Numerical Equivalence Between SPH and Probabilistic Mass Transfer Methods for Lagrangian Simulation of Dispersion

Several Lagrangian methodologies have been proposed in recent years to simulate advection-dispersion of solutes in fluids as a mass exchange between numerical particles carrying the fluid. In this paper, we unify these methodologies, showing that mass transfer particle tracking (MTPT) algorithms can be framed within the context of smoothed particle hydrodynamics (SPH), provided the choice of a Gaussian smoothing kernel whose bandwidth depends on the dispersion and the time discretization. Numerical simulations are performed for a simple dispersion problem, and they are compared to an analytical solution. Based on the results, we advocate for the use of a kernel bandwidth of the size of the characteristic dispersion length $\ell=\sqrt{2D\Delta t}$, at least given a "dense enough" distribution of particles, for in this case the mass transfer operation is not just an approximation, but in fact the exact solution, of the solute's displacement by dispersion in a time step

Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations

We recalculate the amplitude for photon splitting in a strong magnetic field below the pair production threshold, using the worldline path integral variant of the Bern--Kosower formalism. Numerical comparison (using programs that we have made available for public access on the Internet) shows that the results of the recalculation are identical to the earlier calculations of Adler and later of Stoneham, and to the recent recalculation by Baier, Milstein, and Shaisultanov.Comment: Revtex, 9 pages, no figure