Redshifted 21cm Signatures Around the Highest Redshift Quasars

The Ly-alpha absorption spectrum of the highest redshift quasars indicates that they are surrounded by giant HII regions, a few Mpc in size. The neutral gas around these HII regions should emit 21cm radiation in excess of the Cosmic Microwave Background, and enable future radio telescopes to measure the transverse extent of these HII regions. At early times, the HII regions expand with a relativistic speed. Consequently, their measured sizes along the line-of-sight (via Ly-alpha absorption) and transverse to it (via 21 cm emission) should have different observed values due to relativistic time-delay. We show that the combined measurement of these sizes would directly constrain the neutral fraction of the surrounding intergalactic medium (IGM) as well as the quasar lifetime. Based on current number counts of luminous quasars at z>6, an instrument like LOFAR should detect >2 redshifted 21cm shells per field (with a radius of 11 degrees) around active quasars as bright as those already discovered by SDSS, and >200 relic shells of inactive quasars per field. We show that Ly-alpha photons from the quasar are unable to heat the IGM or to couple the spin and kinetic temperatures of atomic hydrogen beyond the edge of the HII region. The detection of the IGM in 21cm emission around high redshift quasars would therefore gauge the presence of a cosmic Ly-alpha background during the reionization epoch.Comment: 11 pages, 6 figures. Submitted to Ap

X-ray emission from pre-main sequence stars with multipolar magnetic fields

The large-scale magnetic fields of several pre-main sequence (PMS) stars have been observed to be simple and axisymmetric, dominated by tilted dipole and octupole components. The magnetic fields of other PMS stars are highly multipolar and dominantly non-axisymmetric. Observations suggest that the magnetic field complexity increases as PMS stars evolve from Hayashi to Henyey tracks in the Hertzsprung–Russell diagram. Independent observations have revealed that X-ray luminosity decreases with age during PMS evolution, with Henyey track PMS stars having lower fractional X-ray luminosities (𝐿X/𝐿∗) compared to Hayashi track stars. We investigate how changes in the large-scale magnetic field topology of PMS stars influences coronal X-ray emission. We construct coronal models assuming pure axisymmetric multipole magnetic fields, and magnetic fields consisting of a dipole plus an octupole component only. We determine the closed coronal emitting volume, over which X-ray emitting plasma is confined, using a pressure balance argument. From the coronal volumes we determine X-ray luminosities. We find that 𝐿X decreases as the degree ℓ of the multipole field increases. For dipole plus octupole magnetic fields we find that 𝐿X tends to decrease as the octupole component becomes more dominant. By fixing the stellar parameters at values appropriate for a solar mass PMS star, varying the magnetic field topology results in two orders of magnitude variation in 𝐿X. Our results support the idea that the decrease in 𝐿X as PMS stars age can be driven by an increase in the complexity of the large-scale magnetic field

X-ray Emission Models for Multipolar fields of Pre-Main Sequence Stars

The large-scale magnetic fields of several pre-main sequence (PMS) stars have been observed to be simple and axisymmetric, dominated by tilted dipole and octupole components. The magnetic fields of other PMS stars are highly multipolar and dominantly non-axisymmetric. Observations suggest that the magnetic field complexity increases as PMS stars evolve from Hayashi to Henyey tracks in the Hertzsprung--Russell diagram. Independent observations have revealed that X-ray luminosity decreases with age during PMS evolution, with Henyey track PMS stars having lower fractional X-ray luminosities ($L_\textrm{X}/L_*$) compared to Hayashi track stars. We investigate how changes in the large-scale magnetic field topology of PMS stars influences coronal X-ray emission. We construct coronal models assuming pure axisymmetric multipole magnetic fields, and magnetic fields consisting of a dipole plus an octupole component only. We determine the closed coronal emitting volume, over which X-ray emitting plasma is confined, using a pressure balance argument. From the coronal volumes we determine X-ray luminosities. We find that $L_\textrm{X}$ decreases as the degree $\ell$ of the multipole field increases. For dipole plus octupole magnetic fields we find that $L_\textrm{X}$ tends to decrease as the octupole component becomes more dominant. By fixing the stellar parameters at values appropriate for a solar mass PMS star, varying the magnetic field topology results in two orders of magnitude variation in $L_\textrm{X}$. Our results support the idea that the decrease in $L_\textrm{X}$ as PMS stars age can be driven by an increase in the complexity of the large-scale magnetic field.Comment: 13 pages with 13 figures, plus 1 page with 1 figure in the appendix, accepted for publication in MNRAS 2023 August 0

