Coaxial Jets and Sheaths in Wide-Angle-Tail Radio Galaxies

We add 20, 6 and 3.6 cm wavelength VLA observations of two WATs, 1231+674 and 1433+553, to existing VLA data at 6 and 20 cm, in order to study the variations of spectral index as a function of position. We apply the spectral tomography process that we introduced in our analysis of 3C67, 3C190 and 3C449. Both spectral tomography and polarization maps indicate that there are two distinct extended components in each source. As in the case of 3C449, we find that each source has a flat spectrum jet surrounded by a steeper spectrum sheath. The steep components tend to be more highly polarized than the flat components. We discuss a number of possibilities for the dynamics of the jet/sheath systems, and the evolution of their relativistic electron populations. While the exact nature of these two coaxial components is still uncertain, their existence requires new models of jets in FR I sources and may also have implications for the dichotomy between FR Is and FR IIs.Comment: 29 text pages plus 13 figures. Scheduled for publication in May 10, 1999 Ap

Persistence in Cluster--Cluster Aggregation

Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are defined as the probabilities, that a site has been either empty or covered by a cluster all the time whereas the cluster persistence gives the probability of a cluster to remain intact. The filled site one is nonuniversal. The empty site and cluster persistences are found to be universal, as supported by analytical arguments and simulations. The empty site case decays algebraically with the exponent $\theta_E = 2/(2 - \gamma)$. The cluster persistence is related to the small $s$ behavior of the cluster size distribution and behaves also algebraically for $0 \le \gamma < 2$ while for $\gamma < 0$ the behavior is stretched exponential. In the scaling limit $t \to \infty$ and $K(t) \to \infty$ with $t/K(t)$ fixed the distribution of intervals of size $k$ between persistent regions scales as $n(k;t) = K^{-2} f(k/K)$, where $K(t) \sim t^\theta$ is the average interval size and $f(y) = e^{-y}$. For finite $t$ the scaling is poor for $k \ll t^z$, due to the insufficient separation of the two length scales: the distances between clusters, $t^z$, and that between persistent regions, $t^\theta$. For the size distribution of persistent regions the time and size dependences separate, the latter being independent of the diffusion exponent $\gamma$ but depending on the initial cluster size distribution.Comment: 14 pages, 12 figures, RevTeX, submitted to Phys. Rev.

First Attempt at Spectroscopic Detection of Gravity Modes in a Long-Period Pulsating Subdwarf B Star -- PG 1627+017

In the first spectroscopic campaign for a PG 1716 variable (or long-period pulsating subdwarf B star), we succeeded in detecting velocity variations due to g-mode pulsations at a level of 1.0-1.5 km/s.The observations were obtained during 40 nights on 2-m class telescopes in Arizona, South Africa,and Australia. The target,PG1627+017, is one of the brightest and largest amplitude stars in its class.It is also the visible component of a post-common envelope binary.Our final radial velocity data set includes 84 hours of time-series spectroscopy over a time baseline of 53 days. Our derived radial velocity amplitude spectrum, after subtracting the orbital motion, shows three potential pulsational modes 3-4 sigma above the mean noise level, at 7201.0s,7014.6s and 7037.3s.Only one of the features is statistically likely to be real,but all three are tantalizingly close to, or a one day alias of, the three strongest periodicities found in the concurrent photometric campaign. We further attempted to detect pulsational variations in the Balmer line amplitudes. The single detected periodicity of 7209 s, although weak, is consistent with theoretical expectations as a function of wavelength.Furthermore, it allows us to rule out a degree index of l= 3 or l= 5 for that mode. Given the extreme weakness of g-mode pulsations in these stars,we conclude that anything beyond simply detecting their presence will require larger telescopes,higher efficiency spectral monitoring over longer time baselines,improved longitude coverage, and increased radial velocity precision.Comment: 39 pages, 9 figures, 4 tables, ApJ accepted. See postscript for full abtrac

Fraction of uninfected walkers in the one-dimensional Potts model

The dynamics of the one-dimensional q-state Potts model, in the zero temperature limit, can be formulated through the motion of random walkers which either annihilate (A + A -> 0) or coalesce (A + A -> A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is investigated numerically and found to decay algebraically, U(t) \sim t^{-\phi(q)}, with a nontrivial exponent \phi(q). Our study is extended to include the coupled diffusion-limited reaction A+A -> B, B+B -> A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as \rho(t) \sim t^{-1/2}. The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) \sim t^{-\theta} with \theta \simeq 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) \sim t^{-\phi}, where \phi \simeq 1.13 when infection occurs between like particles only, and \phi \simeq 1.93 when we also include cross-species contamination.Comment: Expanded introduction with more discussion of related wor

Position-specific Performance Indicators that Discriminate between Successful and Unsuccessful Teams in Elite Women’s Indoor Field Hockey: Implications for Coaching

