ABSTRACT
Surtseyan eruptions are an important class of mostly basaltic volcanic eruptions first identified in the 1960s, where erupting magma at an air-water interface interacts with large quantities of slurry, a mixture of previously ejected tephra that re-enters the crater together with water. During a Surtseyan eruption, hot magma bombs are ejected that initially contain pockets of slurry. Despite the formation of steam and anticipated subsequent high pressures inside these bombs, many survive to land without exploding. We seek to explain this by building and solving a simplified spherical mathematical model that describes the coupled evolution of pressure and temperature due to the flashing of liquid to vapour within a Surtseyan bomb while it is in flight. Analysis of the model provides a criterion for fragmentation of the bomb due to steam pressure build-up, and predicts that if diffusive steam flow through the porous bomb is sufficiently rapid the bomb will survive the flight intact. This criterion explicitly relates fragmentation to bomb properties, and describes how a Surtseyan bomb can survive in flight despite containing flashing liquid water, contributing to an ongoing discussion in volcanology about the origins of the inclusions found inside bombs.
ABSTRACT
A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. Using a standard method (Matlab function fminsearch) to calculate the parameter values led to unacceptable run times or non-convergence. Consequently we developed an algorithm which first finds the most important model parameters and uses these as a basis for a four stage process which accurately determines all parameter values. This process is then applied to data from three ICU patients. Good agreement between the model and measured arterial pressure is demonstrated in all cases.
