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Faculty of Social Sciences

PhD defense by Lasse Søgaard Ledet

PhD defense by Lasse Søgaard Ledet

A novel method for solving problems in linear dynamics using bi-orthogonality relations


11.10.2019 kl. 09.00 - 13.00



Dynamic systems appear everywhere in nature and may be everything from chaotic to almost static (quasi-static) in behaviour. They appear in almost all areas of science ranging from physics and engineering science to sociology and psychology. More specifically, this thesis is concerned with analysis of time-invariant linear dynamic systems within engineering and mathematical physics.  

A novel approach for analysing the behaviour of such linear dynamic systems has been developed. The method is based on specially derived bi-orthogonality relations which originate from the classical reciprocity relation and are formulated for associated eigenfunctions. Application of the bi-orthogonality relation for free waves (eigenfunctions) provides, for a broad class of problems in e.g. waveguide theory, convenient analytical closed-form solutions. These explicit solutions offer full transparency when analysing e.g. the energy transmission properties and thus permit an enhanced insight into the physical phenomena occurring in waveguides. Likewise, the method offers insight into the formation of standing waves when extended to so-called 'finite' waveguides, that is, waveguides subjected to additional boundary conditions. The novel approach of bi-orthogonality developed here is found to be an efficient tool for solving a wide range of problems in physics such as in, for example, mechanics, acoustics, electromagnetics, seismics, optics and even quantum mechanics as well as any coupled problem of the latter.

Assessment CommitteE     

  • Associate Professor Thomas Møller Søndergaard (chairman) - Aalborg University, Denmark
  • Professor Lars Vabbersgaard Andersen, Department of Engineering - Aarhus University, Denmark
  • Professor Goran Pavic, National Institut of Science (INSA) - Lyon, France


  • Professor Sergey Sorokin - Aalborg University, Denmark

Co-supervisor (Grundfos)

  • Brian Lundsted Poulsen, Grundfos Holding A/S
  • Jan Balle Larsen, Grundfos Holding A/S
  • Nicholas Pedersen, Grundfos Holding A/S

The PhD defense will be hosted by Moderator Associate professor Thomas Møller Søndergaard. The lecture constitutes a 45 minutes presentation by Lasse Søgaard Ledet followed by a short break and a discussion session with questions from the opponents and the auditorium.

After the defense, at approx. 13.00 hours, the Department of Materials and Production will welcome all to a reception in Fibigerstræde 14, Common Room.


Department of Materials and Production


Room 1.108, Fibigerstræde 16, 9220 Aalborg Denmark