Solar system

Abstract:

We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 American Institute of Physics.

Abstract:

The standardisation of 210Pb is complicated by the presence of the daughters, 210Bi and 210Po. In addition, the low energies of the beta emissions from 210Pb make it difficult to obtain high detection efficiencies in an atmospheric proportional counter and hence produce the need for large extrapolations with consequential large uncertainties when extrapolating to unit efficiency with the conventional 4pi(PC)-gamma-coincidence technique. In order to produce a reliable standardisation, it is necessary to remove the daughter products. A solution of 210Pb was therefore chemically separated from its daughters and then standardised using the conventional 4pi(LS)-gamma-coincidence technique. The low energy (46 keV) and low emission probability (4%) of the associated photon emissions effectively rules out the possibility of using ionisation chambers as secondary standard transfer instruments for this nuclide. A germanium spectrometer therefore was calibrated for this purpose using 241Am as a normalising agent. The results of this work are presented together with an analysis of the standardisation uncertainties that can be achieved in practice.