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Analysis of effects of microstructure and phase transition on wave propagation, more attention to meso- and nano-mechanics with dispersive effects, solitons, their interaction and behaviour in force fields.
Intention to elaborate a more defined Physiome project with Estonian (Tartu University and National Institute of Chemical Physics and Biophysics) and international partners for in silico modelling of cell energetics. More applications of fractal theory and lattice modelling in interdisciplinary areas. Attention to practical applications for diagnostic purposes.
Development of nonlinear theory of integrated photoelasticity and its algorithms for solving inverse problem without restricting assumptions. Recent progress is based on the earlier fundamental results of the same group during three decades.
The group will concentrate on general wave theory, with applications in wind wave forecast and wave generation anomalies in the Baltic Sea area. Problems related to topographic wave anomalies as well as specific properties of wave evolution in an strongly stratified medium and on sheared currents will be studied in detail. An extensive field campaign, combined with numerical wave simulation, is planned in order to clarify details of soliton-like ship wash created by high speed craft ships in Gulf of Tallinn.
Construction of an exterior calculus with d3 = 0 on braided line, quantum plane and free associative algebra with n generators. The generalized cohomologies are studied. The set of first order differentials is extended by adding to it the higher order differentials of local co-ordinates of a manifold and this extension allows to construct a generalized exterior calculus. The tensorial behaviour of the higher order differentials is restored with the help of a connection and its higher order analogies.
Developing of a new method for studying non-linear processes: dynamical system considered as the flow of a vector field in the space-time acts on tensor fields; this is useful to describe by means of a Lie derivative. An entire classification of 2-semiparallel surfaces in general case will be given.
Application of nonlinear methods (fractal analysis, order statistics based methods) to the detection of various diseases and abnormal patient states from physiological signal like ECG and EEG. The main interest is focused on detecting states leading to sudden cardiac death from the ECG signals as well as ischaemic and hypoxic states of the brain from EEG signals. The methods are compared to traditional linear methods and the ability of the methods to detect the abnormal states is evaluated.