Coupling multi-fluid dynamics equipped with Landau closures to the particle-in-cell method

The particle-in-cell (PIC) method is successfully used to study magnetized plasmas. However, this requires large computational costs and limits simulations to short physical run-times and often to setups in less than three spatial dimensions. Traditionally, this is circumvented either via hybrid-PIC methods (adopting massless electrons) or via magneto-hydrodynamic-PIC methods (modelling the background plasma as a single charge-neutral magneto-hydrodynamical fluid). Because both methods preclude modelling important plasma-kinetic effects, we introduce a new fluid-PIC code that couples a fully explicit and charge-conservative multi-fluid solver to the PIC code SHARP through a current-coupling scheme and solve the full set of Maxwell's equations. This avoids simplifications typically adopted for Ohm's Law and enables us to fully resolve the electron temporal and spatial scales while retaining the versatility of initializing any number of ion, electron, or neutral species with arbitrary velocity distributions. The fluid solver includes closures emulating Landau damping so that we can account for this important kinetic process in our fluid species. Our fluid-PIC code is second-order accurate in space and time. The code is successfully validated against several test problems, including the stability and accuracy of shocks and the dispersion relation and damping rates of waves in unmagnetized and magnetized plasmas. It also matches growth rates and saturation levels of the gyro-scale and intermediate-scale instabilities driven by drifting charged particles in magnetized thermal background plasmas in comparison to linear theory and PIC simulations. This new fluid-SHARP code is specially designed for studying high-energy cosmic rays interacting with thermal plasmas over macroscopic timescales.Comment: 35 pages, 11 figures, submitted to JPP. Comments are welcom

Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization

We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior, data likelihood, and numerical inverse extra-regularization schemes are derived and classified. The Bayesian methodology presented in this paper tries to unify and extend the following methods: Wiener-filtering, Tikhonov regularization, Ridge regression, Maximum Entropy, and inverse regularization techniques. The inverse techniques considered here are the asymptotic regularization, the Jacobi, Steepest Descent, Newton-Raphson, Landweber-Fridman, and both linear and non-linear Krylov methods based on Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The structures of the up-to-date highest-performing algorithms are presented, based on an operator scheme, which permits one to exploit the power of fast Fourier transforms. Using such an implementation of the generalized Wiener-filter in the novel ARGO-software package, the different numerical schemes are benchmarked with 1-, 2-, and 3-dimensional problems including structured white and Poissonian noise, data windowing and blurring effects. A novel numerical Krylov scheme is shown to be superior in terms of performance and fidelity. These fast inverse methods ultimately will enable the application of sampling techniques to explore complex joint posterior distributions. We outline how the space of the dark-matter density field, the peculiar velocity field, and the power spectrum can jointly be investigated by a Gibbs-sampling process. Such a method can be applied for the redshift distortions correction of the observed galaxies and for time-reversal reconstructions of the initial density field.Comment: 40 pages, 11 figure

In-Vivo Three Dimensional Proton Hadamard Spectroscopic Imaging in the Human Brain

Magnetic resonance spectroscopic imaging (MRSI) is a useful tool for obtaining information on the biochemical processes underlying various pathologies. A widely used multi-voxel localization method is chemical shift imaging (CSI) which uses gradients for phase encoding. Although simple to implement, low in specific absorption rate (SAR) and immune to chemical shift displacement (CSD), it also suffers from some well known drawbacks caused by its sinc-shaped point spread function (PSF). This results in loss of both signal-to-noise ratio (SNR) as well as localization, an effect that is exacerbated at low resolutions. In contrast, an alternative localization method, Hadamard spectroscopic imaging (HSI) benefits from a theoretically ideal PSF and consequently does not suffer from these drawbacks. In this work we exploit the theoretically ideal PSF of HSI encoding to develop a novel three dimensional (3D) multi-voxel MR localization method based on transverse HSI (T-HSI). The advantages of T HSI are that unlike gradient phase-encoding: (i) the volume of interest (VOI) does not need to be smaller than the field-of-view to prevent aliasing; (ii) the number of partitions in each direction can be small, 8, 4 or even 2 at no cost in PSF; (iii) the VOI does not have to be contiguous; and (iv) the voxel profile depends on the available B1 and pulse synthesis paradigm and can therefore, at least theoretically, approach "ideal" "1" inside and "0" elsewhere. Clinical utility of the new method is shown by spectra obtained from the brain of a healthy volunteer. The benefits of T-HSI are demonstrated by a quantitative comparison to CSI of the SNR and localization in a phantom in both one and three dimensions at clinical resolutions. A novel matrix formalism is used to quantify the impact of non-ideal flip angles on T-HSI. The superior PSF of T-HSI is then used to demonstrate the feasibility of scanning regions near or on the skull while limiting the impact of lipid contamination and obtaining quantifiable spectra. A comparison to spectra obtained using CSI is shown for a healthy volunteer. The new method is also used in a clinical pathology: to scan multiple sclerosis (MS) lesions occurring near the skull. To maintain the benefits provided by the PSF of HSI at higher fields, despite its susceptibility to CSD, a additional hybrid sequence is also developed that limits both the SAR and the CSD, regardless of the size of the VOI. A comparison to CSI in a phantom and in-vivo is carried out and spectra obtained from the brain of a healthy volunteer at 3T are shown. Finally, future research avenues involving extension of this research to ultra high fields (7T) are discussed and possible clinical uses are described

