Nonlinear wave dynamics research group
TalTech priority area
Research classification (Frascati)
Head of the research group
Research group member
Doctoral students
Keyword
theory of internal variables
nonlinear waves
solitons
nondestructive testing of materials
numerical experiments
Overview
The activities of the research group are focusedon wave propagation in complex media and corresponding applications. In the case of directproblems, the goal is to analyse how waves ofdifferent types propagate and interact in materials with known properties. In the case of inverseproblems, the aim is to determine the propertiesof materials, the presence of defects, residualstresses, etc. making use of quantities measuredfrom physical experiments.Main research directions: Theory of continua and internal variables.Developed mathematical models takeinto account nonlinear, dispersive andtemperature effects, and multiscale of amicrostructure. Solitons and solitary waves. Boussinesqtype (two-wave) models and KdV-type(one-wave) models, which describe wavesin microstructured solids and mechanicalwaves in biomembranes, are applied. Conditions for formation of solitonic solutionsare determined. Numerical analysis of nonlinear wavepropagation. Fourier transform and Haarwavelets related are elaborated in order toexamine time-space behaviour of complexwave-structures. Nondestructive testing of materials. Methods for determining of mechanical properties of nonhomogeneous materials and fordetection of defects in laminated objectsare developed.
Important results
Some results in 2021: In order to elucidate nonlinear phenomenaof sound generation in string instruments,oscillations of bow excited violin stringwere studied experimentally and corresponding nonlinear hysterical model forsimulating oscillations of violin stringswas worked out. Activities in the field of non-destructivetesting of materials (collaboration withPRG 737) have led to the development ofpractical applications. Activities in the field of non-destructivetesting of materials (collaboration withdepartment of Civil engineering and Architecture) have led to the development ofpractical applications.
Related projects
Related department
- Engelbrecht, J., Tamm, K., Peets, T. Modelling of complex signals in nerves. Cham : Springer, 2021. XIII, 186 p.
https://doi.org/10.1007/978-3-030-75039-8 - Berezovski, A. Heat conduction in microstructured solids under localised pulse loading // Continuum mechanics and thermodynamics (2021) vol. 33, 6, p. 2493-2507.
https://doi.org/10.1007/s00161-021-01032-0 - Ratas, M., Majak, J., Salupere, A. Solving nonlinear boundary value problems using the higher order Haar wavelet Method // Mathematics (2021) vol. 9, 21, art. 2809.
https://doi.org/10.3390/math9212809 - Majak, J., Shvartsman, B., Ratas, M., Bassir, D., Pohlak, M., Karjust, K., Eerme, M. Higher-order Haar wavelet method for vibration analysis of nanobeams // Materials today communications (2020) vol. 25, art. 101290, 6 p. : tab.
https://doi.org/10.1016/j.mtcomm.2020.101290 - Berezovski, A., Yildizdag, M.E., Scerrato, D. On the wave dispersion in microstructured solids // Continuum mechanics and thermodynamics (2020) vol. 32, 3, p. 569-588.
https://doi.org/10.1007/s00161-018-0683-1 - Ratas, M., Salupere, A., Majak, J. Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids // Mathematical modelling and analysis (2021) vol. 26, 1, p. 147−169.
https://doi.org/10.3846/mma.2021.12920 - Ratas, M., Salupere, A. Application of higher order Haar wavelet method for solving nonlinear evolution equations // Mathematical modelling and analysis (2020) vol. 25, 2, p. 271-288.
https://doi.org/10.3846/mma.2020.11112 - Engelbrecht, J., Tamm, K., Peets, T. On mechanisms of electromechanophysiological interactions between the components of signals in axons // Proceedings of the Estonian Academy of Sciences (2020) vol. 69, 2, p. 81–96 : ill.
https://doi.org/10.3176/proc.2020.2.03 - Engelbrecht, J., Tamm, K., Peets, T. Internal variables used for describing the signal propagation in axons // Continuum mechanics and thermodynamics (2020) vol. 32, 6, p. 1619-1627.
https://doi.org/10.1007/s00161-020-00868-2 - Engelbrecht, J., Tamm, K., Peets, T. Modelling of processes in nerve fibres at the interface of physiology and mathematics // Biomechanics and modeling in mechanobiology (2020) vol. 19, 6, p. 2491−2496.
https://doi.org/10.1007/s10237-020-01350-3 - Lints, M., Salupere, A., Dos Santos, S. Numerical simulation of ultrasonic time reversal on defects in carbon fibre reinforced polymer // Wave motion (2020) vol. 94, art. 102526, 10 p. : ill.
