Mathematical Models for Flame Balls

Hulshof, J. [Promotor]Brauner, C.M. [Promotor]Berg, G.J.B. van den [Copromotor

An operative gamma camera for sentinel lymph node procedure in case of breast cancer

Large field of view gamma cameras are widely used to perform lymphoscintigraphy in the sentinel lymph nodes (SLN) procedure in case of breast cancer. However, they are not specified for this application and their sizes do not enable their use in the operative room to control the excision of the all SLN. We present the results obtained with a prototype of a new mini gamma camera developed especially for the operative lymphoscintigraphy of the axillary area in case of breast cancer. This prototype is composed of 10 mm thick parallel lead collimator, a 2 mm thick GSO:Ce inorganic scintillating crystal from Hitachi and a Hamamatsu H8500 flat panel multianode (64 channels) photomultiplier tube (MAPMT) equipped with a dedicated electronics. Its actual field of view is 50 × 50mm2. The gamma interaction position in the GSO scintillating plate is obtained by calculating the center of gravity of the fired MAPMT channels. The measurements performed with this prototype demonstrate the usefulness of this mini gamma camera for the pre, per and post-operative identification of SLN's and how its complementary role with an intraoperative handheld gamma probe enables to improve the efficiency of this practice. A 100 × 100mm2 field of view camera designated to cover the entire axillary area is under investigation

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory

Flame balls for a free boundary combustion model with radiative transfer

We study radial flame ball solutions of a three-dimensional free boundary problem (FBP), which models combustion of a gaseous mixture with dust in a microgravity environment. The model combines diffusion of mass and temperature with reaction at the flame front, the reaction rate being temperature dependent. The radiative flux due to the presence of dust enters the equation for the temperature in the form of a divergence term. This flux is modeled by Eddington's radiative transfer equation. The main parameters are the dimensionless opacity and the ratio of radiative and thermal fluxes. We prove existence of spherical flame ball solutions for the FBP. Bifurcation diagrams are obtained, exhibiting the multiplicity of solutions. Singular limit cases of the parameter values are also discussed. © 2006 Society for Industrial and Applied Mathematics