An Object-Oriented, Python-Based Moving Mesh Hydrodynamics Code Inspired by Astrophysical Problems

The role of radiative cooling plays an important role in the formation of structures in collapsing gas. In this dissertation I examine the impact of cooling in two formation scenarios: first, the role of H2 cooling in collapsing gas in primordial dark matter halos in the possible formation of supermassive black holes; second, low metallicity cooling in collapsing clouds and its possible role in explaining low-metallicity globular clusters. Further, I introduce a new hydrodynamics code, with a design guided by current software principles. In chapter 2, I examined the proposed mechanism to explain the formation of super-massive black holes through direct collapse. The presence of quasars at redshifts z > 6 indicates the existence of supermassive black holes (SMBHs) as massive as a few times 10^9 mass of the sun, challenging models for SMBH formation. One pathway is through the direct collapse of gas in T_vir ≳ 10^4 K halos; however, this requires the suppression of H2 cooling to prevent fragmentation. In this dissertation, I examine a proposed mechanism for this suppression which relies on cold-mode accretion flows leading to shocks at high densities (n > 10^4 cm^−3 ) and temperatures (T > 10^4 K). In such gas, H2 is efficiently collisionally dissociated. I use high-resolution numerical simulations to test this idea, demonstrating that such halos typically have lower temperature progenitors, in which cooling is efficient. Those halos do show filamentary flows; however, the gas shocks at or near the virial radius (at low densities), thus preventing the proposed collisional mechanism from operating. I do find that, if we artificially suppress H2 formation with a high UV background, so as to allow gas in the halo center to enter the high-temperature, high-density “zone of no return”, it will remain there even if the UV flux is turned off, collapsing to high density at high temperature. Due to computational limitations, we simulated only three halos. However, we demonstrate, using Monte Carlo calculations of 10^6 halo merger histories, that a few rare halos could assemble rapidly enough to avoid efficient H2 cooling in all of their progenitor halos, provided that the UV background exceeds J_21 ∼ few at redshifts as high as z ∼ 20. In chapter 3, I explore the relative role of small-scale fragmentation and global collapse in low-metallicity clouds, pointing out that in such clouds the cooling time may be longer than the dynamical time, allowing the cloud to collapse globally before it can fragment. This, I suggest, may help to explain the formation of the low-metallicity globular cluster population, since such dense stellar systems need a large amount of gas to be collected in a small region (without significant feedback during the collapse). To explore this further, I carried out numerical simulations of low-metallicity Bonner-Ebert stable gas clouds, demonstrating that there exists a critical metallicity (between 0.001 and 0.01 metallicity of the sun ) below which the cloud collapses globally without fragmentation. I also run simulations including a background radiative heating source, showing that this can also produce clouds that do not fragment, and that the critical metallicity – which can exceed the no-radiation case – increases with the heating rate. Lastly in chapter 4, I describe the structure and implementation of the new open-source parallel moving-mesh hydrodynamic code, Python Hydro-Dynamics (phd). The code has been written from the ground up to be easy to use and facilitate future modifications. The code is written in a mixture of Python and Cython and makes extensive use of object-oriented programming. I outline the algorithms used and describe the design philosophy and the reasoning of my choices during the code development. I end by validating the code through a series of test problems

IST Austria Thesis

Fabrication of curved shells plays an important role in modern design, industry, and science. Among their remarkable properties are, for example, aesthetics of organic shapes, ability to evenly distribute loads, or efficient flow separation. They find applications across vast length scales ranging from sky-scraper architecture to microscopic devices. But, at the same time, the design of curved shells and their manufacturing process pose a variety of challenges. In this thesis, they are addressed from several perspectives. In particular, this thesis presents approaches based on the transformation of initially flat sheets into the target curved surfaces. This involves problems of interactive design of shells with nontrivial mechanical constraints, inverse design of complex structural materials, and data-driven modeling of delicate and time-dependent physical properties. At the same time, two newly-developed self-morphing mechanisms targeting flat-to-curved transformation are presented. In architecture, doubly curved surfaces can be realized as cold bent glass panelizations. Originally flat glass panels are bent into frames and remain stressed. This is a cost-efficient fabrication approach compared to hot bending, when glass panels are shaped plastically. However such constructions are prone to breaking during bending, and it is highly nontrivial to navigate the design space, keeping the panels fabricable and aesthetically pleasing at the same time. We introduce an interactive design system for cold bent glass façades, while previously even offline optimization for such scenarios has not been sufficiently developed. Our method is based on a deep learning approach providing quick and high precision estimation of glass panel shape and stress while handling the shape multimodality. Fabrication of smaller objects of scales below 1 m, can also greatly benefit from shaping originally flat sheets. In this respect, we designed new self-morphing shell mechanisms transforming from an initial flat state to a doubly curved state with high precision and detail. Our so-called CurveUps demonstrate the encodement of the geometric information into the shell. Furthermore, we explored the frontiers of programmable materials and showed how temporal information can additionally be encoded into a flat shell. This allows prescribing deformation sequences for doubly curved surfaces and, thus, facilitates self-collision avoidance enabling complex shapes and functionalities otherwise impossible. Both of these methods include inverse design tools keeping the user in the design loop

Investigation into Intelligent Image Preprocessor Techniques for Artificial Neural Networks

In this thesis we will discuss the process for data preparation of visual or image data ready for use in Artificial Neural Network systems. The thesis will present these concepts, their location in the broader field and the arguments as why certain practices are considered required for these systems; before presenting a number of novel algorithms that are intended as alternatives with desirable properties. These novel algorithms will then be testing in a practical domain (simulating the challenge of face-detection within a scene), followed up by discussions of their successes and failures. The findings presented show that some of the novel algorithms can show statistically significant improvement in accuracy compared to some of the traditional methods used in the field. This thesis concludes with recommendations in which situations the novel algorithms may (if at all) be suitable for use in future designs and potential avenues for further research

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions