Dynamical Analysis of Attractor Behavior in Constant Roll Inflation

There has been considerable recent interest in a new class of non-slow roll inflationary solutions known as \textit{constant roll} inflation. Constant roll solutions are a generalization of the ultra-slow roll (USR) solution, where the first Hubble slow roll parameter $\epsilon$ is small, but the second Hubble slow roll parameter $\eta$ is not. While it is known that the USR solutions represent dynamical transients, there has been some disagreement in literature about whether or not large-$\eta$ constant roll solutions are attractors or are also a class of transient solutions. In this paper we show that the large-$\eta$ constant roll solutions do in fact represent transient solutions by performing stability analysis on the exact analytic (large-$\eta$) constant roll solutions.Comment: V3: 23 pages, 17 figures. Section added. Accepted to JCAP for publicatio

Accelerator performance analysis of the Fermilab Muon Campus

Fermilab is dedicated to hosting world-class experiments in search of new physics that will operate in the coming years. The Muon g-2 Experiment is one such experiment that will determine with unprecedented precision the muon anomalous magnetic moment, which offers an important test of the Standard Model. We describe in this study the accelerator facility that will deliver a muon beam to this experiment. We first present the lattice design that allows for efficient capture, transport, and delivery of polarized muon beams. We then numerically examine its performance by simulating pion production in the target, muon collection by the downstream beam line optics, as well as transport of muon polarization. We finally establish the conditions required for the safe removal of unwanted secondary particles that minimizes contamination of the final beam.Comment: 10 p

Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

Optical Structure and Proper-Motion Age of the Oxygen-rich Supernova Remnant 1E 0102-7219 in the Small Magellanic Cloud

We present new optical emission-line images of the young SNR 1E 0102-7219 (E0102) in the SMC obtained with the HST Advanced Camera for Surveys (ACS). E0102 is a member of the oxygen-rich class of SNRs showing strong oxygen, neon , and other metal-line emissions in its optical and X-ray spectra, and an absence of H and He. The progenitor of E0102 may have been a Wolf-Rayet star that underwent considerable mass loss prior to exploding as a Type Ib/c or IIL/b SN. The ejecta in this SNR are fast-moving (V > 1000 km/s) and emit as they are compressed and heated in the reverse shock. In 2003, we obtained optical [O III], H-alpha, and continuum images with the ACS Wide Field Camera. The [O III] image captures the full velocity range of the ejecta, and shows considerable high-velocity emission projected in the middle of the SNR that was Doppler-shifted out of the narrow F502N bandpass of a previous Wide Field and Planetary Camera 2 image from 1995. Using these two epochs separated by ~8.5 years, we measure the transverse expansion of the ejecta around the outer rim in this SNR for the first time at visible wavelengths. From proper-motion measurements of 12 ejecta filaments, we estimate a mean expansion velocity for the bright ejecta of ~2000 km/s and an inferred kinematic age for the SNR of \~2050 +/- 600 years. The age we derive from HST data is about twice that inferred by Hughes et al.(2000) from X-ray data, though our 1-sigma error bars overlap. Our proper-motion age is consistent with an independent optical kinematic age derived by Eriksen et al.(2003) using spatially resolved [O III] radial-velocity data. We derive an expansion center that lies very close to X-ray and radio hotspots, which could indicate the presence of a compact remnant (neutron star or black hole).Comment: 28 pages, 8 figures. Accepted to the Astrophysical Journal, to appear in 20 April 2006 issue. Full resolution figures are posted at: http://stevenf.asu.edu/figure

2D full-waveform modeling of seismic waves in layered karstic media

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent Q can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels

Acoustic Energy and Momentum in a Moving Medium

By exploiting the mathematical analogy between the propagation of sound in a non-homogeneous potential flow and the propagation of a scalar field in a background gravitational field, various wave ``energy'' and wave ``momentum'' conservation laws are established in a systematic manner. In particular the acoustic energy conservation law due to Blokhintsev appears as the result of the conservation of a mixed co- and contravariant energy-momentum tensor, while the exchange of relative energy between the wave and the mean flow mediated by the radiation stress tensor, first noted by Longuet-Higgins and Stewart in the context of ocean waves, appears as the covariant conservation of the doubly contravariant form of the same energy-momentum tensor.Comment: 25 Pages, Late

Predicting the knowledge–recklessness distinction in the human brain

Criminal convictions require proof that a prohibited act was performed in a statutorily specified mental state. Different legal consequences, including greater punishments, are mandated for those who act in a state of knowledge, compared with a state of recklessness. Existing research, however, suggests people have trouble classifying defendants as knowing, rather than reckless, even when instructed on the relevant legal criteria. We used a machine-learning technique on brain imaging data to predict, with high accuracy, which mental state our participants were in. This predictive ability depended on both the magnitude of the risks and the amount of information about those risks possessed by the participants. Our results provide neural evidence of a detectable difference in the mental state of knowledge in contrast to recklessness and suggest, as a proof of principle, the possibility of inferring from brain data in which legally relevant category a person belongs. Some potential legal implications of this result are discussed

Population gene introgression and high genome plasticity for the zoonotic pathogen Streptococcus agalactiae

The influence that bacterial adaptation (or niche partitioning) within species has on gene spillover and transmission among bacteria populations occupying different niches is not well understood. Streptococcus agalactiae is an important bacterial pathogen that has a taxonomically diverse host range making it an excellent model system to study these processes. Here we analyze a global set of 901 genome sequences from nine diverse host species to advance our understanding of these processes. Bayesian clustering analysis delineated twelve major populations that closely aligned with niches. Comparative genomics revealed extensive gene gain/loss among populations and a large pan-genome of 9,527 genes, which remained open and was strongly partitioned among niches. As a result, the biochemical characteristics of eleven populations were highly distinctive (significantly enriched). Positive selection was detected and biochemical characteristics of the dispensable genes under selection were enriched in ten populations. Despite the strong gene partitioning, phylogenomics detected gene spillover. In particular, tetracycline resistance (which likely evolved in the human-associated population) from humans to bovine, canines, seals, and fish, demonstrating how a gene selected in one host can ultimately be transmitted into another, and biased transmission from humans to bovines was confirmed with a Bayesian migration analysis. Our findings show high bacterial genome plasticity acting in balance with selection pressure from distinct functional requirements of niches that is associated with an extensive and highly partitioned dispensable genome, likely facilitating continued and expansive adaptation