Stability of Filters for the Navier-Stokes Equation

Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in a on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise filtering can be performed exactly using the Kalman filter. For nonlinear systems it can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the properties of these ad hoc filters, working in the context of the 2D incompressible Navier-Stokes equation. By working in this infinite dimensional setting we provide an analysis which is useful for understanding high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to accurately track the signal itself (filter stability), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. Numerical results are given which illustrate the theory. In a simplified scenario we also derive, and study numerically, a stochastic PDE which determines filter stability in the limit of frequent observations, subject to large observational noise. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters perform poorly in reproducing statistical variation about the true signal

CO2-gasification of a lignite coal in the presence of an iron-based oxygen carrier for chemical-looping combustion

AbstractChemical-looping combustion (CLC) has the inherent property of separating the product CO2 from flue gases. Instead of air, it uses an oxygen carrier, usually in the form of a metal oxide, to provide oxygen for combustion. All techniques so far proposed for chemical looping with solid fuels involve initially the gasification of the solid fuel in order for the gaseous products to react with the oxygen carrier. Here, the rates of gasification of coal were compared when gasification was undertaken in a fluidised bed of either (i) an active Fe-based oxygen carrier used for chemical looping or (ii) inert sand. This enabled an examination of the ability of chemical looping materials to enhance the rate of gasification of solid fuels. Batch gasification and chemical-looping combustion experiments with a German lignite and its char are reported, using an electrically-heated fluidised bed reactor at temperatures from 1073 to 1223K. The fluidising gas was CO2 in nitrogen. The kinetics of the gasification were found to be significantly faster in the presence of the oxygen carrier, especially at temperatures above 1123K. A numerical model was developed to account for external and internal mass transfer and for the effect of the looping agent. The model also included the effects of the evolution of the pore structure at different conversions. The presence of Fe2O3 led to an increase in the rate of gasification because of the rapid oxidation of CO by the oxygen carrier to CO2. This resulted in the removal of CO and maintained a higher mole fraction of CO2 in the mixture of gas around the particle of char, i.e. within the mass transfer boundary layer surrounding the particle. This effect was most prominent at about 20% conversion when (i) the surface area for reaction was at its maximum and (ii) because of the accompanying increase in porosity and pore size, intraparticle resistance to gas mass transfer within the particle of char had fallen, compared with that in the initial particle. Excellent agreement was observed between the rates predicted by the numerical model and those observed experimentally

Statistical Approach to Raman Analysis of Graphene-Related Materials: Implications for Quality Control

A statistical method to determine the number of measurements required from nanomaterials to ensure reliable and robust analysis is described. Commercial products utilizing graphene are in their infancy and recent investigations of commercial graphene manufacture have attributed this to the lack of robust metrology and standards by which graphene and related carbon materials can be measured and compared. Raman spectroscopy is known to be a useful tool in carbon nanomaterial characterization, but to provide meaningful information, in particular for quality control or management, multiple spectra are needed. Herein we present a statistical method to quantify the number of different spectra or other microscale measurements that should be taken to reliably characterize a graphene material. We have recorded a large number of Raman measurements and studied the statistical convergence of these data sets. We use a graphical approach to monitor the change in summary statistics and a Monte Carlo based bootstrapping method of data analysis to computationally resample the data demonstrating the effects of underanalyzing a material; for example, graphene nanoplatelets may require over 500 spectra before information about the exfoliation efficiency, particle size, layer number, and chemical functionalization is accurately obtained

