Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

A laser scanning technique has been used to obtain the Josephson current distributions in two-dimensional Josephson tunnel junctions. For zero external magnetic field, current distributions of cross-type junctions using symmetric and asymmetric feed configurations are found to be qualitatively different from the published theoretical results. In addition the current distributions in various magnetic fields are also presented.

Symmetric vortex-antivortex and asymmetric vortex-vortex modes have been observed in long Josephson tunnel junctions. These two modes manifest themselves as two nearly identical resistive branches in the current-voltage characteristics. The voltage spacing between the symmetric vortex-antivortex and the asymmetric vortex-vortex modes is only about 3% of the voltage spacing between the first and second resistive branches. Except for a slight displacement in current these two modes almost completely overlap in voltage and current.