https://doi.org/10.1016/j.wavemoti.2020.102526 - Engelbrecht, J., Tamm, K., Peets, T. Continuum mechanics and signals in nerves // Proceedings of the Estonian Academy of Sciences (2021) vol. 70, 1, p. 3–18.
https://doi.org/10.3176/proc.2021.1.02 https://doi.org/wp-content/plugins/kirj/pub/proc-1-2021-3-18_20210112191450.pdf - Engelbrecht, J., Tamm, K., Peets, T. On the physical background of nerve pulse propagation : heat and energy // Journal of non-equilibrium thermodynamics (2021) vol. 46, 4, p. 343-353 : ill.
https://doi.org/10.1515/jnet-2021-0007 - Tamm, K., Peets, T., Engelbrecht, J. Mechanical waves in myelinated axons // Biomechanics and modeling in mechanobiology (2022) vol. 21, p. 1285-1297.
https://doi.org/10.1007/s10237-022-01591-4 - Berezovski, A. Causality in strain gradient elasticity: An internal variables approach // Mechanics research communications (2022) vol. 125, art. 103997.
https://doi.org/10.1016/j.mechrescom.2022.103997 - Berezovski, A. Internal variables as a tool for extending Navier-Stokes equations // Journal of non-equilibrium thermodynamics (2022) vol. 47, 3, p. 1-14.
https://doi.org/10.1515/jnet-2021-0089 - Mračko, M., Adámek, V., Berezovski, A., Kober, J., Kolman, R. Experimental, analytical, and numerical study of transient elastic waves from a localized source in an aluminium strip // Applied acoustics (2021) vol. 178, art. 107983.
https://doi.org/10.1016/j.apacoust.2021.107983 - Kartofelev, D., Goidyk, O., Herrmann, H. A case study on the spatial variability of strength in a SFRSCC slab and its correlation with fibre orientation // Proceedings of the Estonian Academy of Sciences (2020) 4, p. 298-310 : ill.
https://doi.org/10.3176/proc.2020.4.03 - Berezovski, A., Berezovski, M. Dynamics of discontinuities in elastic solids // Mathematics and mechanics of solids (2020) vol. 25, 7, p. 1416-1428.
https://doi.org/10.1177/1081286517718603 - Engelbrecht, J., Tamm, K., Peets, T. Physics shapes signals in nerves // The European Physical Journal Plus (2022) vol. 137, art. 696.
https://doi.org/10.1140/epjp/s13360-022-02883-5 - Adámek, V., Berezovski, A., Mračko, M., Kolman, R. A two-layer elastic strip under transverse impact loading : analytical solution, finite element, and finite volume simulations // Mathematics and computers in simulation (2021) vol. 189, p. 126-140.
https://doi.org/10.1016/j.matcom.2020.10.007 - Ratas, M. Application of the Adaptive Higher Order Haar Wavelet based methods for solving the sine-Gordon equation // AIP conference proceedings. New York : AIP, 2022. art. 380006. (AIP conference proceedings ; 2425, 1).
https://doi.org/10.1063/5.0081491 - Järv, J., Engelbrecht, J. Proceedings of the Estonian Academy of Sciences celebrates volume 70 // Proceedings of the Estonian Academy of Sciences (2021) vol. 70, 1, p. 1-2 : phot.
https://doi.org/10.3176/proc.2021.1.05 https://kirj.ee/wp-content/plugins/kirj/pub/proc-1-2021-1-2_20210218113638.pdf - Kartofelev, D., Arro, J.G., Välimäki, V. Insights into the string-barrier interaction dynamics based on high-speed camera measurements // SMC 2020 : Proceedings of the 17th Sound and Music Computing Conference, Torino, Italy, June 24th - 26th 2020. Torino : Sound and Music Computing Network, Xea sas/SMC Network, 2020. p. 169-176.
https://smc2020torino.it/adminupload/file/SMC2020Proceedings.pdf - Ratas, M., Chemori, A., Kruusmaa, M. PHA-based feedback control of a biomimetic AUV for diver following : design, simulations and real-time experiments // European Control Conference (ECC). : IEEE, 2022. p. 503-509.
https://doi.org/10.23919/ECC55457.2022.9838054 - Engelbrecht, J., Tamm, K., Peets, T. Signals in nerves from the philosophical viewpoint // Proceedings of the Estonian Academy of Sciences (2022) vol. 71, 4, p. 369-375 : ill.
