Variational Estimates of Internal Interface Perturbations and a New Variational Functional for Inhomogeneous Transport Problems

Variational perturbation theory is applied to internal interface perturbations in neutral-particle inhomogeneous transport problems. The leakage from a radioactive system is the quantity of interest. The Schwinger and Roussopolos variational functionals are used with volume- and surface-integral formulations of the integrals of perturbed quantities. In numerical one-dimensional spherical tests of source radius perturbations, the Roussopolos functional in the surface-integral formulation worked better when the source was large, and the Schwinger functional in the volume-integral formulation worked better when the source was small. A new variational functional is presented that formally allows a combination of the Schwinger and Roussopolos functionals; the contribution of each to the total estimate is adjusted with a parameter introduced in one of the trial functions. When the parameter is correctly chosen, the new functional is generally more accurate than either the Schwinger or Roussopolos functional alone. An analytic monodirectional slab transport problem is also considered.