List of publications

Papers

  1. Wave propagation in a 3-D optical waveguide. (with Oleg Alexandrov) Math. Models Methods Appl. Sci. (M3AS),  14 (2004), no.6, 819-852.(pdf)

  2. Wave propagation in non rectilinear waveguides. Le Matematiche, Fascicolo II, Vol LX (2005), 445-450. (pdf)

  3. Non-rectilinear waveguides: analytical and numerical results based on the Green's function. Ph.D. Thesis (2006). (pdf)

  4. Analytical results for 2-D non-rectilinear waveguides based on the Green's function,  (with Rolando Magnanini), Math. Methods Appl. Sci., 31 (2008), no.13, pp. 1587-1606. (arXiv:0704.3847)

  5. A method of variation of boundaries for waveguide grating couplers, Applicable Analysis, 87 (2008), no.9, 1019-1040. (pdf)

  6. A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides, (with Rolando Magnanini), Math. Methods Appl. Sci., 32 (2009), no.10, pp. 1183-1206. (arXiv:0710.1950)

  7. Wave propagation in a 3-D optical waveguide II. Numerical results.  (with Oleg Alexandrov) More Progresses in Analysis, Proceedings of the 5th International ISAAC Congress, World Scientific (2009), 627-636.(pdf)

  8. A radiation condition for the 2-D Helmholtz equation in stratified media, Comm. Partial Differential Equations, 34 (2009), no.12, pp. 1592-1606. (arXiv:0909.1662)

  9. Spectral theory of a Neumann-Poincaré-type operator and analysis of cloaking due to anomalous localized resonance (with H. Ammari, H. Kang, H. Lee, G. Milton). Submitted. (arXiv:1109.0479)

  10. A viscosity equation for minimizers of a class of very degenerate elliptic functionals. Submited.(pdf)

    In preparation

  1. Symmetry of solutions of elliptic and parabolic equations with a level surface parallel to the boundary (with R. Magnanini, S. Sakaguchi).

  2. Wood's anomalies in periodic interface problems  (with H. Ammari, H. Kang, H. Lee).





Reports

  1. Surface Registration via Umbilics. (pdf) (with Thomas Grandine (Boeing), Jung-ha An, Viktoria Averina, Wondimagegnehu Geremew, Derek Hansen, Guo Luo, Todd Moeller). You can find more informations about this project at IMA's web page. (2004)