Lane H. Rogers | Searcharxiv

arXiv2026

Modeling and Stabilization of Transport-Dominated Flows

This report explores and compares numerical stabilization methods for transport-dominated flows arising in atmospheric modeling. The Streamline-Upwind (SU) and Streamline-Upwind Petrov-Galerkin (SUPG) stabilization formulations are implemented in Julia's ClimaCore.jl package and Python's Firedrake package for a test problem with slotted-cylinder initial conditions. These methods are compared for their ability to mitigate spurious oscillations while preserving sharp features against existing hyperdiffusion and quasi-monotone limiter methods, alongside various combinations. For this benchmark, quasi-monotone limiters were most effective at minimizing un-physical extrema, at the expense of diffusing the overall structure. The SUPG method was not found to improve upon the no stabilization case, for this test case in the computed error metrics. However, it performs best at preserving sharp feature and overall structure, among tested stabilized runs. Theoretical properties of SUPG are analyzed, and an asymptotics-based SUPG algorithm is proposed as future work.

physics.flu-dyn↗

arXiv2025

Destabilizing a Social Network Model via Intrinsic Feedback Vulnerabilities

Social influence plays a significant role in shaping individual sentiments and actions, particularly in a world of ubiquitous digital interconnection. The rapid development of generative AI has engendered well-founded concerns regarding the potential scalable implementation of radicalization techniques in social media. Motivated by these developments, we present a case study investigating the effects of small but intentional perturbations on a simple social network. We employ Taylor's classic model of social influence and tools from robust control theory (most notably the Dynamical Structure Function (DSF)), to identify perturbations that qualitatively alter the system's behavior while remaining as unobtrusive as possible. We examine two such scenarios: perturbations to an existing link and perturbations that introduce a new link to the network. In each case, we identify destabilizing perturbations of minimal norm and simulate their effects. Remarkably, we find that small but targeted alterations to network structure may lead to the radicalization of all agents, exhibiting the potential for large-scale shifts in collective behavior to be triggered by comparatively minuscule adjustments in social influence. Given that this method of identifying perturbations that are innocuous yet destabilizing applies to any suitable dynamical system, our findings emphasize a need for similar analyses to be carried out on real systems (e.g., real social networks), to identify the places where such dynamics may already exist.

cs.SI↗