The aim of this investigation was to establish median performance profiles for the six playing positions in elite women’s indoor hockey and then identify whether these position-specific profiles could discriminate between qualifying (top four), mid-table and relegated teams in the 2011-12 England Hockey premier league. Successful passing in relegated teams was significantly lower (p<0.008) than in mid-table and qualifying teams in four of the five outfield positions. Furthermore, the right backs of qualifying teams demonstrated significantly fewer (p<0.008) unsuccessful passes (x̃=15.5 ±CLs 15.0 and 10.0 respectively) and interceptions (x̃=4.0 ±CLs 4.0 and 3.0 respectively) than relegated teams (x̃=19.5 ±CLs 21.0 and 17.0; x̃=7.5 ±CLs 8.0 and 6.0 respectively). Finally, the right forwards of relegated teams demonstrated significantly fewer (p<0.008) successful interceptions (x̃=4.0 ±CLs 5.0 and 4.0 respectively) than qualifying teams (x̃=5.0 ±CLs 6.0 and 3.0 respectively) and significantly more (p<0.008) unsuccessful interceptions (x̃=5.5 ±CLs 6.0 and 4.0 respectively) than mid-table teams (x̃=3.0 ±CLs 3.0 and 2.0 respectively). Based on these findings, coaches should adapt tactical strategies and personnel deployment accordingly to enhance the likelihood of preparing a qualifying team. Research should build from these data to examine dribbling, pressing and patterns of play when outletting

Cluster persistence in one-dimensional diffusion--limited cluster--cluster aggregation

The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem maps to the survival of three annihilating random walkers with time-dependent noise correlations. For $\gamma \ge 0$ the motion of persistent clusters becomes asymptotically irrelevant and the mean-field theory provides a correct description. For $\gamma < 0$ the spatial fluctuations remain relevant and the persistence probability is overestimated by the random walk theory. The decay of persistence determines the small size tail of the cluster size distribution. For $0 < \gamma < 2$ the distribution is flat and, surprisingly, independent of $\gamma$.Comment: 11 pages, 6 figures, RevTeX4, submitted to Phys. Rev.

Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models

The distribution, n(k,t), of the interval sizes, k, between clusters of persistent sites in the dynamical evolution of the one-dimensional q-state Potts model is studied using a combination of numerical simulations, scaling arguments, and exact analysis. It is shown to have the scaling form n(k,t) = t^{-2z} f(k/t^z), with z= max(1/2,theta), where theta(q) is the persistence exponent which characterizes the fraction of sites which have not changed their state up to time t. When theta > 1/2, the scaling length, t^theta, for the interval-size distribution is larger than the coarsening length scale, t^{1/2}, that characterizes spatial correlations of the Potts variables.Comment: RevTex, 11 page

Persistence properties of a system of coagulating and annihilating random walkers

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In 1-dimension, the system models the zero temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations. Using perturbative renormalization group analysis for d < 2, we show that, if the number of coagulations m is much less than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q + Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q) epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+ O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q)) ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.Comment: 12 pages, revtex, 5 figure

Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an annihilation process has not occurred at a given site has the asymptotic form $P(t) -> const + t^{-\theta}$, where $\theta$ is the persistence exponent (``type I persistence''). We argue that, for a density of particles $\rho >> 1$, this non-trivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, where $\theta \approx 0.1207$. In the case of an initially low density, $\rho_0 << 1$, we find $\theta \approx 1/4$ asymptotically. The probability that a site remains unvisited by any random walker (``type II persistence'') is also investigated and found to decay with a stretched exponential form, $P(t) \sim \exp(-const \rho_0^{1/2}t^{1/4})$, provided $\rho_0 << 1$. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.Comment: 11 RevTeX pages, 19 EPS figure

Global upper-atmospheric heating on Jupiter by the polar aurorae

Jupiter’s upper atmosphere is considerably hotter than expected from the amount of sunlight that it receives1,2,3. Processes that couple the magnetosphere to the atmosphere give rise to intense auroral emissions and enormous deposition of energy in the magnetic polar regions, so it has been presumed that redistribution of this energy could heat the rest of the planet4,5,6. Instead, most thermospheric global circulation models demonstrate that auroral energy is trapped at high latitudes by the strong winds on this rapidly rotating planet3,5,7,8,9,10. Consequently, other possible heat sources have continued to be studied, such as heating by gravity waves and acoustic waves emanating from the lower atmosphere2,11,12,13. Each mechanism would imprint a unique signature on the global Jovian temperature gradients, thus revealing the dominant heat source, but a lack of planet-wide, high-resolution data has meant that these gradients have not been determined. Here we report infrared spectroscopy of Jupiter with a spatial resolution of 2 degrees in longitude and latitude, extending from pole to equator. We find that temperatures decrease steadily from the auroral polar regions to the equator. Furthermore, during a period of enhanced activity possibly driven by a solar wind compression, a high-temperature planetary-scale structure was observed that may be propagating from the aurora. These observations indicate that Jupiter’s upper atmosphere is predominantly heated by the redistribution of auroral energy