## Research Groups

Head of the group: Senior Lecturer ALAR LEIBAK, alar.leibak@taltech.ee

Members of the group: Peeter Puusemp, Piret Puusemp

Doctoral student Märt Umbleja

**Topics and Competences**

Keywords: group theory, endomorphism semigroups, applications of algebra

The research is focused on the study of the connections between groups and their endomorphism semigroups, and the applications of group theory.

The aim is to describe some well-known classes of finite groups by their endomorphism semigroups and to decide whether a group is determined by its endomorphism semigroup in the class of all groups or not. We started to describe all *small groups* that are determined by their endomorphism semigroups. Further, if a group G is not determined by its endomorphism semigroup, then to provide the complete list of nonisomorphic groups having the endomorhism semigroup isomorphic to that of G. As the computational group theory and the software GAP ( http://www.gap-system.org) are becoming more popular among people working in applied algebra, we started to develop algorithms what are able to decide automatically whether or not a given finite group is determined by its endomorphism semigroup.

Main results:

- It was proved that there are only five semidirect products of C
_{2}^{n}x C_{2}^{n}by C_{6}for each n>3, if C_{6}is embedded into the automorphism group (joint work with Tatjana Tamberg at Tallinn University). - The distribution of the multi-party Diffie-Hellman common secret keys were studied if the platform group is an arbitrary finite cyclic group. As a result, it was proved that the probability function is multiplicative.

Head of the group: Professor JAAN JANNO, jaan.janno@taltech.ee

Members of the group: Lassi Päivärinta, Margus Pihlak, Kari Kasemets, Nataliia Kinash

Doctoral students: Sadia Sadique

**Topics and Competences**

Keywords: inverse problems, fractional diffusion and wave motion, Bayesian methods, nonparametric statistics

The research is focused on analysis of inverse problems as well as on development of stochastic methods for inverse problems and other applications. The main directions of research are:

**Inverse problems for equations containing fractional derivatives.**Inverse problems for linear and nonlinear fractional differential equations are studied. The unknowns to be determined are coefficients, source terms and kernels of generalized fractional time derivatives. Such problems occur in modelling of diffusion and mechanical processes in porous, fractal and biological media. The research is focused on both theoretical aspects (existence, uniqueness and stability of solutions) and elaboration of numerical methods.**Stochastic methods in inverse problems.**Inverse problems for fractional Brownian motion (FBM) and Bayesian inverse problems are considered. The particular problems are the reconstruction of the Hurst parameter of FBM and construction of prior distributions with stable processes for Bayesian inverse problems that preserve edges in order to better detect anomalies. Applications are manifold starting from medical imaging and atmospheric remote sensing and ending with mathematics of finance.**Elaboration of nonparametric statistical methods***.*The theory of nonparametric statistical methods is developed and these methods are applied in environmental and building engineering.

Results in 2019: theoretical analysis of an inverse problem to determine a time- and space-dependent source in a generalized fractional diffusion equation in case observations are given in a neighborhood of a final time.

Imagine all atoms in your body, food, all materials around you telling: “Hi, this is me, I am here! Those over there are my neighbors. Next millisecond I shall move to that position”. This is in principle what Nuclear Magnetic Resonance spectroscopy is all about. NMR can identify all molecules, understand all structures, predict their properties and figure out how to make new and better ones. However, atoms, actually nuclear spins, sing in a huge choir and at a very feeble voice. Our research group is dedicated to separate those voices and make them audible. A basic technology used is Magic Angle Spinning, which rotates the structures of interest at a special, 54.7^{0 }angle to the magnetic field. We have achieved spinning frequencies over 200,000 turns every second, which allows e.g. to understand the whisper of ubiquitous hydrogen atoms. As a part of the global research community, we are refining the MAS technology, developing the hardware and promoting applications in diverse areas of current interest: biomedicine, wood chemistry and energy storage materials to name few.

