Simulating 3D Radiation Transport, a modern approach to discretisation and an exploration of probabilistic methods

Light, or electromagnetic radiation in general, is a profound and invaluable resource to investigate our physical world. For centuries, it was the only and it still is the main source of information to study the Universe beyond our planet. With high-resolution spectroscopic imaging, we can identify numerous atoms and molecules, and can trace their physical and chemical environments in unprecedented detail. Furthermore, radiation plays an essential role in several physical and chemical processes, ranging from radiative pressure, heating, and cooling, to chemical photo-ionisation and photo-dissociation reactions. As a result, almost all astrophysical simulations require a radiative transfer model. Unfortunately, accurate radiative transfer is very computationally expensive. Therefore, in this thesis, we aim to improve the performance of radiative transfer solvers, with a particular emphasis on line radiative transfer. First, we review the classical work on accelerated lambda iterations and acceleration of convergence, and we propose a simple but effective improvement to the ubiquitously used Ng-acceleration scheme. Next, we present the radiative transfer library, Magritte: a formal solver with a ray-tracer that can handle structured and unstructured meshes as well as smoothed-particle data. To mitigate the computational cost, it is optimised to efficiently utilise multi-node and multi-core parallelism as well as GPU offloading. Furthermore, we demonstrate a heuristic algorithm that can reduce typical input models for radiative transfer by an order of magnitude, without significant loss of accuracy. This strongly suggests the existence of more efficient representations for radiative transfer models. To investigate this, we present a probabilistic numerical method for radiative transfer that naturally allows for uncertainty quantification, providing us with a mathematical framework to study the trade-off between computational speed and accuracy. Although we cannot yet construct optimal representations for radiative transfer problems, we point out several ways in which this method can lead to more rigorous optimisation

Financial market volatility: informative in predicting recessions

It is commonly agreed that the term spread and stock returns are useful in predicting recessions. We extend these empirical findings by examining interest rate and stock market volatility as additional recession indicators. Both risk-return analysis and the theory of investment under uncertainty provide a rationale for this extension. The results for the United States, Germany and Japan show that interest rate and stock return volatility contribute significantly to the forecasting of future recessions. This holds in particular for short term predictions.business cycles; stock market volatility; interest rate volatility; probit model

What determines euro area bank CDS spreads ?

This paper decomposes the explained part of the CDS spread changes of 31 listed euro area banks according to various risk drivers. The choice of the credit risk drivers is inspired by the Merton (1974) model. Individual CDS liquidity and other market and business variables are identified to complement the Merton model and are shown to play an important role in explaining credit spread changes. Our decomposition reveals, however, highly changing dynamics in the credit, liquidity, and business cycle and market wide components. This result is important since supervisors and monetary policy makers extract different signals from liquidity based CDS spread changes than from business cycle or credit risk based changes. For the recent financial crisis, we confirm that the steeply rising CDS spreads are due to increased credit risk. However, individual CDS liquidity and market wide liquidity premia played a dominant role. In the period before the start of the crisis, our model and its decomposition suggest that credit risk was not correctly priced, a finding which was correctly observed by e.g. the International Monetary Fundcredit default spreads, credit risk, financial crisis, financial sector, liquidity premia, structural model

An ALMA view of CS and SiS around oxygen-rich AGB stars

We aim to determine the distributions of molecular SiS and CS in the circumstellar envelopes of oxygen-rich asymptotic giant branch stars and how these distributions differ between stars that lose mass at different rates. In this study we analyse ALMA observations of SiS and CS emission lines for three oxygen-rich galactic AGB stars: IK Tau, with a moderately high mass-loss rate of $5\times10^{-6}$M$_\odot$ yr$^{-1}$, and W Hya and R Dor with low mass loss rates of $\sim1\times10^{-7}$M$_\odot$ yr$^{-1}$. These molecules are usually more abundant in carbon stars but the high sensitivity of ALMA allows us to detect their faint emission in the low mass-loss rate AGB stars. The high spatial resolution of ALMA also allows us to precisely determine the spatial distribution of these molecules in the circumstellar envelopes. We run radiative transfer models to calculate the molecular abundances and abundance distributions for each star. We find a spread of peak SiS abundances with $\sim10^{-8}$ for R Dor, $\sim10^{-7}$ for W Hya, and $\sim3\times10^{-6}$ for IK Tau relative to H$_2$. We find lower peak CS abundances of $\sim7\times10^{-9}$ for R Dor, $\sim7\times10^{-8}$ for W Hya and $\sim4\times10^{-7}$ for IK Tau, with some stratifications in the abundance distributions. For IK Tau we also calculate abundances for the detected isotopologues: C$^{34}$S, $^{29}$SiS, $^{30}$SiS, Si$^{33}$S, Si$^{34}$S, $^{29}$Si$^{34}$S, and $^{30}$Si$^{34}$S. Overall the isotopic ratios we derive for IK Tau suggest a lower metallicity than solar.Comment: 16 page

