The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Further examination of the Xist promoter-switch hypothesis in X inactivation: Evidence against the existence and function of a P0 promoter

The onset of X inactivation coincides with accumulation of Xist RNA along the future inactive X chromosome. A recent hypothesis proposed that accumulation is initiated by a promoter switch within Xist. In this hypothesis, an upstream promoter (P0) produces an unstable transcript, while the known downstream promoter (P1) produces a stable RNA. To test this hypothesis, we examined expression and half-life of Xist RNA produced from an Xist transgene lacking P0 but retaining P1. We confirm the previous finding that P0 is dispensable for Xist expression in undifferentiated cells and that P1 can be used in both undifferentiated and differentiated cells. Herein, we show that Xist RNA initiated at P1 is unstable and does not accumulate. Further analysis indicates that the transcriptional boundary at P0 does not represent the 5′ end of a distinct Xist isoform. Instead, P0 is an artifact of cross-amplification caused by a pseudogene of the highly expressed ribosomal protein S12 gene Rps12. Using strand-specific techniques, we find that transcription upstream of P1 originates from the DNA strand opposite Xist and represents the 3′ end of the antisense Tsix RNA. Thus, these data do not support the existence of a P0 promoter and suggest that mechanisms other than switching of functionally distinct promoters control the up-regulation of Xist.