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The evolution equation for the radius of an isolated premixed flame ball is derived in the framework of a new method that strongly simplifies previous ones and highlights that they are based on Gaussian modelling of diffusion. The main idea is to split the flame ball in two components: the inner kernel, which is driven by a Poisson-type equation with a general polynomial forcing term, and the outer part, which is driven by a generalized diffusion process valid for fractional diffusive media. The evolution equation for the radius of the flame ball is finally determined as the evolution equation for the interface that matches the solution of the inner spherical kernel and the solution of the outer diffusive part and it emerges to be a nonlinear fractional differential equation. The effects of fractional diffusion on stability of solution are also picked out.

Failure of chemotherapy with anthracyclines as a result of drug resistance and toxicity is a major problem in the clinical management of neoplasia. The aim of the present study was to evaluate the activity of medroxyprogesterone acetate (MPA) as a chemosensitiser on anthracycline cytotoxicity. The study investigated whether such an effect could be related to an increase in lipid peroxidation, nitric oxide production, membrane fluidity and intracellular anthracycline concentration. The results showed that anthracyclines decreased nitric oxide production but increased membrane viscosity (polarisation constant) and lipid hydroperoxide formation in canine mammary tumour cells. Moreover, it was found that both drug-induced cytotoxicity and membrane viscosity increased in the presence of MPA. Conversely, lipid hydroperoxides decreased in MPA-supplemented cells. Medroxyprogesterone acetate did not show any effect on nitric oxide production. The two anthracyclines used (doxorubicin and idarubicin) showed differential intranuclear accumulation in canine mammary tumour cells, and MPA significantly modified intracellular concentration of anthracyclines.

• One of the most complete and extensive sensitivity analysis for wildfire simulation. • Identification of the most important parameters in a given model. • Parameter ordering in wildfire propagation model with turbulence and fire-spotting. • Comparison of surrogate models (gPC vs. GP) with the use of cross-validation. • Reduction of the problem dimension using sparse approach. Many nonlinear phenomena, whose numerical simulation is not straightforward, depend on a set of parameters in a way which is not easy to predict beforehand. Wildland fires in presence of strong winds fall into this category, also due to the occurrence of firespotting. We present a global sensitivity analysis of a new sub-model for turbulence and fire-spotting included in a wildfire spread model based on a stochastic representation of the fireline. To limit the number of model evaluations, fast surrogate models based on generalized Polynomial Chaos (gPC) and Gaussian Process are used to identify the key parameters affecting topology and size of burnt area. This study investigates the application of these surrogates to compute Sobol' sensitivity indices in an idealized test case. The performances of the surrogates for varying size and type of training sets as well as for varying parameterization and choice of algorithms have been compared. In particular, different types of truncation and projection strategies are tested for gPC surrogates. The best performance was achieved using a gPC strategy based on a sparse least-angle regression (LAR) and a low-discrepancy Halton's sequence. Still, the LAR-based gPC surrogate tends to filter out the information coming from parameters with large length-scale, which is not the case of the cleaning-based gPC surrogate. The wind is known to drive the fire propagation. The results show that it is a more general leading factor that governs the generation of secondary fires. Using a sparse surrogate is thus a promising strategy to analyze new models and its dependency on input parameters in wildfire applications. [ABSTRACT FROM AUTHOR]