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.

Empirical laws of survival and evolution: Their universality and implications

Presented analysis of human and fly life tables proves that with the specified accuracy their entire survival and mortality curves are uniquely determined by a single point (e.g., by the birth mortality q0), according to the law, which is universal for species as remote as humans and flies. Mortality at any age decreases with the birth mortality q0. According to life tables, in the narrow vicinity of a certain q0 value (which is the same for all animals of a given species, independent of their living conditions), the curves change very rapidly and nearly simultaneously for an entire population of different ages. The change is the largest in old age. Because probability to survive to the mean reproductive age quantifies biological fitness and evolution, its universal rapid change with q0 (which changes with living conditions) manifests a new kind of an evolutionary spurt of an entire population. Agreement between theoretical and life table data is explicitly seen in the figures. Analysis of the data on basic metabolism reduces it to the maximal mean lifespan (for animals from invertebrates to mammals), or to the maximal mean fission time (for bacteria), and universally scales them with the total number of body atoms only. Phenomenological origin of this unification and universality of metabolism, survival, and evolution is suggested. Their implications and challenges are discussed.