Daniel Stone

Daniel Stone, Sebastian Geiger, Gabriel Lord

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations are introduced, which is based on the principle of allowing quanta of mass to pass through faces of a Cartesian finite volume grid. The timescales of these events are linked to the flux on the the face, and the schemes are self-adaptive, local in time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate results where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased.

Daniel Stone, Gabriel Lord

A new numerical scheme for conservation equations based on evolution by asynchronous discrete events is presented. During each event of the scheme only two cells of the underlying Cartesian grid are active, and an event is processed as the exact evolution of this subsystem. This naturally leads to and adaptive scheme in space and time. Numerical results are presented which show that the error of the asynchronous scheme decreases to zero as a control parameter is reduced. The construction of the scheme allows it to be expressed as repeated multiplications of matrix exponentials on an initial state vector; thus techniques such as the Goldberg series and the Baker Campbell Hausdorff (BCH) formula can be used to explore the theoretical properties of the scheme. We present the framework of a convergence proof in this manner.

Daniel Stone

Metaphors fundamentally shape how we reason about complex issues like artificial intelligence, yet current approaches to metaphor analysis in political discourse suffer from inconsistent definitions and methodologies. This paper introduces Narrative Frames, a novel categorisation system that addresses these limitations by providing a standardised framework for identifying and analysing metaphors in AI policy debates. Building on Lakoff and Johnson's conceptual metaphor theory, we derive 49 distinct narrative frames through a two-stage process: inductively coding 685 metaphors from the MetaNet database, then cross-referencing findings with 82 critical metaphor analysis studies. This methodology grounds the typology in both empirical data and established theoretical concepts while resolving definitional ambiguities that have hindered cross-study comparison. The Narrative Frames system offers researchers, journalists, and policymakers a shared vocabulary for analysing how metaphors shape public perception and policy priorities in AI governance. By revealing both the frames present and notably absent in discourse, this approach enables more transparent analysis of underlying assumptions and power dynamics. We discuss limitations and propose future applications, including computational scaling using large language models.

Daniel Stone, Gabriel Lord

Exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ODE system. This class of schemes requires the approxima- tion of a matrix exponential in every step, and one successful modern method is the Krylov subspace projection method. We investigate the effect of breaking down a single timestep into arbitrary multiple substeps, recycling the Krylov subspace to minimise costs. For these recyling based schemes we analyse the lo- cal error, investigate them numerically and show they can be applied to a large system with 106 unknowns. We also propose a new second order integrator that is found using the extra information from the substeps to form a corrector to increase the overall order of the scheme. This scheme is seen to compare favourably with other order two integrators.