Binding the Diproton in Stars: Anthropic Limits on the Strength of Gravity

We calculate the properties and investigate the stability of stars that burn via strong (and electromagnetic) interactions, and compare their properties with those that, as in our Universe, include a rate-limiting weak interaction. It has been suggested that, if the diproton were bound, stars would burn ~10^{18} times brighter and faster via strong interactions, resulting in a universe that would fail to support life. By considering the representative case of a star in our Universe with initially equal numbers of protons and deuterons, we find that stable, "strong-burning" stars adjust their central densities and temperatures to have familiar surface temperatures, luminosities and lifetimes. There is no "diproton disaster". In addition, strong-burning stars are stable in a much larger region of the parameter space of fundamental constants, specifically the strength of electromagnetism and gravity. The strongest anthropic bound on stars in such universes is not their stability, as is the case for stars limited by the weak interaction, but rather their lifetime. Regardless of the strength of electromagnetism, all stars burn out in mere millions of years unless the gravitational coupling constant is extremely small, \alpha_G < 10^{-30}.Comment: 16 pages, 4 figures. Accepted for publication in JCA

Testing the Multiverse: Bayes, Fine-Tuning and Typicality

Theory testing in the physical sciences has been revolutionized in recent decades by Bayesian approaches to probability theory. Here, I will consider Bayesian approaches to theory extensions, that is, theories like inflation which aim to provide a deeper explanation for some aspect of our models (in this case, the standard model of cosmology) that seem unnatural or fine-tuned. In particular, I will consider how cosmologists can test the multiverse using observations of this universe.Comment: 19 pages, 3 figures. Conference proceedings: to appear in "The Philosophy of Cosmology", edited by Khalil Chamcham, Joseph Silk, John D. Barrow, and Simon Saunders. Cambridge University Press, 201

The effects of molecular structure on the electrical conductivity of polymers

The role of Quantum Theoretical Methods is both predictive and supportive of experimental results in Chemistry. Present day methods are able to calculate vibrational spectra and stereochemical interactions for molecules of moderate size (up to 20 atoms). As for the predictive side, the electronic structure of molecules and polymers can be calculated in order to narrow down the field of many potential candidates, which would have the novel properties looked for. The following has been accomplished at the Rutgers Camden Chemistry Department as results of calculations on molecular and polymeric systems of interest to the Polymers Branch of the NASA Lewis Research Center, under Grant NAG3-956

Sensitivity of principal Hessian direction analysis

We provide sensitivity comparisons for two competing versions of the dimension reduction method principal Hessian directions (pHd). These comparisons consider the effects of small perturbations on the estimation of the dimension reduction subspace via the influence function. We show that the two versions of pHd can behave completely differently in the presence of certain observational types. Our results also provide evidence that outliers in the traditional sense may or may not be highly influential in practice. Since influential observations may lurk within otherwise typical data, we consider the influence function in the empirical setting for the efficient detection of influential observations in practice.Comment: Published at http://dx.doi.org/10.1214/07-EJS064 in the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonlinear Galactic Dynamos and the Magnetic Pitch Angle

Pitch angles $p$ of the large-scale magnetic fields $\overline{\bf{\it{B}}}$ of spiral galaxies have previously been inferred from observations to be systematically larger in magnitude than predicted by standard mean-field dynamo theory. This discrepancy is more pronounced if dynamo growth has saturated, which is reasonable to assume given that such fields are generally inferred to be close to energy equipartition with the interstellar turbulence. This 'pitch angle problem' is explored using local numerical mean-field dynamo solutions as well as asymptotic analytical solutions. It is first shown that solutions in the saturated or kinematic regimes depend on only five dynamo parameters, two of which are tightly constrained by observations of galaxy rotation curves. The remaining 3-dimensional (dimensionless) parameter space can be constrained to some extent using theoretical arguments. Predicted values of $|p|$ can be as large as $\sim40^\circ$, which is similar to the largest values inferred from observations, but only for a small and non-standard region of parameter space. We argue, based on independent evidence, that such non-standard parameter values are plausible. However, these values are located toward the boundary of the allowed parameter space, suggesting that additional physical effects may need to be incorporated. We therefore suggest possible directions for extending the basic model considered.Comment: 11 pages, 5 figures, 1 table, edited to match ApJ versio