Rotating Accretion Flows: From Infinity to the Black Hole

Accretion onto a supermassive black hole of a rotating inflow is a particularly difficult problem to study because of the wide range of length scales involved. There have been broadly utilized analytic and numerical treatments of the global properties of accretion flows, but detailed numerical simulations are required to address certain critical aspects. We use the ZEUS code to run hydrodynamical simulations of rotating, axisymmetric accretion flows with Bremsstrahlung cooling, considering solutions for which the centrifugal balance radius significantly exceeds the Schwarzschild radius, with and without viscous angular momentum transport. Infalling gas is followed from well beyond the Bondi radius down to the vicinity of the black hole. We produce a continuum of solutions with respect to the single parameter Mdot_Bondi/Mdot_Edd, and there is a sharp transition between two general classes of solutions at an Eddington ratio of Mdot_Bondi/Mdot_Edd ~ few x 10^(-2). Our high inflow solutions are very similar to the standard Shakura & Sunyaev (1973) results. But our low inflow results are to zeroth order the stationary Papaloizou and Pringle (1984) solution, which has no accretion. To next order in the small, assumed viscosity they show circulation, with disk and conical wind outflows almost balancing inflow. These solutions are characterized by hot, vertically extended disks, and net accretion proceeds at an extremely low rate, only of order alpha times the inflow rate. Our simulations have converged with respect to spatial resolution and temporal duration, and they do not depend strongly on our choice of boundary conditions.Comment: accepted for publication in Ap

Geographic Equity in Hospital Utilization: Canadian Evidence Using a Concentration-Index Approach

Distance-related geographic barriers challenge the ability of health systems to allocate health care resources equitably according to need. The paper adapts the concentration-index approach, commonly used for measuring income-related equity, to assess distance-related equity in hospital utilization in the province of Ontario, Canada. The analysis is based on individual-level data from the Canadian Community Health Survey, which provides information on respondents’ hospital utilization, health status, demographic, socio-economic status and location, merged with data on Ontario hospitals, and a geo-coded measure of each respondent’s distance to the nearest general acute-care hospital. We find no evidence of a relationship between distance to the nearest hospital and either the probability of hospitalization or the annual number of hospital nights. Supplementary analyses provide insight into hypothesized pathways between distance and hospitalization. Although having a regular medical doctor is positively associated with distance to the nearest hospital, controlling for this does not affect the estimated distance-hospitalization relationship. Both the size and occupancy rate of the nearest hospital are correlated with distance and are strongly related to the probability of hospitalization, but again controlling for these factors did not affect the estimated relationship between hospital use and distance to the nearest hospital. We do, however, find a strong positive gradient between the probability of hospitalization and distance to the nearest large hospital. This gradient is driven by the fact that, for most of those far from a large hospital, the nearest hospital is small with a low occupancy rate. Calculation of the distance-related horizontal inequity index confirms no distance-related inequity in hospital utilization when distance is measured to the nearest hospital of any size; however, when distance is instead measured to the nearest large hospital, we observe large, pro-distance inequity. These distance-use relationships are not captured by traditional geographic measures based on measures of urbanization/ruralness.hospital utilization, equity, geography

Time Dependent Saddle Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter $p(\tau)$ and its corresponding `dynamic' (time-dependent) saddle-node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the {\em breaking time} $\hat{\tau}$ at which the corresponding autonomous system with a time-independent parameter $p_{a}= p(\hat{\tau})$ undergoes a bifurcation. A dimensionless parameter $\alpha=\lambda p_0^3V^{-2}$ is introduced, in which $\lambda$ is the curvature of the autonomous saddle-node bifurcation according to parameter $p(\tau)$, which has an initial value of $p_{0}$ and a constant rate of change $V$. We find that the breaking time $\hat{\tau}$ is always less than the actual point of no return $\tau^*$ after which the critical transition is irreversible; specifically, the relation $\tau^*-\hat{\tau}\simeq 2.338(\lambda V)^{-\frac{1}{3}}$ is analytically obtained. For a system with a small $\lambda V$, there exists a significant window of opportunity $(\hat{\tau},\tau^*)$ during which rapid reversal of the environment can save the system from catastrophe

