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The Kassiopeia particle tracking framework is an object-oriented software package using modern C++ techniques, written originally to meet the needs of the KATRIN collaboration. Kassiopeia features a new algorithmic paradigm for particle…
We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones…
Krein space quantization and the ambient space formalism have been successfully applied to address challenges in quantum geometry (e.g., quantum gravity) and the axiomatic formulation of quantum Yang-Mills theory, including phenomena such…
Studies Beyond the Standard Model (BSM) will become more and more important in the near future with a rapidly increasing amount of data from different experiments around the world. The full study of BSM models is in general an extremely…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
The Green's functions of QCD encode important information about the infrared dynamics of the theory. The main non-perturbative tools used to study them are their own equations of motion, known as Schwinger-Dyson equations, and large-volume…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be…
Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is…
The particular choice of the gauge group for Yang-Mills theory plays an important role when it comes to the influence of matter fields. In particular, both the chosen gauge group and the representation of the matter fields yield structural…
A method is proposed of constructing quantum correlators for a general gauge system whose classical equations of motion do not necessarily follow from the least action principle. The idea of the method is in assigning a certain BRST…
A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to…
We present a simple yet powerful framework for solving inverse problems by leveraging automatic differentiation. Our method is broadly applicable whenever a smooth cost function can be defined near the true solution, and a numerical…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
A number of automated techniques and tools were proposed in the research literature over the years which aim to support the spreadsheet developer in the process of testing and debugging a faulty spreadsheet. One underlying assumption of…
Spreadsheet workbook contents are simple programs. Because of this, probabilistic programming techniques can be used to perform Bayesian inversion of spreadsheet computations. What is more, existing execution engines in spreadsheet…
We study the Schwinger-Dyson equations of a matrix model for an open-closed string theory. The free energy with source terms for scaling operators satisfies the same Virasoro conditions as those of the pure closed string and is obtained…
We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…
This thesis carries out a detailed investigation of the action for pure Yang- Mills theory which L. Mason formulated in twistor space. The rich structure of twistor space results in greater gauge freedom compared to the theory in ordinary…