Drums

First few modes of the negative laplacian on a maple leaf

  • state 1
  • Fundamental Mode
  • state 5
  • First excited state
  • state 5     
  • Second excited state
  • state 5
  • Third excited state
  • state 5
  • Fourth excited state
  • state 5          
  • Fifth excited state
  • state 5
  • Sixth excited state
Research

My research is mainly focused on problems of mathematical and computational physics; an example of this class of problems is the calculation of the normal modes of an arbitrary domain in two dimensions. This calculation may be done analytically within perturbation theory if the domain is a perturbation of a reference domain (rectangle, circle), or it may carried out numerically, in the case of a general domain.

The images on the left display the first few modes of a domain having the shape of a maple leaf; the modes obey Dirichlet boundary conditions at the border. The internal thin red lines are nodal lines, i.e. lines where the eigenfunction vanishes; the black (solid and dashed) lines are level curves.

You can find a list of my publications at the ArXiv

Here you find a short CV

Here is my page at google scholar

Selected publications
  • P. Amore, "Exact sum rules for inhomogeneous drums", accepted Annals of Physics (2013)
  • P. Amore, "Exact sum rules for inhomogeneous strings", accepted Annals of Physics (2013) 
  • P. Amore, "A perturbative approach to the calculation of  the spectral zeta functions of strings, drums and quantum billiards", Journal of Mathematical Physics 53, 123519 (2012);
  • P. Amore and F.M. Fernandez, "Bound states for the quantum dipole moment in two dimensions",  Journal of Physics B 45, 235004 (2012);
  • P. Amore, M. Rodriguez and C.Terrero, "Bound states in open coupled asymmetrical waveguides and quantum wires", JPA 45, 105303 (2012)
  • C. Alvarado and P. Amore, "Spectroscopy of annular drums and quantum rings...", Journal of Mathematical Physics 52, 063516 (2011)
  • P. Amore, "The string of variable density: further results", Annals of Physics 326, 2315-2355 (2011)
  • P. Amore, "The string of variable density: perturbative and nonperturbative results",  Annals of Physics 325, 2679-2696 (2010)
  • P. Amore, "Can one hear the density of a drum? ...", Europhysics Letters 92 (2010)
  • P. Amore et al., "Collocation method for fractional quantum mechanics", Journal of Mathematical Physics 51, 122101 (2010)
  • P. Amore, "Spectroscopy of drums and quantum billiards: perturbative and non perturbative results",  Journal of Mathematical Physics 51, 052105 (2010)