Supernova Feedback and the Hot Gas Filling Fraction of the Interstellar Medium

Supernovae (SN), the most energetic stellar feedback mechanism, are crucial for regulating the interstellar medium (ISM) and launching galactic winds. We explore how supernova remnants (SNRs) create a multiphase medium by performing 3D hydrodynamical simulations at various SN rates, $S$, and ISM average densities, $\bar{n}$. The evolution of a SNR in a self-consistently generated three-phase ISM is qualitatively different from that in a uniform or a two-phase warm/cold medium. By travelling faster and further in the low-density hot phase, the domain of a SNR increases by $>10^{2.5}$. Varying $\bar{n}$ and $S$, we find that a steady state can only be achieved when the hot gas volume fraction $f_{\rm{V,hot}}\lesssim 0.6 \pm 0.1$. Above that level, overlapping SNRs render connecting topology of the hot gas, and the ISM is subjected to thermal runaway. Photoelectric heating (PEH) has a surprisingly strong impact on $f_{\rm{V,hot}}$. For \bar{n}\gtrsim 3 \cm-3 , a reasonable PEH rate is able to suppress the thermal runaway. Overall, we determine the critical SN rate for the onset of thermal runaway to be S_{\rm{crit}} = 200 (\bar{n}/1\cm-3)^k (E_{\rm{SN}}/10^{51}\erg)^{-1} \kpc^{-3} \myr-1, where $k = (1.2,2.7)$ for $\bar{n} \leq 1$ and > 1\cm-3 , respectively. We present a fitting formula of the ISM pressure $P(\bar{n}$, $S$), which can be used as an effective equation of state in cosmological simulations. Despite the 5 orders of magnitude span of $(\bar{n},S)$, the average Mach number varies little: $\mathcal{M} \approx \ 0.5\pm 0.2, \ 1.2\pm 0.3,\ 2.3\pm 0.9$ for the hot, warm and cold phases, respectively.Comment: 57 pages, 16 figures, 3 tables. ApJ accepte

EPR Study of Spin Labeled Brush Polymers in Organic Solvents

Spin-labeled polylactide brush polymers were synthesized via ring-opening metathesis polymerization (ROMP), and nitroxide radicals were incorporated at three different locations of brush polymers: the end and the middle of the backbone, and the end of the side chains (periphery). Electron paramagnetic resonance (EPR) was used to quantitatively probe the macromolecular structure of brush polymers in dilute solutions. The peripheral spin-labels showed significantly higher mobility than the backbone labels, and in dimethylsulfoxide (DMSO), the backbone end labels were shown to be more mobile than the middle labels. Reduction of the nitroxide labels by a polymeric reductant revealed location-dependent reactivity of the nitroxide labels: peripheral nitroxides were much more reactive than the backbone nitroxides. In contrast, almost no difference was observed when a small molecule reductant was used. These results reveal that the dense side chains of brush polymers significantly reduce the interaction of the backbone region with external macromolecules, but allow free diffusion of small molecules

Gravitational Lensing by a Compound Population of Halos: Standard Models

Based on observed rotation curves of galaxies and theoretical simulations of dark matter halos, there are reasons for believing that at least three different types of dark matter halos exist in the Universe classified by their masses M and the inner slope of mass density -\alpha: Population A (galaxies): 10^{10} h^{-1} M_\odot < M < 2 \times 10^{13} h^{-1} M_\odot, \alpha = 2; Population B (cluster halos): M > 2 \times 10^{13} h^{-1} M_\odot, \alpha = 1.3; and Population C (dwarf halos): M < 10^{10} h^{-1} M_\odot, \alpha = 1.3. In this paper we calculate the lensing probability produced by such a compound population of dark halos, for both image separation and time delay, assuming that the mass function of halos is given by the Press-Schechter function and the Universe is described by an LCDM, OCDM, or SCDM model. The LCDM model is normalized to the WMAP observations, OCDM and SCDM models are normalized to the abundance of rich clusters. We compare the predictions of the different cosmological models with observational data and show that, both LCDM and OCDM models are marginally consistent with the current available data, but the SCDM model is ruled out. The fit of the compound model to the observed correlation between splitting angle and time delay is excellent but the fit to the number vs splitting angle relation is only adequate using the small number of sources in the objective JVAS/CLASS survey. A larger survey of the same type would have great power in discriminating among cosmological models. Furthermore, population C in an LCDM model has a unique signature in the time domain, an additional peak at ~3 seconds potentially observable in GRBs, which makes it distinguishable from variants of CDM scenarios, such as warm dark matter, repulsive dark matter, or collisional dark matter.Comment: 26 pages, including 9 figure

Chronic pain detection from resting-state raw EEG signals using improved feature selection

We present an automatic approach that works on resting-state raw EEG data for chronic pain detection. A new feature selection algorithm - modified Sequential Floating Forward Selection (mSFFS) - is proposed. The improved feature selection scheme is rather compact but displays better class separability as indicated by the Bhattacharyya distance measures and better visualization results. It also outperforms selections generated by other benchmark methods, boosting the test accuracy to 97.5% and yielding a test accuracy of 81.4% on an external dataset that contains different types of chronic painComment: 9 pages, 4 figures, journal submissio