Systematic Errors in the Estimation of Black Hole Masses by Reverberation Mapping

The mass of the central black hole in many active galactic nuclei has been estimated on the basis of the assumption that the dynamics of the broad emission line gas are dominated by the gravity of the black hole. The most commonly-employed method is to estimate a characteristic size-scale $r_*$ from reverberation mapping experiments and combine it with a characteristic velocity $v_*$ taken from the line profiles; the inferred mass is then estimated by $r_* v_*^2/G$. We critically discuss the evidence supporting the assumption of gravitational dynamics and find that the arguments are still inconclusive. We then explore the range of possible systematic error if the assumption of gravitational dynamics is granted. Inclination relative to a flattened system may cause a systematic underestimate of the central mass by a factor $\sim (h/r)^2$, where $h/r$ is the aspect ratio of the flattening. The coupled effects of a broad radial emissivity distribution, an unknown angular radiation pattern of line emission, and sub-optimal sampling in the reverberation experiment can cause additional systematic errors as large as a factor of 3 or more in either direction.Comment: 19 pages, 4 figures, AASLaTeX, accepted by Ap

Microcanonical Origin of the Maximum Entropy Principle for Open Systems

The canonical ensemble describes an open system in equilibrium with a heat bath of fixed temperature. The probability distribution of such a system, the Boltzmann distribution, is derived from the uniform probability distribution of the closed universe consisting of the open system and the heat bath, by taking the limit where the heat bath is much larger than the system of interest. Alternatively, the Boltzmann distribution can be derived from the Maximum Entropy Principle, where the Gibbs-Shannon entropy is maximized under the constraint that the mean energy of the open system is fixed. To make the connection between these two apparently distinct methods for deriving the Boltzmann distribution, it is first shown that the uniform distribution for a microcanonical distribution is obtained from the Maximum Entropy Principle applied to a closed system. Then I show that the target function in the Maximum Entropy Principle for the open system, is obtained by partial maximization of Gibbs-Shannon entropy of the closed universe over the microstate probability distributions of the heat bath. Thus, microcanonical origin of the Entropy Maximization procedure for an open system, is established in a rigorous manner, showing the equivalence between apparently two distinct approaches for deriving the Boltzmann distribution. By extending the mathematical formalism to dynamical paths, the result may also provide an alternative justification for the principle of path entropy maximization as well.Comment: 12 pages, no figur

Tourniquetless Total Knee Arthroplasty With Modern Perioperative Protocols Decreases Pain and Opioid Consumption in Women

Background This study examined whether a modern total knee arthroplasty (TKA) protocol without a tourniquet results in less patient-reported pain and in-hospital opioid consumption compared to TKA with a tourniquet. Methods A retrospective study of 203 primary unilateral cemented TKAs consecutively performed with or without tourniquet was performed. Identical perioperative pain and blood loss protocols were used in all cases. In tourniquetless TKAs, the tourniquet was not inflated at any time, and sterile CO2 gas compression maximized cement interdigitation. Results After exclusions for scientific confounds, 184 TKAs (93 with tourniquet; 91 tourniquetless) were analyzed. Controlling for multiple covariates, females with a tourniquet reported significantly more pain (P = .002) and opioid consumption (P < .001) the first 24 hours after surgery compared to females without a tourniquet. There were no differences in pain (P = .192) or amount of opioids consumed (P = .203) among males with and without a tourniquet. Tourniquet use resulted in a significant reduction in blood loss for both females (P ≤ .040) and males (P ≤ .020), although the total blood savings of approximately 200 mL is of unknown clinical significance. Conclusion Avoiding tourniquet use during TKA for females may be a relatively risk-free adjunct to minimize opioid consumption during hospitalization. Further study is warranted to elucidate the factors accounting for different outcomes in females and males

D3 branes in a Melvin universe: a new realm for gravitational holography

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) - a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size - the scale of non-locality in the PFT - and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen - a throat in the geometry - that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces - akin to other non-local settings that employ quantum group structures.Comment: 44 pages, 13 figures; v2: minor corrections, citations added; v3: typos corrected in section on local operators, some asymptotic expansions improved and made more consistent with rest of paper in section on non-local operator

Optical conductivity in non-equilibrium d-wave superconductors

We consider the optical conductivity of a d-wave BCS superconductor in the presence of a non-equilibrium distribution of excess quasiparticles. Two different simplified models used in the past for the s-wave case are considered and results compared. In the $T^\ast$-model of Parker the excess quasiparticles are assumed to be in a thermal distribution at some temperature $T^\ast$ larger than the equilibrium sample temperature. In the $\mu^\ast$- model of Owen and Scalapino a chemical potential is introduced to accommodate the excess quasiparticles. Some of the results obtained are specific to the model, most are qualitatively similar in both.Comment: 11 pages, 6 figures this manuscript has been accepted for publication in abbreviated form by Physical Review