Approximate inference in astronomy

This thesis utilizes the rules of probability theory and Bayesian reasoning to perform inference about astrophysical quantities from observational data, with a main focus on the inference of dynamical systems extended in space and time. The necessary assumptions to successfully solve such inference problems in practice are discussed and the resulting methods are applied to real world data. These assumptions range from the simplifying prior assumptions that enter the inference process up to the development of a novel approximation method for resulting posterior distributions. The prior models developed in this work follow a maximum entropy principle by solely constraining those physical properties of a system that appear most relevant to inference, while remaining uninformative regarding all other properties. To this end, prior models that only constrain the statistically homogeneous space-time correlation structure of a physical observable are developed. The constraints placed on these correlations are based on generic physical principles, which makes the resulting models quite flexible and allows for a wide range of applications. This flexibility is verified and explored using multiple numerical examples, as well as an application to data provided by the Event Horizon Telescope about the center of the galaxy M87. Furthermore, as an advanced and extended form of application, a variant of these priors is utilized within the context of simulating partial differential equations. Here, the prior is used in order to quantify the physical plausibility of an associated numerical solution, which in turn improves the accuracy of the simulation. The applicability and implications of this probabilistic approach to simulation are discussed and studied using numerical examples. Finally, utilizing such prior models paired with the vast amount of observational data provided by modern telescopes, results in Bayesian inference problems that are typically too complex to be fully solvable analytically. Specifically, most resulting posterior probability distributions become too complex, and therefore require a numerical approximation via a simplified distribution. To improve upon existing methods, this work proposes a novel approximation method for posterior probability distributions: the geometric Variational Inference (geoVI) method. The approximation capacities of geoVI are theoretically established and demonstrated using numerous numerical examples. These results suggest a broad range of applicability as the method provides a decrease in approximation errors compared to state of the art methods at a moderate level of computational costs.Diese Dissertation verwendet die Regeln der Wahrscheinlichkeitstheorie und Bayes’scher Logik, um astrophysikalische Größen aus Beobachtungsdaten zu rekonstruieren, mit einem Schwerpunkt auf der Rekonstruktion von dynamischen Systemen, die in Raum und Zeit definiert sind. Es werden die Annahmen, die notwendig sind um solche Inferenz-Probleme in der Praxis erfolgreich zu lösen, diskutiert, und die resultierenden Methoden auf reale Daten angewendet. Diese Annahmen reichen von vereinfachenden Prior-Annahmen, die in den Inferenzprozess eingehen, bis hin zur Entwicklung eines neuartigen Approximationsverfahrens für resultierende Posterior-Verteilungen. Die in dieser Arbeit entwickelten Prior-Modelle folgen einem Prinzip der maximalen Entropie, indem sie nur die physikalischen Eigenschaften eines Systems einschränken, die für die Inferenz am relevantesten erscheinen, während sie bezüglich aller anderen Eigenschaften agnostisch bleiben. Zu diesem Zweck werden Prior-Modelle entwickelt, die nur die statistisch homogene Raum-Zeit-Korrelationsstruktur einer physikalischen Observablen einschränken. Die gewählten Bedingungen an diese Korrelationen basieren auf generischen physikalischen Prinzipien, was die resultierenden Modelle sehr flexibel macht und ein breites Anwendungsspektrum ermöglicht. Dies wird anhand mehrerer numerischer Beispiele sowie einer Anwendung auf Daten des Event Horizon Telescope über das Zentrum der Galaxie M87 verifiziert und erforscht. Darüber hinaus wird als erweiterte Anwendungsform eine Variante dieser Modelle zur Simulation partieller Differentialgleichungen verwendet. Hier wird der Prior als Vorwissen benutzt, um die physikalische Plausibilität einer zugehörigen numerischen Lösung zu quantifizieren, was wiederum die Genauigkeit der Simulation verbessert. Die Anwendbarkeit und Implikationen dieses probabilistischen Simulationsansatzes werden diskutiert und anhand von numerischen Beispielen untersucht. Die Verwendung solcher Prior-Modelle, gepaart mit der riesigen Menge an Beobachtungsdaten moderner Teleskope, führt typischerweise zu Inferenzproblemen die zu komplex sind um vollständig analytisch lösbar zu sein. Insbesondere ist für die meisten resultierenden Posterior-Wahrscheinlichkeitsverteilungen eine numerische Näherung durch eine vereinfachte Verteilung notwendig. Um bestehende Methoden zu verbessern, schlägt diese Arbeit eine neuartige Näherungsmethode für Wahrscheinlichkeitsverteilungen vor: Geometric Variational Inference (geoVI). Die Approximationsfähigkeiten von geoVI werden theoretisch ermittelt und anhand numerischer Beispiele demonstriert. Diese Ergebnisse legen einen breiten Anwendungsbereich nahe, da das Verfahren bei moderaten Rechenkosten eine Verringerung des Näherungsfehlers im Vergleich zum Stand der Technik liefert

