Fakultät für Mathematik und Physik
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- ItemNeural Network Assisted Reduced Order Modeling of Black Hole Mergers(Hannover : Gottfried Wilhelm Leibniz Universität Hannover; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), 2025) Berg, Julian LucaSince 2015, the detection of gravitational waves gives us the possibility to study objects in the universe such as black holes and neutron stars. By parameter estimation, we can approximate properties of these objects. This includes the masses, spins, and distances. To perform reliable parameter estimation, it is important to have precise and fast models for the corresponding gravitational waves. One approach to speed up numerical computations is reduced order modeling. In this thesis, an approach by J.S. Hesthaven and S. Ubbiali is applied to gravitational wave models that performs reduced order modeling with neural networks. Therein, a neural network is built that can quickly compute a reduced order model for a given set of parameters such that the solution is still a reliable approximation. We first implement this for non-spinning black hole mergers and then expand the parameter space to spin-aligned black hole mergers. Our approach is substantiated with some numerical analysis by investigating the mismatches and the speedups in different regions of the parameter space.
- ItemDevelopment of new methods in nuclear forensics to determine the origin of single radioactive particles(Institutionelles Repositorium der Leibniz Universität Hannover, 2025) Leifermann, LauraIn the field of nuclear forensics, clarifying the origin and age of an unknown sample is a central question. Analytical results from spent nuclear fuel are used to gain insight into its burnup, initial enrichment, and reactor operations. During the Chornobyl nuclear accident in 1986, fragments of the nuclear fuel were released into the environment. Besides uranium the nuclear fuel also contained fission products, like Cs-137 or Eu-154, and breeding products like Pu-239 or Am-241. These fragments, so called "hot particles", remained in the environment around Chornobyl until today and underwent continuous weathering. The central question of this thesis is how much information can be extracted from particles 40 years later. Hot particles were localized using scanning electron microscopy, identified with energy-dispersive spectroscopy, and then extracted onto tungsten needles using a micromanipulator for further investigation. Subsequently, the isotope ratios of uranium, plutonium, zirconium and americium were analyzed using Secondary Ion Mass Spectrometry and Secondary Neutral Mass Spectrometry. In addition, a FIB was employed to cut single particles, and noble gas mass spectroscopy was utilized to measure trapped krypton and xenon isotopes in the particles. In this study, the methodology of particle extraction was refined and established as a workflow. During the extraction of various hot particles from different soil samples from the Chornobyl exclusion zone, one particle was identified as a lava particle. This type of particle had not previously been found outside the reactor building. Furthermore, five particles were sliced using FIB, revealing an undisturbed pore structure which is characteristic of spent nuclear fuel and lead to the assumption of trapped gas inclusions. Noble gas measurements of six particles were used to determine the age of the particles by krypton radiochronology and enabling calculations of the neutron flux from xenon isotopic ratios. Additionally the isotopic ratios of spent nuclear fuel provide insights into the source of the fission (U-235 or Pu-239). The results prove that even particles which have undergone weathering and are decades old still contain information of great importance in the field of nuclear forensics. Consequently, the assignment of fuel particles to a specific reactor type is possible.
- ItemRandom-Matrix Models of Monitored Quantum Circuits(New York, NY [u.a.] : Springer Science + Business Media B.V., 2024) Bulchandani, Vir B.; Sondhi , S. L.; Chalker, J. T.We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.
- ItemNumerical approach for Corvino-type gluing of Brill-Lindquist initial data(Bristol : IOP Publ., 2019) Pook-Kolb, Daniel; Giulini, DomenicoBuilding on the work of Giulini and Holzegel (2005 (arXiv:gr-qc/0508070)), a new numerical approach is developed for computing Cauchy data for Einstein's equations by gluing a Schwarzschild end to a Brill-Lindquist metric via a Corvino-type construction. In contrast to, and in extension of, the numerical strategy of Doulis and Rinne (2016 Class. Quantum Grav. 33 075014), the overdetermined Poisson problem resulting from the Brill wave ansatz is decomposed to obtain two uniquely solvable problems. A pseudospectral method and a Newton-Krylov root finder are utilized to perform the gluing. The convergence analysis strongly indicates that the numerical strategy developed here is able to produce highly accurate results. It is observed that Schwarzschild ends of various ADM masses can be glued to the same interior configuration using the same gluing radius.
- Item2-OGC: Open Gravitational-wave Catalog of Binary Mergers from Analysis of Public Advanced LIGO and Virgo Data(London : Institute of Physics Publ., 2020) Nitz, Alexander H.; Dent, Thomas; Davies, Gareth S.; Kumar, Sumit; Capano, Collin D.; Harry, Ian; Mozzon, Simone; Nuttall, Laura; Lundgren, Andrew; Tápai, MártonWe present the second Open Gravitational-wave Catalog (2-OGC) of compact-binary coalescences, obtained from the complete set of public data from Advanced LIGO's first and second observing runs. For the first time we also search public data from the Virgo observatory. The sensitivity of our search benefits from updated methods of ranking candidate events including the effects of nonstationary detector noise and varying network sensitivity; in a separate targeted binary black hole merger search we also impose a prior distribution of binary component masses. We identify a population of 14 binary black hole merger events with probability of astrophysical origin >0.5 as well as the binary neutron star merger GW170817. We confirm the previously reported events GW170121, GW170304, and GW170727 and also report GW151205, a new marginal binary black hole merger with a primary mass of 67-17+28 M⊙ that may have formed through hierarchical merger. We find no additional significant binary neutron star merger or neutron star-black hole merger events. To enable deeper follow-up as our understanding of the underlying populations evolves, we make available our comprehensive catalog of events, including the subthreshold population of candidates and posterior samples from parameter inference of the 30 most significant binary black hole candidates.