NGC 1300 Dynamics: II. The response models

We study the stellar response in a spectrum of potentials describing the barred spiral galaxy NGC 1300. These potentials have been presented in a previous paper and correspond to three different assumptions as regards the geometry of the galaxy. For each potential we consider a wide range of $\Omega_p$ pattern speed values. Our goal is to discover the geometries and the $\Omega_p$ supporting specific morphological features of NGC 1300. For this purpose we use the method of response models. In order to compare the images of NGC 1300 with the density maps of our models, we define a new index which is a generalization of the Hausdorff distance. This index helps us to find out quantitatively which cases reproduce specific features of NGC 1300 in an objective way. Furthermore, we construct alternative models following a Schwarzschild type technique. By this method we vary the weights of the various energy levels, and thus the orbital contribution of each energy, in order to minimize the differences between the response density and that deduced from the surface density of the galaxy, under certain assumptions. We find that the models corresponding to $\Omega_p\approx16$\ksk and $\Omega_p\approx22$\ksk are able to reproduce efficiently certain morphological features of NGC 1300, with each one having its advantages and drawbacks.Comment: 13 pages, 10 figures, accepted for publication in MNRA

Comment on "Correlation between Compact Radio Lout Quasars and Ultrahigh Energy Cosmic Rays"

In a recent paper, Farrar and Biermann argue that there is a strong correlation between the direction of the five highest-energy cosmic-ray events and compact, radio-loud quasars. This Comment shows that this analysis contains several inconsistencies and errors so that the significance of any such correlation is certainly greatly overestimated and perhaps nonexistent.Comment: 2 pages, REVTE

Covariant EBK quantization of the electromagnetic two-body problem

We discuss a method to transform the covariant Fokker action into an implicit two-degree-of-freedom Hamiltonian for the electromagnetic two-body problem with arbitrary masses. This dynamical system appeared 100 years ago and it was popularized in the 1940's by the still incomplete Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. The Hamiltonian formalism is then used to motivate an EBK quantization based on the classical trajectories with a non-perturbative formula that predicts energies free of infinities.Comment: 21 page

Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an endpoint along each trajectory plus the respective segment of trajectory for the other particle inside the lightcone of each endpoint. We show that the conditions for an extremum of our functional are the mixed-type-neutral-equations with implicit state-dependent-delay of the electromagnetic-two-body problem. We put the functional on a natural Banach space and show that the functional is Frechet-differentiable. We develop a method to calculate the second variation for C2 orbital perturbations in general and in particular about circular orbits of large enough radii. We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii. Our results suggest a bifurcation at some radius below which the circular orbits become saddle-point extrema. We give a precise definition for the distributional-like integrals of the Fokker action and discuss a generalization to a Sobolev space of trajectories where the equations of motion are satisfied almost everywhere. Last, we discuss the existence of solutions for the state-dependent delay equations with slightly perturbated arcs of circle as the boundary conditions and the possibility of nontrivial solenoidal orbits

Consumer Boycotts and Freedom of Association: A Comment on a Recently Proposed Theory

This Essay comments on a recent article by Professor Michael Harper, which suggested that the United States Constitution guarantees a right to boycott. The authors argue that, while there can be no unconditional right to boycott, constitutional values are properly invoked in defense of boycotts and that the government should have to better articulate countervailing values in order to suppress a particular boycott or class of boycotts

RASS-SDSS Galaxy Cluster Survey. VI. The dependence of the cluster SFR on the cluster global properties

Using a subsample of 79 nearby clusters from the RASS-SDSS galaxy cluster catalogue of Popesso et al. (2005a), we perform a regression analysis between the cluster integrated star formation rate (Sigma_SFR) the cluster total stellar mass (M_star), the fractions of star forming (f_SF) and blue (f_b) galaxies and other cluster global properties, namely its richness (N_gal, i.e. the total number of cluster members within the cluster virial radius), velocity dispersion (sigma_v), virial mass (M_200), and X-ray luminosity (L_X). All cluster global quantities are corrected for projection effects before the analysis. Galaxy SFRs and stellar masses are taken from the catalog of Brinchmann et al. (2004), which is based on SDSS spectra. We only consider galaxies with M_r <= -20.25 in our analysis, and exclude AGNs. We find that both Sigma_SFR and M_star are correlated with all the cluster global quantities. A partial correlation analysis show that all the correlations are induced by the fundamental one between Sigma_SFR and N_gal, hence there is no evidence that the cluster properties affect the mean SFR or M_star per galaxy. The relations between Sigma_SFR and M_star, on one side, and both N_gal and M_200, on the other side, are linear, i.e. we see no evidence that different clusters have different SFR or different M_star per galaxy and per unit mass. The fraction f_SF does not depend on any cluster property considered, while f_b does depend on L_X. We note that a significant fraction of star-forming cluster galaxies are red (~25% of the whole cluster galaxy population). We conclude that the global cluster properties are unable to affect the SF properties of cluster galaxies, but the presence of the X-ray luminous intra-cluster medium can affect their colors, perhaps through the ram-pressure stripping mechanism.Comment: 14 pages, 12 figures, accepted for publication on A&A; corrected coefficient in Tab.

Alternative derivation of the relativistic contribution to perihelic precession

An alternative derivation of the first-order relativistic contribution to perihelic precession is presented. Orbital motion in the Schwarzschild geometry is considered in the Keplerian limit, and the orbit equation is derived for approximately elliptical motion. The method of solution makes use of coordinate transformations and the correspondence principle, rather than the standard perturbative approach. The form of the resulting orbit equation is similar to that derived from Newtonian mechanics and includes first-order corrections to Kepler's orbits due to general relativity. The associated relativistic contribution to perihelic precession agrees with established first-order results. The reduced radius for the circular orbit is in agreement to first-order with that calculated from the Schwarzschild effective potential. The method of solution is understandable by undergraduate students.Comment: 12 pages, 2 figures. Accepted for publication in the American Journal of Physic

Hamiltonian Formulation of Two Body Problem in Wheeler-Feynman electrodynamics

A Hamiltonian formulation for the classical problem of electromagnetic interaction of two charged relativistic particles is found.Comment: 22 pages, 8 Uuencoded Postscript figure

Dynamics of the Fisher Information Metric

We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional $J[g^{\mu\nu}(\theta^i)]$, where $g^{\mu\nu}(\theta^i)$ is the Fisher metric. We postulate that this functional of the dynamical variable $g^{\mu\nu}(\theta^i)$ is stationary with respect to small variations of these variables. Our approach enables a dynamical approach to Fisher information metric. It allows to impose symmetries on a statistical system in a systematic way. This work is mainly motivated by the entropy approach to nonmonotonic reasoning.Comment: 11 page