Head of the group: Senior Research Scientist GERT TAMBERG, gert.tamberg@taltech.ee

Members of the group, PhD students Olga Graf, Olga Meronen

**Topics and Competences**

Keywords: sampling operators, approximation theory, signal processing

The main directions of research are as follows:

- Studying the generalized Shannon sampling operators that mean the representations of functions in terms of series, where the expansion coefficients are its samples and expansion functions are translates of certain kernel function. In the case of Kantorovich-type sampling operators we take, instead of point estimates, some local averages as Fejer-type singular integrals.
- Studying applications of the generalized sampling operators in Signal Processing, especially in imaging applications, where the generalized sampling operators are a natural tool for image resampling. We also study applications in HDR imaging. We study the applications of sampling operators in time series analysis and linear prediction.

Main results:

- We clarified approximation properties of sampling operators with unnecessary even kernel, especially for sampling operators with strongly asymmetric kernels.
- We applied image-resampling algorithms, based on sampling operators in super resolution algorithms.
- We applied sampling operators in time series analysis and linear prediction, especially for energy prediction. A hardware realization was proposed.

Head of the group: Professor ANDRUS SALUPERE, andrus.salupere@taltech.ee

Members of the group: Arkadi Berezovski, Tanel Peets, Kert Tamm, Dmitri Kartofelev, Martin Lints, Jüri Engelbrecht, Mart Ratas

**Topics and Competences**

Keywords: continuum mechanics, theory of internal variables, nondestructive testing of materials, nonlinear waves, solitons, numerical experiments

The activities of the research group are focused on wave propagation in complex media and corresponding applications. On the one hand, this includes direct problems, where the goal is to analyse how waves of different types propagate and interact in materials, the properties of which are known. On the other hand, the aim is to solve inverse problems, in order to determine the properties of materials, existence of defects, residual stresses, etc. by making use of quantities measured from physical experiments.

Main research directions

*Theory of continua and internal variables.*The internal structure of materials is described using internal fields. The corresponding mathematical models of wave motion in microstructured solids take into account nonlinear, dispersive and temperature effects and possible multiscale of a microstructure.*Solitons and solitary waves.*Boussinesq-type (two-wave) models and KdV-type (one-wave) models, which describe waves in microstructured solids and mechanical waves in biomembranes, are applied. Conditions for formation of solitonic solutions are determined.*Discrete spectral analysis.*Fourier spectrum related spectral characteristics are applied in order to examine time-space behaviour of complex wave-structures.*Nondestructive testing of materials.*Nonhomogeneous materials (incl. laminated materials) are under consideration. Methods for determining of mechanical properties of materials and for detection of defects in laminated objects are developed.

Some recent results

- An original signal processing method called delayed Time Reversal-Nonlinear Elastic Wave Spectroscopy (delayed TR-NEWS) is under development.
- A coupled model is derived for describing the propagation of mechanical wave that accompanies the nerve pulse during its propagation along the nerve axon. Numerical experiments demonstrate that soliton-like waves can be formed from arbitrary inputs.
- In acoustics of musical instruments a theoretical model has been developed for describing the interaction between the string and the obstacle. The model is tested experimentally for string instruments.
- Mathematical models are formulated in order to simulate heat production and corresponding temperature changes, which accompany the propagation of an action potential.

Head of the group: Senior Research Scientist HEIKO HERRMANN, hh@cens.ioc.ee

Members of the group: Andres Braunbrück, Dmitri Kartofelev

Doctoral student: Oksana Goidyk

**Topics and Competences**

Keywords: mechanics of materials, continuum mechanics, fiber concrete, fiber orientations, computational rheology, image analysis, 3D visualization

