Tichy, Wolfgang

In the current world of fast-paced data production, statistics and machine learning tools are essential for interpreting and utilizing the full potential of this data. This dissertation comprises three studies employing statistical analysis and Convolutional Neural Network models. First, the research investigates the genetic evolution of the SARS-CoV-2 RNA molecule, emphasizing the role of epistasis in the RNA virus’s ability to adapt and survive. Through statistical tests, this study validates the significant impacts of genetic interactions and mutations on the virus’s structural changes over time, offering insights into its evolutionary dynamics. Secondly, the dissertation explores medical diagnosis by implementing Convolutional Neural Networks to differentiate between lung CT-scans of COVID-19 and non-COVID patients. This portion of the research demonstrates the capability of deep learning to enhance diagnostic processes, thereby reducing time and increasing accuracy in clinical settings. Lastly, we delve into gravitational wave detection, an area of astrophysics requiring precise data analysis to identify signals from cosmic events such as black hole mergers. Our goal is to utilize Convolutional Neural Network models in hopes of improving the sensitivity and accuracy of detecting these difficult to catch signals, pushing the boundaries of what we can observe in the universe. The findings of this dissertation underscore the utility of combining statistical methods and machine learning models to solve problems that are not only varied but also highly impactful in their respective fields.

Core-Collapse Supernovae (CCSNe) are some of the most powerful events in the universe liberating an astonishing 3×1053 ergs of the gravitational binding energy released by the collapse of the stellar core to a nascent neutron star (PNS) that is formed in these events. The visible display is capable of outshining the entire galaxy where it inhabits. Most of this energy, ~ 99%, is carried away by neutrinos of all flavors, however.
According to the favored theory of CCSNe, the production and transport of neutrinos from the dense core through the less dense mantle is believed to deposit energy in the mantle and thereby initiate the supernova explosion. Numerically modeling these events realistically to validate the model therefore requires an accurate neutrino transport algorithm coupled to sophisticated neutrino microphysics to compute the emission, transport, and energy deposition of neutrinos.
The CHIMERA code is a radiation-hydrodynamics code that has been developed to numerically model CCSNe in multiple spatial dimensions. The neutrino transport algorithm currently incorporated in CHIMERA is based upon the Multigroup Flux-Limited Diffusion (MGFLD) method. This current method basically uses only the zeroth angular moment of the Boltzmann equation and closes the system with terms dropped from the first angular moment to produce a diffusion-like equation. A flux-limiter is added to interpolate between the diffusive and free-streaming regimes, and to prevent the algorithm from computing acausal, i.e., faster than light transport, in regions where the neutrino mean free paths are large.

Unveiling the secrets of gravity necessitates numerical relativity simulations of gravitational systems, as observations made by gravitational wave detectors expect an interpretation. In the other hand, these numerical simulations require physical and constraint-satisfying initial data. Therefore, the accuracy of simulations go hand in hand with the accuracy of initial data. As such, constructing accurate initial data is an indispensable task and it is the very subject of this dissertation.
Here, we present the newly developed pseudospectral code Elliptica, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, Elliptica deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of Elliptica and the initial data construction algorithm for black hole-neutron star binary systems. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude ~ 0.8.

The main purpose of this dissertation is to study the inspiral and merger of binary neutron stars. The inspiral, in such a system, is caused by the loss of energy and angular momentum that is carried away by the emitted gravitational waves. Newly-formed neutron stars, after supernova explosions, are very hot. They cool down during the hundreds of millions of years, which is needed to bring the two stars in a neutron star binary close enough together to start investigating them with numerical relativity simulations. Thus, they can be considered as fluids at zero temperature to very high accuracy, when we start numerical simulations. In this description, the stars also have a well-defined star surface, beyond which there is a true vacuum. This vacuum, outside the stars, will persist until the stars get so close that mass can be ejected due to tidal forces, and later, when they come into contact and eject streams of hot matter. To date, all current numerical relativity programs use an artificial atmosphere from the very beginning. They do this, to avoid numerical problems arising from the sharp transition of the matter region to the vacuum outside the stars. To be more precise, they take the initial data and fill all the vacuum regions with a very low-density zero velocity atmosphere. While this atmosphere is not physical and used only for numerical reasons, it can still influence the results of the simulations. For example, studies of merger dynamics, merger remnant, disk mass, ejecta mass, and kinetic energy of ejecta, are hampered by the presence of the artificial zero velocity low-density material. To avoid this problem, we have developed a new method to evolve the neutron star systems, without the need for an artificial atmosphere. We describe this method, which we call vacuum method, we present tests with it, and compare it to the conventional atmosphere method. For these tests, we first consider the evolution of stable, oscillating, and collapsing single neutron stars. We also study simulations of the inspiral and merger of binaries using both methods. We find better mass conservation in low-density regions and near refinement boundaries, as well as better ejecta material conservation for the new method. However, the gravitational wave predictions produced by our simulations are almost identical for both methods, since they are mainly due to the bulk motion of the stars which is not strongly affected by the presence or absence of an artificial atmosphere.