RESUMEN
We consider the arrival
process of infinitely many identical independent diffusion processes from an
infinite bath to an absorbing boundary. Previous results on this problem were
confined to independent Brownian particles arriving at an absorbing sphere. The
present paper extends these results to general diffusion processes, without any
symmetries and without resorting to explicit
expressions for solutions to the relevant equations. It is shown that for
general absorbing boundaries and force fields, the steady stream of arrivals is
Poissonian with rate equal to the total flux on the
absorbing boundary, as calculated from the continuum theory of diffusion with
transport. The considered arrival problem arises in the theory of Langevin simulations of ions in electrolytic solutions. In
a Langevin simulation ions enter and exit the
simulation region, and it is necessary to compute the probability laws for
their entrance times into the simulation. While the simulated ions inside the
small simulation region interact with each other and with the far field of the
surrounding bath and the applied voltage, the physical chemistry continuum
description of the surrounding bath implies independent diffusion in a mean
field. Under these conditions the result of this paper applies to the stream of
new ions that arrive from the continuum bath into the discrete simulation
region. The recirculation problem, of ions that have already visited and exited
the simulation region, as well as the integration of these results into a
simulation of interacting ions will be studied in separate papers.