Scattered acoustic waves are used in seismic tomography and nondestructive testing (NDT) of solids and materials. Many materials and media have attenuating or other complex properties that disfigure wave profiles (e.g. soil, viscoelastic materials, disordered materials). Wave processes in such media are described by equations involving nonlocal terms in time and/or in space. Nonlocal terms may be usual fractional derivatives or their generalizations (e.g. distributed fractional derivatives, tempered fractional derivatives). Generalized fractional derivatives include more degrees of freedom, therefore they enable more exact modelling of wave dynamics. Problems to determine inhomogeneities of nonlocal media by means of boundary measurements of scattered waves are scarcely studied. Results are available in cases the equations contain non-local lower terms or usual fractional derivatives in principal terms. The aim of the PhD project is to study inverse problems to determine inhomogeneities of media whose motion is governed by wave equations involving generalized fractional derivatives in principal terms. The investigation will contain both theoretical study (existence, uniqueness and stability of solutions) and development of effective numerical solvers. However, depending on the background and/or preferences of the student, the main focus of the research can be either theory or numerics.
Responsibilities and tasks: investigation of inverse problems, collaboration with other scientists of a research group, publishing results of the research in scientific journals, presenting the results in scientific conferences and seminars, participation in other working activities of the group (e.g., organization of conferences), writing and defending PhD thesis within 4+1 years.
Qualifications: master’s degree in mathematics, physics or a related field.
The applicant should fulfill the following requirements:
good knowledge about partial differential equations and numerical methods
The nominal time of the study is 4 years and it will begin in February 2021.
The applications must be submitted on the website https://taltech.glowbase.com
between 16.11.2020 00.00 and 16.12.2020 23.59 (Europe/Zürich time)