-realistic masses on L_t=4 lattices. Our results are based on {\cal{O}}(10^3-10^4) configurations.Comment: 9 pages, 4 figures. Talk given at Budapest'02 Workshop on Quark and Hadron Dynamics, Budapest, March 3-7, 200

Propagation of ultrahigh energy cosmic rays and compact sources

The clustering of ultrahigh energy (>10^{20} eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. Statistical analysis (Dubovsky et al., 2000) estimated the source density. We extend their analysis to give also the confidence intervals (CI) for the source density using a.) no assumptions on the relationship between clustered and unclustered events; b.) nontrivial distributions for the source luminosities and energies; c.) the energy dependence of the propagation. We also determine the probability that a proton created at a distance r with energy E arrives at earth above a threshold E_c. Using this function one can determine the observed spectrum just by one numerical integration for any injection spectrum. The observed 14 UHECR events above 10^{20} eV with one doublet gives for the source densities 180_{-165}^{+2730}\cdot 10^{-3} Mpc^{-3} (on the 68% confidence level).Comment: 4 pages, 1 figure, talk to be presented at the 27th International Cosmic Ray Conference, Hamburg, Germany, August 7-15, 200

Ultrahigh energy cosmic rays as a Grand Unification signal

We analyze the spectrum of the ultrahigh energy (above \approx 10^{9} GeV) cosmic rays. With a maximum likelihood analysis we show that the observed spectrum is consistent with the decay of extragalactic GUT scale particles. The predicted mass for these superheavy particles is m_X=10^b GeV, where b=14.6_{-1.7}^{+1.6}.Comment: 4 pages, 3 figures, talk to be presented at the 27th International Cosmic Ray Conference, Hamburg, Germany, August 7-15, 200

The Bar-Halo Interaction - II. Secular evolution and the religion of N-body simulations

This paper explores resonance-driven secular evolution between a bar and dark-matter halo using N-body simulations. We make direct comparisons to our analytic theory (Weinberg & Katz 2005) to demonstrate the great difficulty that an N-body simulation has representing these dynamics for realistic astronomical interactions. In a dark-matter halo, the bar's angular momentum is coupled to the central density cusp (if present) by the Inner Lindblad Resonance. Owing to this angular momentum transfer and self-consistent re-equilibration, strong realistic bars WILL modify the cusp profile, lowering the central densities within about 30% of the bar radius in a few bar orbits. Past results to the contrary (Sellwood 2006, McMillan & Dehnen 2005) may be the result of weak bars or numerical artifacts. The magnitude depends on many factors and we illustrate the sensitivity of the response to the dark-matter profile, the bar shape and mass, and the galaxy's evolutionary history. For example, if the bar length is comparable to the size of a central dark-matter core, the bar may exchange angular momentum without changing its pattern speed significantly. We emphasise that this apparently simple example of secular evolution is remarkably subtle in detail and conclude that an N-body exploration of any astronomical scenario requires a deep investigation into the underlying dynamical mechanisms for that particular problem to set the necessary requirements for the simulation parameters and method (e.g. particle number and Poisson solver). Simply put, N-body simulations do not divinely reveal truth and hence their results are not infallible. They are unlikely to provide useful insight on their own, particularly for the study of even more complex secular processes such as the production of pseudo-bulges and disk heating.Comment: 23 pages, 18 figures, submitted to Monthly Notices. For paper with figures at full resolution: http://www.astro.umass.edu/~weinberg/weinberg_katz_2.ps.g