Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces

This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on particular fractals and further less regular cases as well. The proof is based on a new chaining argument and it is free of volume growth assumptions

The extinction and dust-to-gas structure of the planetary nebula NGC 7009 observed with MUSE

The large field and wavelength range of MUSE is well suited to mapping Galactic planetary nebulae (PN). The bright PN NGC 7009 was observed with MUSE on the VLT during the Science Verification of the instrument in seeing of 0.6". Emission line maps in hydrogen Balmer and Paschen lines were formed from analysis of the MUSE cubes. The measured electron temperature and density from the MUSE cube were employed to predict the theoretical hydrogen line ratios and map the extinction distribution across the nebula. After correction for the interstellar extinction to NGC 7009, the internal dust-to-gas ratio (A_V/N_H) has been mapped for the first time in a PN. The extinction map of NGC 7009 has considerable structure, broadly corresponding to the morphological features of the nebula. A large-scale feature in the extinction map, consisting of a crest and trough, occurs at the rim of the inner shell. The nature of this feature was investigated and instrumental and physical causes considered; no convincing mechanisms were identified to produce this feature, other than mass loss variations in the earlier asymptotic giant branch phase. The dust-to-gas ratio A_V/N_H increases from 0.7 times the interstellar value to >5 times from the centre towards the periphery of the ionized nebula. The integrated A_V/N_H is about 2 times the mean ISM value. It is demonstrated that extinction mapping with MUSE provides a powerful tool for studying the distribution of PN internal dust and the dust-to-gas ratio. (Abridged.)Comment: 10 pages, 7 figures. Accepted by A&

Distribution of Time-Averaged Observables for Weak Ergodicity Breaking

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $$.Comment: 5 pages, 2 figure

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

Upper estimate of martingale dimension for self-similar fractals

We study upper estimates of the martingale dimension $d_m$ of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that $d_m=1$ for natural diffusions on post-critically finite self-similar sets and that $d_m$ is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

Variability Tests for Intrinsic Absorption Lines in Quasar Spectra

Quasar spectra have a variety of absorption lines whose origins range from energetic winds expelled from the central engines to unrelated, intergalactic clouds. We present multi-epoch, medium resolution spectra of eight quasars at z~2 that have narrow ``associated'' absorption lines (AALs, within $\pm$5000 km s^{-1} of the emission redshift). Two of these quasars were also known previously to have high-velocity mini-broad absorption lines (mini-BALs). We use these data, spanning ~17 years in the observed frame with two to four observations per object, to search for line strength variations as an identifier of absorption that occurs physically near (``intrinsic'' to) the central AGN. Our main results are the following: Two out of the eight quasars with narrow AALs exhibit variable AAL strengths. Two out of two quasars with high-velocity mini-BALs exhibit variable mini-BAL strengths. We also marginally detect variability in a high-velocity narrow absorption line (NAL) system, blueshifted \~32,900 km s^{-1}$ with respect to the emission lines. No other absorption lines in these quasars appeared to vary. The outflow velocities of the variable AALs are 3140 km s^{-1} and 1490 km s^{-1}. The two mini-BALs identify much higher velocity outflows of ~28,400 km s^{-1} and ~52,000 km s^{-1}. Our temporal sampling yields upper limits on the variation time scales from 0.28 to 6.1 years in the quasar rest frames. The corresponding minimum electron densities in the variable absorbers, based on the recombination time scale, are \~40,000 cm^{-3} to ~1900 cm^{-3}. The maximum distances of the absorbers from the continuum source, assuming photoionization with no spectral shielding, range from ~1.8 kpc to ~7 kpc.Comment: 16 pages, 4 figures, ApJ, accepte

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

Remarkable dynamics of nanoparticles in the urban atmosphere

Nanoparticles emitted from road traffic are the largest source of respiratory exposure for the general public living in urban areas. It has been suggested that the adverse health effects of airborne particles may scale with the airborne particle number, which if correct, focuses attention on the nanoparticle (less than 100 nm) size range which dominates the number count in urban areas. Urban measurements of particle size distributions have tended to show a broadly similar pattern dominated by a mode centred on 20–30 nm diameter particles emitted by diesel engine exhaust. In this paper we report the results of measurements of particle number concentration and size distribution made in a major London park as well as on the BT Tower, 160 m high. These measurements taken during the REPARTEE project (Regents Park and BT Tower experiment) show a remarkable shift in particle size distributions with major losses of the smallest particle class as particles are advected away from the traffic source. In the Park, the traffic related mode at 20–30 nm diameter is much reduced with a new mode at <10 nm. Size distribution measurements also revealed higher number concentrations of sub-50 nm particles at the BT Tower during days affected by higher turbulence as determined by Doppler Lidar measurements and indicate a loss of nanoparticles from air aged during less turbulent conditions. These results suggest that nanoparticles are lost by evaporation, rather than coagulation processes. The results have major implications for understanding the impacts of traffic-generated particulate matter on human health