Mathematical methods in science and modern technology. Physical processes governed by partial differential equations. Wave propagation and vibration theory. Partition and equipartion of energy connected to wave phenomena in continnum mechanics. Asymptotic and finite time energy behaviour for the coupled wave fields of elasticity, thermoelasticity, visioelasticity and magnetoelasticity.

Scattering of acoustic, electromagnetic, elastic, thermoelastic and magnetoelastic waves by impenetrable, as well as penetrable, objects. Low frequency theory of scattering processes. Scattering by simple objects. Ellipsoidal geometry in scattering theory.Potential theory in the presence of ellipsoidal bodies.Inverse scattering theory connected to shape reconstruction and determination of physical parameters within inaccessible regions.

Ultrasound techniques and tomography in medical imaging. Medical and biological applications of wave propagation and scattering methods. Medical technology connected to diagnostics. Mathematical models for the physiological process of human color vision based on fuzzy set theory,probabilistic metric spaces and non standard mathematics. Belief networks in medical decision making.

Mathematical models for the determination of the oxygen pressure within relatively large tumors.
Stokes flow around non spherical objects. Theory of semiseparable solutions for the stokes stream functions in spheroidal geometry. Representation theory in low Reynolds number hydrodynamics.

Underwater acoustics. Inverse problems for scattering of sound waves in the sea environment. Velocity profile inversion and sea bottom reconstruction. Submerged bodies indentification.

• "Tackling magnetoencephalography with particle swarm optimization"
  Parsopoulos, K.E., Kariotou, F., Dassios, G., Vrahatis, M.N. (2009)
  International Journal of Bio-Inspired Computation 1 (1-2) , pp. 32-49

  "The mass accommodation coefficient of ammonium nitrate aerosol"
  Dassios, K.G., Pandis, S.N. (1999)
  Atmospheric Environment 33 (18) , pp. 2993-3003

  "Magnetoencephalography in ellipsoidal geometry"
  Dassios, G., Kariotou, F. (2003)
  Journal of Mathematical Physics 44 (1) , pp. 220-241

  "Point source excitation in direct and inverse scattering: The soft and the hard small sphere"
  Dassios, G., Kamvyssas, G. (1995)
  IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) 55 (1) , pp. 67-84

  "Generalized eigenfunctions and complete semiseparable solutions for Stokes flow in spheroidal coordinates"
  Dassios, G., Hadjinicolaou, M., Peyatakes, A.C. (1994)
  Quarterly of Applied Mathematics 52 (1) , pp. 157-191

  "Stokes flow in spheroidal particle-in-cell models with rappel and kuwabara boundary conditions"
  Dassios, G., Hadjinicolaou, M., Coutelieris, F.A., Payatakes, A.C. (1995)
  International Journal of Engineering Science 33 (10) , pp. 1465-1490

  "On the non-uniqueness of the inverse MEG problem"
  Dassios, G., Fokas, A.S., Kariotou, F. (2005)
  Inverse Problems 21 (2) , pp. L1-L5