Existence theorems for trapped modes

Virial theorems for trapped cold atoms

Existence Theorems for Warfield Groups

Warfield studied p-local groups that are summands of simply presented groups, introducing invariants that, together with Ulm invariants, determine these groups up to isomorphism. In this paper, necessary and sufficient conditions are given for the existence of a Warfield group with prescribed Ulm and Warfield invariants. It is shown that every Warfield group is the direct sum of a simply presen...

Trapped Acoustic Modes for Adhesive Strength Determination

Trapped modes for periodic structures in waveguides

The Laplace operator is considered for waveguides perturbed by a periodic structure consisting of N congruent obstacles spanning the waveguide. Neumann boundary conditions are imposed on the periodic structure, and either Neumann or Dirichlet conditions on the guide walls. It is proven that there are at least N (resp. N−1) trapped modes in the Neumann case (resp. Dirichlet case) under fairly ge...

Trapped Modes in Tesla Cavities

In the TESLA linear collider scheme [1] the existence of trapped modes [2] within a TESLA cavity could be a severe problem to be overcome. Damping of trapped modes seems impossible due to their localization within the cavity, which prevents a coupling to the HOM dampers mounted to both ends of the beam pipes. As a consequence the energy of a trapped mode can achieve considerable values after se...