Verification of Euler / Navier-Stokes Codes using the Method of Manufactured Solutions C. J. Roy,1,*,† C. C. Nelson,2 T. M. Smith,3 and C. C. Ober3 1Aerospace Engineering Department, Auburn University, AL 36849-5338, U.S.A. 2740 Fourth St., Arnold Engineering Development Center,§ Arnold AFB, TN 37389-6001, U.S.A. 3MS 0316, Sandia National Laboratories,‡ PO Box 5800, Albuquerque, NM 87185-0316, ...

'Center for Tropical Forest Science Arnold Arboretum Asia Program, Harvard University Herbaria, Harvard University, Cambridge, MA 02138, USA, Center for Tropical Forest Science, Smithsonian Tropical Research Institute, PO Box 0843-03092, Balboa, Panama, Republic of Panama, 3 Forest Research Institute Malaysia, Kepong 52109, Selangor, Malaysia and Center for Tropical Forest Science-Arnold Arbore...

We consider the problem of Arnold Diiusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diiusion takes place with fast (polynomial) speed, even though the \splitting determinant" is exponentially small.

We recall our approach through discretizations for path integrals and its general results for representations of probability densities. It is shown that the result of Arnold [P. Arnold, Phys. Rev. E 61, 6099 (2000)] is a particular case of our work.