Patterns of Mesenchymal Condensation in a Multiscale, Discrete Stochastic Model

Cells of the embryonic vertebrate limb in high-density culture undergo chondrogenic pattern formation, which results in the production of regularly spaced “islands” of cartilage similar to the cartilage primordia of the developing limb skeleton. The first step in this process, in vitro and in vivo, is the generation of “cell condensations,” in which the precartilage cells become more tightly packed at the sites at which cartilage will form. In this paper we describe a discrete, stochastic model for the behavior of limb bud precartilage mesenchymal cells in vitro. The model uses a biologically motivated reaction–diffusion process and cell-matrix adhesion (haptotaxis) as the bases of chondrogenic pattern formation, whereby the biochemically distinct condensing cells, as well as the size, number, and arrangement of the multicellular condensations, are generated in a self-organizing fashion. Improving on an earlier lattice-gas representation of the same process, it is multiscale (i.e., cell and molecular dynamics occur on distinct scales), and the cells are represented as spatially extended objects that can change their shape. The authors calibrate the model using experimental data and study sensitivity to changes in key parameters. The simulations have disclosed two distinct dynamic regimes for pattern self-organization involving transient or stationary inductive patterns of morphogens. The authors discuss these modes of pattern formation in relation to available experimental evidence for the in vitro system, as well as their implications for understanding limb skeletal patterning during embryonic development

1970 Problems in Legal Education

Five problems in legal education, much discussed recently, were posed by the Editors of this Review to a number of administrative figures in the law school world. These questions were and are frankly difficult and controversial, but their answers are important to our system of legal education and to our society. Capsule answers given by these concerned legal education administrators are believed to be interesting and significant. Each is a personal rather than a representative opinion. Brief answers such as these, of course, are not expected to be, nor do they pretend to be, complete or profound. Their purpose is to indicate succinctly the approach of some law school administrative opinion makers to difficult policy problems of legal education

1970 Problems in Legal Education

Five problems in legal education, much discussed recently, were posed by the Editors of this Review to a number of administrative figures in the law school world. These questions were and are frankly difficult and controversial, but their answers are important to our system of legal education and to our society. Capsule answers given by these concerned legal education administrators are believed to be interesting and significant. Each is a personal rather than a representative opinion. Brief answers such as these, of course, are not expected to be, nor do they pretend to be, complete or profound. Their purpose is to indicate succinctly the approach of some law school administrative opinion makers to difficult policy problems of legal education

Redistribution of cytoplasmic VEGF to the basolateral aspect of renal tubular cells in ischemia-reperfusion injury

Redistribution of cytoplasmic VEGF to the basolateral aspect of renal tubular cells in ischemia-reperfusion injury.BackgroundVascular endothelial growth factor (VEGF) mRNA and protein expression are increased by hypoxia in a variety of cell types and organs. In the kidney, however, chronic hypoxia does not up-regulate VEGF mRNA. This suggests that VEGF may be regulated by unique mechanisms in the kidney.MethodsUnilateral ischemia was induced in rats by vascular cross-clamping (40 min) followed by reperfusion (0, 20, 40, and 80 min). The distribution of VEGF protein was determined by immunohistochemical staining and Western blotting. mRNA was detected by Northern blotting and semiquantitative reverse transcription-polymerase chain reaction (RT-PCR). Immunohistochemical staining for VEGF was verified using two VEGF antibodies. To further substantiate the immunohistochemical findings, laser scanning confocal fluorescence microscopy was used to demonstrate the distribution of VEGF protein in rat renal tubular epithelial cells (NRK52-E) subjected to hypoxia (40 min) and re-oxygenation (0, 5, 20, 40 and 80 min).ResultsNormal kidneys showed diffuse immunohistochemical staining for VEGF in all tubules of the renal cortex and medulla. Following ischemia, staining demonstrated a prominent shift of cytoplasmic VEGF to the basolateral aspect of tubular cells with both VEGF antibodies. The distribution of cytoplasmic VEGF returned to normal following 40 and 80 minutes of reperfusion. Western blots of cytoplasmic samples from ischemic kidneys reperfused for 0 and 20 minutes showed decreased levels of VEGF164 compared with normal (P < 0.01). VEGF164 and VEGF188 levels in the membrane fraction showed no change. Northern blots and semiquantitative RT-PCR showed no significant up-regulation of VEGF mRNA or change in the splice pattern. NRK52-E cells subjected to hypoxia and re-oxygenation for 0 and 5 minutes showed increased staining for VEGF compared with normal, with prominent VEGF staining at the periphery of the cell, similar to the appearance in ischemic kidneys. VEGF staining became more diffuse with further re-oxygenation.ConclusionAlthough synthesis of VEGF mRNA and protein is not increased during ischemia reperfusion injury, pre-existing VEGF in the tubular cell cytoplasm redistributes to the basolateral aspect of the cells. These data suggest that the kidney may have evolved unique patterns of VEGF regulation to cope with acute hypoxia