On the Stability of Thermonuclear Burning Fronts in Type Ia Supernovae

The propagation of cellularly stabilized thermonuclear flames is investigated by means of numerical simulations. In Type Ia supernova explosions the corresponding burning regime establishes at scales below the Gibson length. The cellular flame stabilization - which is a result of an interplay between the Landau-Darrieus instability and a nonlinear stabilization mechanism - is studied for the case of propagation into quiescent fuel as well as interaction with vortical fuel flows. Our simulations indicate that in thermonuclear supernova explosions stable cellular flames develop around the Gibson scale and that deflagration-to-detonation transition is unlikely to be triggered from flame evolution effects here.Comment: 6 pages, 2 figures, to appear in the proceedings of the IAU Colloquium 192, "Supernovae (10 years of SN1993J)", 22-26 April 2003, Valencia, Spain, Eds. J.M. Marcaide and K.W. Weiler, Springer Verla

Moment instabilities in multidimensional systems with noise

We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a simple, dominant eigenvalue and stationary, white noise. When the noise is small, we obtain general expressions for the approximate asymptotic distribution and moment Lyapunov exponents. In the case of larger noise, the second moment is calculated using a different approach, which gives an exact result for some types of noise. We analyze the dependence of the moments on the system's dimension, relevant system properties, the form of the noise, and the magnitude of the noise. We determine a critical value for noise strength, as a function of the unperturbed system's convergence rate, above which the second moment diverges and large fluctuations are likely. Analytical results are validated by numerical simulations. We show that our results cannot be extended to the continuous time limit except in certain special cases.Comment: 21 pages, 15 figure

A Wasserstein approach to the one-dimensional sticky particle system

We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of "sticky" particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolution semigroup in a measure-theoretic phase space, allowing mass distributions with finite quadratic moment and corresponding L^2-velocity fields. We investigate various interesting properties of this semigroup, in particular its link with the gradient flow of the (opposite) squared Wasserstein distance. Our arguments rely on an equivalent formulation of the evolution as a gradient flow in the convex cone of nondecreasing functions in the Hilbert space L^2(0,1), which corresponds to the Lagrangian system of coordinates given by the canonical monotone rearrangement of the measures.Comment: Added reference

Dynamics of a thin shell in the Reissner-Nordstrom metric

We describe the dynamics of a thin spherically symmetric gravitating shell in the Reissner-Nordstrom metric of the electrically charged black hole. The energy-momentum tensor of electrically neutral shell is modelled by the perfect fluid with a polytropic equation of state. The motion of a shell is described fully analytically in the particular case of the dust equation of state. We construct the Carter-Penrose diagrams for the global geometry of the eternal black hole, which illustrate all possible types of solutions for moving shell. It is shown that for some specific range of initial parameters there are possible the stable oscillating motion of the shell transferring it consecutively in infinite series of internal universes. We demonstrate also that this oscillating type of motion is possible for an arbitrary polytropic equation of state on the shell.Comment: 17 pages, 7 figure

The met and unmet health needs for HIV, hypertension, and diabetes in rural KwaZulu-Natal, South Africa: analysis of a cross-sectional multimorbidity survey

BACKGROUND: The convergence of infectious diseases and non-communicable diseases in South Africa is challenging to health systems. In this analysis, we assessed the multimorbidity health needs of individuals and communities in rural KwaZulu-Natal and established a framework to quantify met and unmet health needs for individuals living with infectious and non-communicable diseases. METHODS: We analysed data collected between May 25, 2018, and March 13, 2020, from participants of a large, community-based, cross-sectional multimorbidity survey (Vukuzazi) that offered community-based HIV, hypertension, and diabetes screening to all residents aged 15 years or older in a surveillance area in the uMkhanyakude district in KwaZulu-Natal, South Africa. Data from the Vukuzazi survey were linked with data from demographic and health surveillance surveys with a unique identifier common to both studies. Questionnaires were used to assess the diagnosed health conditions, treatment history, general health, and sociodemographic characteristics of an individual. For each condition (ie, HIV, hypertension, and diabetes), individuals were defined as having no health needs (absence of condition), met health needs (condition that is well controlled), or one or more unmet health needs (including diagnosis, engagement in care, or treatment optimisation). We analysed met and unmet health needs for individual and combined conditions and investigated their geospatial distribution. FINDINGS: Of 18 041 participants who completed the survey (12 229 [67·8%] were female and 5812 [32·2%] were male), 9898 (54·9%) had at least one of the three chronic diseases measured. 4942 (49·9%) of these 9898 individuals had at least one unmet health need (1802 [18·2%] of 9898 needed treatment optimisation, 1282 [13·0%] needed engagement in care, and 1858 [18·8%] needed a diagnosis). Unmet health needs varied by disease; 1617 (93·1%) of 1737 people who screened positive for diabetes, 2681 (58·2%) of 4603 people who screened positive for hypertension, and 1321 (21·7%) of 6096 people who screened positive for HIV had unmet health needs. Geospatially, met health needs for HIV were widely distributed and unmet health needs for all three conditions had specific sites of concentration; all three conditions had an overlapping geographical pattern for the need for diagnosis. INTERPRETATION: Although people living with HIV predominantly have a well controlled condition, there is a high burden of unmet health needs for people living with hypertension and diabetes. In South Africa, adapting current, widely available HIV care services to integrate non-communicable disease care is of high priority. FUNDING: Fogarty International Center and the National Institutes of Health, the Bill & Melinda Gates Foundation, the South African Department of Science and Innovation, the South African Medical Research Council, the South African Population Research Infrastructure Network, and the Wellcome Trust. TRANSLATION: For the isiZulu translation of the abstract see Supplementary Materials section

First M87 Event Horizon Telescope Results. VII. Polarization of the Ring

In 2017 April, the Event Horizon Telescope (EHT) observed the near-horizon region around the supermassive black hole at the core of the M87 galaxy. These 1.3 mm wavelength observations revealed a compact asymmetric ring-like source morphology. This structure originates from synchrotron emission produced by relativistic plasma located in the immediate vicinity of the black hole. Here we present the corresponding linear-polarimetric EHT images of the center of M87. We find that only a part of the ring is significantly polarized. The resolved fractional linear polarization has a maximum located in the southwest part of the ring, where it rises to the level of similar to 15%. The polarization position angles are arranged in a nearly azimuthal pattern. We perform quantitative measurements of relevant polarimetric properties of the compact emission and find evidence for the temporal evolution of the polarized source structure over one week of EHT observations. The details of the polarimetric data reduction and calibration methodology are provided. We carry out the data analysis using multiple independent imaging and modeling techniques, each of which is validated against a suite of synthetic data sets. The gross polarimetric structure and its apparent evolution with time are insensitive to the method used to reconstruct the image. These polarimetric images carry information about the structure of the magnetic fields responsible for the synchrotron emission. Their physical interpretation is discussed in an accompanying publication