The competences of the group have a broad range, from constitutive theory over numerical computer simulations and image analysis to virtual reality visualization of scientific data. The main research topic is concerned with the mechanical properties of composites containing short fibres. The core application is steel fibre reinforced concrete, a construction material, the use of which is gaining momentum in the building industry. The mechanical properties largely depend on the orientation of short fibres, which in turn are influenced by the production process of the structural parts made of fibre concrete. In particular, the flow of the fresh concrete mass, which is mixed with the fibres, determines the fibre orientations. Analysis of fibre orientations in experiment samples is done by x-ray computed tomography, fibre orientations are then extracted from the tomography. The group has developed its own software for this purpose. The production process of concrete parts, in particular the casting, is simulated using computational fluid dynamics (CFD) coupled to an orientation equation. Further, simulations of bending tests and split tests are performed with particle based discrete element simulations. On the theoretical side, the group has developed constitutive models for the influence of the fibre orientations distribution on the mechanical and thermal properties of fibre concrete.

This involves the research on stereoscopic semi-immersive 3D visualization (virtual reality), which is conducted on the self-developed „Kyb3“ system. The main task of the system is the visualization of the computed tomography of fibre concrete and CFD simulations. It is used to visually inspect measurement and simulation results.

Head of the group: Senior Research Scientist MARKO VENDELIN, marko.vendelin@taltech.ee

Members of the group: Rikke Birkedal, Mari Kalda-Kroon, Martin Laasmaa

Doctoral student: Jelena Branovets, Romain Bernasconi

**Topics and Competences**

Keywords: heart; biophysics; bioenergetics; electrophysiology; biomechanics; intracellular diffusion; fluorescence microscopy; fluorescence correlation spectroscopy

The Laboratory of Systems Biology was founded in 2007 with the help of the funding from Wellcome Trust. We use interdisciplinary approaches to tackle questions in cardiac physiology. For that, we have formed a team of researchers with backgrounds in biophysics, biology, and applied mathematics/physics. As a result, we are able to approach scientific questions on different scales, from organ to molecular level, using combinations of different experimental and theoretical techniques by focusing on quantitative analysis of the data.

We study diffusion in cardiomyocytes by tracking the movement of fluorescent molecules using extended raster image correlation spectroscopy. Our results suggest that diffusion barriers are arranged in a 3D lattice with relatively small openings. Based on the analysis of autofluorescence response, we demonstrated that mitochondrial outer membrane and cytosolic diffusion barriers reduce the movement of molecules to a similar extent. We study effects of creatine deficiency to establish the role of creatine kinase shuttle in the heart.

We are studying excitation-contraction coupling of the heart by focusing on interaction between the processes. Mechanical contraction is initiated through entry of calcium ions into the cell. We developed a method to quantify the Ca^{2+} influx pathways. The novelty of our method lies in the mathematical analysis of measured transsarcolemmal Ca^{2+} currents and their impact on the corresponding Ca ^{2+} transient during gradual inhibition of the currents in action potential clamp. The developed method resolves the major problem on how to separate highly interconnected fluxes in AP clamp and allows studying of Ca^{2+} fluxes in cardiomyocytes under conditions close to *in vivo*.

We have been active in the development of new techniques and distribute them as open-source tools: deconvolution software for confocal imaging, symbolic flux analysis for genome-scale metabolic networks, and real-time sarcomere length estimation techniques. This development work has raised interest in companies with an outreach of incorporating our algorithms and software into their products.

Head of the group: Professor JAAN KALDA, jaan.kalda@taltech.ee

Members of the group: Raavo Josepson, Mihhail Klopov, Mihkel Kree, Tanel Mullari, Vladislav-Veniamin Pustõnski

Postdoctoral researcher: Jesus Alva Samos

Doctoral students: Inderek Mandre, Siim Ainsaar, Mihkel Heidelberg, Madis Ollikainen, Stephanie Rendon De La Torre, Iram Tufail, Eero Uustalu, Marek Vilipuu

**Topics and Competences**

Keywords: turbulence, photovoltaic materials, econphysics, complex systems, tools for physics education

The rapidly developing solar cell technology has brought to the forefront the problem about **the properties** **of inexpensive and efficient photovoltaic materials**. One of our research topics is calculation of the basic physical parameters of new photovoltaic materials (hybrid-perovskite and CZTS) using quantum chemical and density functional theory methods. For material technology applications, it is important to understand the **localized oscillations in solids** and the physical mechanisms of LLM (Linear Localized Modes); we have determined the conditions of excitation of ILM (Intrinsic Localized Modes) in various three-dimensional crystals and compared theory with an experiment.

