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General Relativity, despite its century-long success, faces conceptual and observational challenges, including singularities, incompatibility with quantum mechanics, and the need to introduce dark matter and dark energy. Precision cosmology…
Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent…
Solar tomography has progressed rapidly in recent years thanks to the development of robust algorithms and the availability of more powerful computers. It can today provide crucial insights in solving issues related to the line-of-sight…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we…
Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot's own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new…
In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions…
Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified…
To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
This thesis investigates late-time cosmic acceleration using modified gravity theories with a focus on $f(Q)$ gravity, as an alternative to the $\Lambda$CDM model. The standard cosmological model attributes the acceleration to a…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for…
Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated…
Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\Lambda$CDM model, based on General Relativity and standard…
Simflowny is an open platform which automatically generates parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support an extended set of families of models,…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose…
Solving Einstein's equations precisely for strong-field gravitational systems is essential to determining the full physics content of gravitational wave detections. Without these solutions it is not possible to infer precise values for…