Time-scale Problem Research Articles

Sharp Fronts within Geochemical Transport Problems

AbstractWe consider some reactive geochemical transport problems in groundwater systems. When incoming fluid is in disequilibrium with the mineralogy sharp transition fronts may develop. We show that this is a generic property for a class of systems where the timescales associated with reaction and diffusion phenomena are much shorter than those associated with advective transport. Such multiple timescale problems are relevant to a variety of processes in natural systems: mathematically methods of singular perturbation theory reduce the dimension of the problems to be solved locally. Furthermore we consider how spatial heterogeneous mineralogy can impact upon the propagation of sharp geochemical fronts.We develop an asymptotic approach in which we solve equations for the evolving geometry of the front and indicate how the non-smooth perturbations due to natural heterogeneity of the mineralogy on underlying ground water flow field are balanced against the smoothing effect of diffusion/dispersive processes. Fronts are curvature damped, and the results here indicate the generic nature of separate front propagation within both model (idealized) and natural (heterogeneous) geochemical systems.

On the applicability of the statistical mechanical theories of violent relaxation

Fundamental problems for statistical mechanical theories of violent relaxation that raise doubts about their applicability are examined. Shu's particle approach predicts a most probable final state that may not be accessible from the initial state, since access would require a violation of Liouville's theorem. Furthermore, it is not clear how to treat the initial shuffling in phase space of different types of particles properly in the particle approach. Lynden-Bell's phase-element approach incorporates Liouville's theorem and takes account of initial shuffling, but overestimates the fine-grained phase-space density of stars by many orders of magnitude (this problem can be cirumvented). Both theories lead in the nondegenerate limit to infinite mass isothermal spheres, which is inconsistent with the assumed finite mass of the initial state. A time-scale problem also remains in both theories. 10 references.

New Approach to General Relativity

A generally covariant scalar field theony of gravitation is presented. The principle of equivalence as well as the principle of gcneral covalance are preserved. A functional solution of Einstein's field equations is obtained for the general time-independent case. The theory predicts correctly the results of the three crucial tests of general relativity. Implications concerning the self- energy of point particles are presented. A ncw theory of cosmology ss given and is application to thc time-scale problem and to the derivation of the Mach principle is discussed. A new principle ealled the principle of observation is introduced. (auth)