Characterization of transport equations with forensic applications (nuclear and social)

Abstract

Convection and diffusion processes are used to understand transport in a wide range of contexts including the spread of diseases, the adoption of ideas within populations and the classical applications to heat and mass transfer. While much attention is typically paid to formulating the appropriate equations to accurately capture the underlaying processes, the parameters that go into these mathematical models are equally important and receive far less attention. The SARS-CoV-2 emerged in late 2019 and caused a worldwide pandemic. Epidemiological models are playing a key role in guiding public health interventions. The SIR model (susceptible, infected, recovered) is used to predict the number of infections over time. Their ability to accurately predict the number of people who will become infected depends on input parameters that are poorly understood. Here the effects of uncertainty on predicted outcomes are explored. The diffusion of ideas on social media is also studied in this context. How ideas propagate can affect societal trends, norms, behaviors, influence markets and the outcomes of elections. The SIR model is again used, but here in combination with sentiment analysis to understand tweet behavior. Different sentiment messages spread at different rates through social media. Parameter estimation in the classical domain is conducted here to understand subsurface transport models that are used for post detonation nuclear forensics. Subsurface gas transport depends on accurately estimating the depth of the underground explosion as well as the geology that surrounds the explosion. The site of the explosions are likely to be denied access sites and parameter estimations must be done remotely. The depth at which a test occurs is known to be a critical parameter, affecting not only the migration time for gases to reach the surface but also their subsequent isotopic ratios. Bayesian data synthesis can improve depth of burst estimates by considering local topology, geology, the presence of surface deformation, yield, and a safety factor (for US tests). Here a method is developed to characterize fracture width, spacing, tortuosity, permeability and porosity at a denied access site. Fractures are treated as fractals with their respective fractal dimensions determined using surface images. The input parameters were applied to a subsurface gas transport model for six underground nuclear explosions conducted by the Democratic People’s Republic of Korea (DPRK).