Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Investigation of the cold crucible melting process: experimental and numerical study

The dynamic process of melting different materials in a cold crucible is being studied experimentally with parallel numerical modelling work. The numerical simulation uses a variety of complementing models: finite volume, integral equation and pseudo-spectral methods combined to achieve the accurate description of the dynamic melting process. Results show the temperature history of the melting process with a comparison of the experimental and computed heat losses in the various parts of the equipment. The free surface visual observations are compared to the numerically predicted surface shapes.