Exact Partition Function Zeros of a Polymer on a Simple-Cubic Lattice

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudo-transition.Comment: 21 pages, 4 figure

A Stochastic Analysis of Proposals for the New US Farm Bill

Most of the large scale modeling systems used in the analysis of agricultural policies produce deterministic projections. In reality, however, the agricultural sector is subject to a high degree of uncertainty as a result of fluctuations in exogenous factors such as the weather or macroeconomic variation. A stochastic approach can provide additional information to policy makers regarding the implications of this uncertainty, through the use of stochastically generated projections. This paper also shows how deterministic analysis may result in systematic errors in the projection of some variables. As an applied example, the FAPRI model of the US agricultural sector is simulated stochastically to analyse the impact of proposals for the new US farm bill.Stochastic simulation, US Farm Bill, policy analysis, Agricultural and Food Policy,

Results of 1/4-Scale Experiments. Vapor Simulant And Liquid Jet A Tests

A quarter-scale engineering model of the center wing tank (CWT) of a 747-100 was constructed. This engineering model replicated the compartmentalization, passageways, and venting to the atmosphere. The model was designed to scale the fluid dynamical and combustion aspects of the explosion, not the structural failure of the beams or spars. The effect of structural failure on combustion was examined by using model beams and spars with deliberately engineered weak connections to the main tank structure. The model was filled with a simulant fuel (a mixture of propane and hydrogen) and ignited with a hot wire. The simulant fuel was chosen on the basis of laboratory testing to model the combustion characteristics (pressure rise and flame speed) of Jet A vapor created by a Jet A liquid layer at 50C at an altitude of 13.8 kft. A series of experiments was carried out in this model in order to: (a) investigate combustion in a CWT geometry; and (b) provide guidance to the TWA 800 crash investigation. The results of the experiments were observed with high-speed film, video, and still cameras, fast and slow pressure sensors, thermocouples, photodetectors, and motion sensors. A special pseudo-schlieren system was used to visualize flame propagation within the tank. This report describes the test program, facility, instrumentation, the first 30 experiments, comparisons between experiments, and performance of the instrumentation; then examines the significance of these results to the TWA 800 crash investigation. The key results of this study are: Flame Motion: The motion of flame was dominated by the effects of turbulence created by jetting through the passageways and vent stringers. A very rapid combustion event (lasting 10 to 20 ms) occurred once the flame traveled outside of the ignition bay and interacted with the turbulent flow. Most of the gas within the tank was burned during this rapid event. Compartments: The combustion time decreased with an increasing number of compartments (bays) within the tank. With six bays, combustion took only 100 to 150 ms to be completed from the time of ignition until the end of the rapid combustion phase. The total combustion event was three to four times shorter with compartments than without. Venting: Venting to the outside of the tank through the model vent stringers had a negligible effect on the combustion progress or on the peak pressure reached at the end of the burn. Ignition Location: Variation of the ignition location produced distinctive pressure loads on the structural components. Liquid Fuel: Lofting of a cold liquid fuel layer was produced by the combustion-induced gas motion. Although this spray of liquid eventually ignited and burned, it did not contribute to the pressure loading. Structural Failure: Structural failure resulted in flame acceleration, decreasing the overall combustion time. TWA 800 Investigation: The pressure loads were sufficiently high, up to 4 bar, and the combustion events were sufficiently short, that the forward portion (spanwise beam 3, front spar) of the CWT structure would fail as a direct consequence of the explosion. A combination of pressure loads was produced in some tests consistent with the TWA 800 wreckage. Replica tests, structural modeling, and sensitivity studies on fuel concentration are needed before any conclusions can be drawn about probable ignition locations. Cargo Bay: Tests with a simplified model of a half-full cargo bay indicated that repeated pressure waves with an amplitude of 1 bar or less are produced when an explosion scenario similar to TWA 800 is tested. Future Testing: Future studies should include replica tests, tests with Jet A vapor and warm liquid Jet A layers, and sensitivity tests to examine ignition location, fuel concentration, and vent area perturbations. Summary: Explosion tests in a 747-100 CWT model reveal that a very complex pattern of combustion occurs due the interaction of the flame and the flow-generated turbulence. A wide range of structural load patterns occur, depending on the location of the ignition source. Some of these load patterns are consistent with damage believed to be associated with the initial explosion event in TWA 800. Sensitivity of the loading to the ignition location indicates that narrowing down the ignition location in TWA 800 may be possible. However, the complexity of the combustion and structural failure processes in the actual center wing tank mandates extremely careful consideration of the uncertainties that enter into this process