Perturbation approximation for higher modes in nearly regular two-dimensional cavities

Asymptotic Approximation of Discrete Breather Modes in Two-Dimensional Lattices

We outline the small amplitude asymptotic approximation for breathers for one-dimensional chains, and two-dimensional lattices with square, triangular/hexagonal, and honeycomb geometries. Two-dimensional lattices are complicated due to the resulting NLS-type equation being either elliptic or hyperbolic in nature. This gives rise to an additional constraint in addition to the usual condition on ...

Regular perturbation theory for two-electron atoms

Article history: Received 23 March 2011 Received in revised form 13 May 2011 Accepted 16 May 2011 Available online 25 May 2011 Communicated by P.R. Holland

Higher Order Modes in Third Harmonic Cavities at Flash

Transverse modes in the 3.9 GHz cavities, designed and fabricated by FNAL, are reported on. These modes have the potential to cause significant emittance dilution if they are not sufficiently suppressed. Recent probebased-experiments have indicated significant discrepancies between modes predicted in stand-alone 9cell cavities compared to those in 4-cavity modules. We employ the code HFSS [1] t...

Efficient Approximation Algorithms for Point-set Diameter in Higher Dimensions

We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Sparse grid methods for higher dimensional approximation