Measurements of production cross-sections and mixing of charm mesons at LHCb

The start of the second running period of the Large Hadron Collider in 2015, delivering proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13\ \mathrm{TeV}$, marks a new era in the study of particles containing charm quarks with samples of unprecedented size being recorded by the LHCb experiment. This thesis first presents cross-section measurements for $D^0$, $D^+$, $D_s^{+}$, and $D^{*+}$ at $\sqrt{s}=13\ \mathrm{TeV}$, supplemented by a measurement of the same cross-sections at $\sqrt{s}=5\ \mathrm{TeV}$, leading to very precise, double-differential cross-section ratios that are hugely beneficial for constraining theoretical uncertainties in quantum chromodynamics. This is followed by a study into the potential for extracting the parameters describing the oscillation of neutral $D^0$ mesons in $D^0\rightarrow K^+\pi^-\pi^+\pi^-$ decays, exploiting the very large data samples recorded at 13 TeV. These studies show that this decay can be used to heavily constrain the mixing parameters, leading to a substantial improvement of the uncertainties on them when included in the world average. However, these large datasets create computational challenges due to the sheer amount of recorded data, which is especially true for the LHCb simulation effort. Therefore, this thesis also discusses work undertaken to increase the speed at which simulated samples can be created by one order of magnitude.