The mathematical modelling for studying the evolution of a grounded temperate icefield flowing from an ice divide is detailed. The conjecture of the existence of a subglacial lake is considered, in particular regarding the influence of physical and geometrical parameters.
Glen's law
moving boundary
subglacial lake
glacier sliding
accumulation/ablation
The numerical procedure for the computational solution of the partial differential system for the dynamical and thermo-dynamical evolution of a grounded glacier and a subglacial lake is here detailed.
finite volumes
front tracking
moving boundaries
multidimensional interpolation
2011Curatela di monografia / trattato scientificometadata only access
Applied Scientific Computing VIII: Numerical Approximation and Simulation Technologies, Mathematics and Computers in Simulation, v 82, Issue 1, September 2011, Elsevier ISSN 0378-4754
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn times determine how long the phase process spends in a state once it has been selected. The main tool is a representation formula for the sample paths of the empirical laws of the phase process. Then, based on assumed joint large deviation behavior of the state selection and sojourn processes, we prove that the empirical laws of the phase process satisfy a sample path large deviation principle. From this large deviation principle, the large deviations behavior of a class of modulated additive processes is deduced. As an illustration of the utility of the general results, we provide an alternate proof of results for modulated Lévy processes. As a practical application of the results, we calculate the large deviation rate function for a processes that arises as the International Telecommunications Union's standardized stochastic model of two-way conversational speech.