Gravitational Lenses as High-Resolution Telescopes

The inner regions of active galaxies host the most extreme and energetic phenomena in the universe including, relativistic jets, supermassive black hole binaries, and recoiling supermassive black holes. However, many of these sources cannot be resolved with direct observations. I review how strong gravitational lensing can be used to elucidate the structures of these sources from radio frequencies up to very high energy gamma rays. The deep gravitational potentials surrounding galaxies act as natural gravitational lenses. These gravitational lenses split background sources into multiple images, each with a gravitationally-induced time delay. These time delays and positions of lensed images depend on the source location, and thus, can be used to infer the spatial origins of the emission. For example, using gravitationally-induced time delays improves angular resolution of modern gamma-ray instruments by six orders of magnitude, and provides evidence that gamma-ray outbursts can be produced at even thousands of light years from a supermassive black hole, and that the compact radio emission does not always trace the position of the supermassive black hole. These findings provide unique physical information about the central structure of active galaxies, force us to revise our models of operating particle acceleration mechanisms, and challenge our assumptions about the origin of compact radio emission. Future surveys, including LSST, SKA, and Euclid, will provide observations for hundreds of thousands of gravitationally lensed sources, which will allow us to apply strong gravitational lensing to study the multi-wavelength structure for large ensembles of sources. This large ensemble of gravitationally lensed active galaxies will allow us to elucidate the physical origins of multi-wavelength emissions, their connections to supermassive black holes, and their cosmic evolution.Comment: Invited (Accepted) review for Physics Report

Quantum scale biomimicry of low dimensional growth: An unusual complex amorphous precursor route to TiO2 band confinement by shape adaptive biopolymer-like flexibility for energy applications

Crystallization via an amorphous pathway is often preferred by biologically driven processes enabling living species to better regulate activation energies to crystal formation that are intrinsically linked to shape and size of dynamically evolving morphologies. Templated ordering of 3-dimensional space around amorphous embedded non-equilibrium phases at heterogeneous polymer-metal interfaces signify important routes for the genesis of low-dimensional materials under stress-induced polymer confinement. We report the surface induced catalytic loss of P=O ligands to bond activated aromatization of C-C C=C and Ti=N resulting in confinement of porphyrin-TiO(2 )within polymer nanocages via particle attachment. Restricted growth nucleation of TiO2 to the quantum scale (˂= 2 nm) is synthetically assisted by nitrogen, phosphine and hydrocarbon polymer chemistry via self-assembly. Here, the amorphous arrest phase of TiO, is reminiscent of biogenic amorphous crystal growth patterns and polymer coordination has both a chemical and biomimetic significance arising from quantum scale confinement which is atomically challenging. The relative ease in adaptability of non-equilibrium phases renders host structures more shape compliant to congruent guests increasing the possibility of geometrical confinement. Here, we provide evidence for synthetic biomimicry akin to bio-polymerization mechanisms to steer disorder-to-order transitions via solvent plasticization-like behaviour. This challenges the rationale of quantum driven confinement processes by conventional processes. Further, we show the change in optoelectronic properties under quantum confinement is intrinsically related to size that affects their optical absorption band energy range in DSSC.This work was supported by the National Research Foundation of Korea (NRF) grant funded by Korea government (MEST) NRF-2012R1A1A2008196, NRF 2012R1A2A2A01047189, NRF 2017R1A2B4008801, 2016R1D1A1A02936936, (NRF-2018R1A4A1059976, NRF-2018R1A2A1A13078704) and NRF Basic Research Programme in Science and Engineering by the Ministry of Education (No. 2017R1D1A1B03036226) and by the INDO-KOREA JNC program of the National Research Foundation of Korea Grant No. 2017K1A3A1A68. We thank BMSI (A*STAR) and NSCC for support. SJF is funded by grant IAF25 PPH17/01/a0/009 funded by A* STAR/NRF/EDB. CSV is the founder of a spinoff biotech Sinopsee Therapeutics. The current work has no conflicting interests with the company. We would like to express our very great appreciation to Ms. Hyoseon Kim for her technical expertise during HRTEM imaging

Roadmap on spatiotemporal light fields

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultrafast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell's equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird's eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges.Comment: This is the version of the article before peer review or editing, as submitted by an author to Journal of Optics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i