Pride and Prejudice in South Korea's Foreign Policy

On the last frontier of the Cold War, nothing is what it seems any more. On the surface, the old alliances still hold, but underneath a new order is gradually taking shape. This article analyses the various historical processes that have contributed to Seoul’s redefinition of its international role. As the international political and economic context changed following the end of the Cold War in Europe, new challenges and opportunities also appeared on the horizon on the Korean peninsula. These were met by a revitalized Korean nation, where a tainted elite was gradually driven from political and economic power. Proud of its democratic institutions and content with its economic success, Seoul engages the world with dignity, looking towards the future with confidence, but sensitive over historical legacies

The unusual 3D distribution of NaCl around the AGB star IK Tau

NaCl is a diatomic molecule with a large dipole moment, which allows for its detection even at relatively small abundances. It has been detected towards several evolved stars, among which is the AGB star IK Tau, around which it is distributed in several clumps that lie off-center from the star. We aim to study the three-dimensional distribution of NaCl around the AGB star IK Tau, and to obtain the abundance of NaCl relative to H$_2$ for each of the clumps. First, a new value for the maximum expansion velocity is determined. The observed ALMA channel maps are then deprojected to create a three-dimensional model of the distribution of NaCl. This model is then used as input for the radiative transfer modelling code magritte, which is used to obtain the NaCl abundances of each of the clumps by comparing the observations with the results of the magritte simulations. Additionally, the rotational temperature of the clumps is determined using population diagrams. We derive an updated value for the maximum expansion velocity of IK Tau $\upsilon_\mathrm{exp}$ = 28.4 km/s. A spiral-like shape can be discerned in our three-dimensional distribution model of the NaCl. This spiral lies more or less in the plane of the sky. The distribution is also flatter in the line-of-sight direction than in the plane of the sky. We find clump abundances between $9 \times 10^{-9}$ and $5 \times 10^{-8}$ relative to H$_2$, where the relative abundance is typically lower for clumps closer to the star. For the first time, we used deprojection to understand the three-dimensional environment of an AGB star and calculated the fractional abundance of NaCl in clumps surrounding the star.Comment: Accepted for publication in A&

MAGRITTE: a new multidimensional accelerated general-purpose radiative transfer code

Magritte is a new deterministic radiative transfer code. It is a ray-tracing code that computes the radiation field by solving the radiative transfer equation along a fixed set of rays for each grid cell. Its ray-tracing algorithm is independent of the type of input grid and thus can handle smoothed-particle hydrodynamics (SPH) particles, structured as well as unstructured grids. The radiative transfer solver is highly parallelized and optimized to have well scaling performance on several computer architectures. Magritte also contains separate dedicated modules for chemistry and thermal balance. These enable it to self-consistently model the interdependence between the radiation field and the local thermal and chemical states. The source code for Magritte will be made publically available at github.com/Magritte-code

A 'match-no match' numerical and graphical kernel density approach to interpreting lead isotope signatures of ancient artefacts

A new method for interpreting lead isotope ratios of artefacts is presented: a numerical and graphical 'match-no match' with possible raw materials. By calculating the definite integral under the kernel density estimate plot of different mining districts, using open-access software and legacy data, the relative probability that an object is made of an ore is indicated. A match with the reference data set may indicate the true origin, while no match indicates an unknown origin, that is, not present in the data set of mineral resources. Likewise, the composite or recycled nature of artefacts can be investigated in a probabilistic manner.Material Culture Studie

Radiative transfer as a Bayesian linear regression problem

Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their implementation, realistic radiative transfer models remain very computationally expensive, such that one often has to resort to approximate descriptions. The complexity of these models makes it difficult to assess the validity of any approximation and to quantify uncertainties on the model results. This impedes scientific rigour, in particular, when comparing models to observations, or when using their results as input for other models. We present a probabilistic numerical approach to address these issues by treating radiative transfer as a Bayesian linear regression problem. This allows us to model uncertainties on the input and output of the model with the variances of the associated probability distributions. Furthermore, this approach naturally allows us to create reduced-order radiative transfer models with a quantifiable accuracy. These are approximate solutions to exact radiative transfer models, in contrast to the exact solutions to approximate models that are often used. As a first demonstration, we derive a probabilistic version of the method of characteristics, a commonly-used technique to solve radiative transfer problems