Simulating Fundamental Physics: Numerical Endeavours in Astronomical and Particle Phenomenology

The fundamental theories of physics, general relativity and quantum field theory allow for the description of highly complex interacting systems. To truly realise the nature of these theories, one must take advantage of the numerical power provided by modern computational hardware. In this thesis, we begin by exploring the possibility, through numerical simulations, that signatures of multi axion phenomenology may be imprinted on the high energy photon spectra of Blazars. We follow this with a presentation of our work on the determination, numerically, of the dynamical friction force that would be experienced by a black hole propagating through a field of scalar particles. Finally, we return from the astrophysical realm, and present a novel code that may allow for the rapid computation of precision matrix elements relevant to future terrestrial collider experience. By accelerating pre-existing implementations of the Laprota algorithm, during the the preliminary benchmarking of our code, we observed a reduction in execution time by an order of magnitude.