**Orbital modelling and planning for satellites**. Within the nanosatellite project ”CubeSat“, we have developed a solar energy balance model, and predicted the positions of its communication windows.**Theoretical analysis and modelling of turbulent mixing**. Our research tools include Fokker-Planck equations for Lagrange stretching statistics, statistical Lagrange dynamics invariants, stochastic matrix products, statistical topography of passive fields, the stochastic baker’s map for reducing dimensionality of the problems. In collaboration with the Wave Dynamics Laboratory, we have modelled litter patchiness in marine environment as a result of coupling between the water flow and wind drag. In cooperation with University of Marseille, we have studied mixing in a porous environment, see Phys. Rev. Fluid (2017) 2, 104502 (Altmetrix score 15).**Econophysics research**. We have studied scale-free properties of economic networks based on the database of wire transfers of Swedbank – these appear to be multifractal networks, see Eur. Phys. J. B (2017) 90: 234 (Altmetrix score 5).

**Development physics study materials. ** It has mainly focused on methods for solving creative problems, and popularizing physics education. The materials available at __https://www.ioc.ee/~kalda/ipho/__ have won great international recognition, with an average download of about 1,000 files per day. TFU initiated the European Physics Olympiad. 170 participants from 35 countries are expected to attend the 4th Olympiad in June 2020 in Romania; see also European Journal of Physics, 39, 064002 (2018) .

Head of the group: Professor TARMO SOOMERE, tarmo.soomere@taltech.ee

Members: Nicole Delpeche-Ellmann, Andrea Giudici, Nadezhda Kudryavtseva, Kevin Ellis Parnell, Katri Pindsoo, Andrus Räämet, Bert Viikmäe, Maris Eelsalu, Rain Männikus

Doctoral students: Fatemeh Najafzadeh, Margus Rätsep

Visiting PhD students: Kuanysh Kussembayeva (al-Farabi Kazakh National Univ.), Aigerim Sakhayeva (al-Farabi Kazakh National Univ.), Ilona Šakurova (Klaipeda Univ.)

**Topics and Competences**

Keywords: wave dynamics, coastal engineering, wave climatology, coastal management, remote sensing

The laboratory (wavelab.ioc.ee) was formed on 01.01.2009 to promote and provide a structure for research in water waves and coastal engineering. The laboratory was a part of the Centre of Excellence in Non-linear Studies in 2009–2016 and now it is one of the core labs of the Department of Cybernetics.

The team focuses on complex and nonlinear phenomena in wave dynamics and coastal engineering, and the applications of mathematical methods in wave studies. The scope of the research involves long wave theory and applications (with emphasize on fast-ferry waves, shallow-water solitons, set-up and run-up phenomena, tsunami research, etc.), surface wave modelling, wave climate studies, and wave-driven phenomena in coastal engineering, with application to integrated coastal zone management.

Rapidly emerging foci are the use of Lagrangian transport of substances in marine environment, adequate description of wave and water level extremes, and preventive methods for mitigation of marine-induced hazards, and the use of various remote sensing methods for studies of both fundamental questions (e.g. filtering techniques of various signals) and applied problems such as spatio-temporal variations in the properties of waves in small inland seas.

The performed research has established several unexpected properties of internal wave fields in semi-enclosed seas such as the Baltic Sea, the Mediterranean Sea and the Sea of Okhotsk and made it possible to quantify changes in the main properties of surface waves in the Baltic Sea. Studies of the impact of ship wakes in the Venice Lagoon ( Zaggia et al. 2017 *PLoS ONE* ) caused massive reaction in Venice.