https://doi.org/10.3176/proc.2022.4.07 - Berezovski, M., Berezovski, A. Discontinuity-driven mesh alignment for evolving discontinuities in elastic solids // Journal of computational physics (2020) vol. 416, art. 109542, 21 p.
https://doi.org/10.1016/j.jcp.2020.109542 - Engelbrecht, J., Šlaus, I. Academies of sciences in the contemporary world // Trames (2022) vol. 26, 2, p. 131-139.
https://doi.org/10.3176/tr.2022.2.01 - Ratas, M., Jena, S.K., Chakraverty, S. Application of Haar wavelet based methods for solving wave propagation problems // AIP conference proceedings. : AIP, 2020. (AIP conference proceedings ; 2293, 1).
https://doi.org/10.1063/5.0026696 - Vilipuu, M., Kartofelev, D., Kalda, J. Use of simplified bowed string model in physics education : a laboratory experiment // Proceedings of Meetings on Acoustics (2022) vol. 48, 1, art. 025001.
https://doi.org/10.1121/2.0001628 - Dos Santos, S., Masood, A., Lints, M., Salupere, A., Kozena, C., Kus, V. et al. Multiscale memristive properties of skin induced by memory effects of cyclic stress-relaxation loadings : data fusion from ground truth nonlinear acousto-mechanical testing // ICSV 2018: 25th International Congress on Sound and Vibration (ICSV25), Hiroshima, Japan, 8-12 July, 2018 : proceedings. Vol. 1. Red Hook : Curran Associates, 2018. p. 1965-1972 : ill.
http://toc.proceedings.com/40638webtoc.pdf https://www.researchgate.net/publication/326668548_MULTISCALE_MEMRISTIVE_PROPERTIES_OF_SKIN_INDUCED_BY_MEMORY_EFFECTS_OF_CYCLIC_STRESS-RELAXATION_LOADINGS_DATA_FUSION_FROM_GROUND_TRUTH_NONLINEAR_ACOUSTO-MECHANICAL_TESTING - Engelbrecht, J. Peets, T., Tamm, K. Soliton trains in dispersive media // Low temperature physics, Fizika nizkikh temperatur (2018) vol. 44, 7, p. 887-892.
https://doi.org/10.1063/1.5041436 - Berezovski, M., Berezovski, A. Numerical simulation of energy localization in dynamic materials // Advances in mechanics of microstructured media and structures. Cham : Springer, 2018. p. 75-83. (Advanced structured materials ; 87).
https://doi.org/10.1007/978-3-319-73694-5_5 - Salupere, A., Rätsep, M. On solitonic solutions for the hyperelastic rod equation // Wave motion (2019) vol. 91, 8 p.
https://doi.org/10.1016/j.wavemoti.2019.102404 - Kartofelev, D., Arro, J. G., Valimäki, V. Experimental verification of dispersive wave propagation on guitar strings // SMC 2019 : Proceedings of the 16th Sound & Music Computing Conference. Malaga : SMC, 2019. p. 324–331 : ill.
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85084386995&partnerID=40&md5=b18526954c2e08531266a8f19f44811e http://smc2019.uma.es/docs/SMC2019_Proceedings.pdf - Engelbrecht, J., Järv, J. Ten years of the renewed Proceedings of the Estonian Academy of Sciences // Proceedings of the Estonian Academy of Sciences (2018) vol. 67, 4, p. 303-304 : phot.
http://www.kirj.ee/public/proceedings_pdf/2018/issue_4/proc-2018-4-303-304.pdf https://www.ester.ee/record=b2355998*est https://artiklid.elnet.ee/record=b2868162*est - Dos Santos, S., Lints, M., Masood, A., Salupere, A. et al. Acousto-mechanical instrumentation of multiscale hysteretic memristive properties of the skin with nonlinear time reversal imaging // 2017 Cosmetic Measurements and Testing (COSMETIC 2017), Cergy-Pontoise, France, 6 - 7 June 2017. Red Hook : IEEE, 2017. p. 16-19 : ill.
http://dx.doi.org/10.1109/COMET.2017.8521466 - Berezovski, A. Internal variables associated with microstructures in solids // Mechanics research communications (2018) vol. 93, p. 30-34.
https://doi.org/10.1016/j.mechrescom.2017.07.011 - Engelbrecht, J., Salupere, A., Berezovski, A., Peets, T., Tamm, K. On nonlinear waves in media with complex properties // Generalized models and non-classical approaches in complex materials ; 1. Cham : Springer, 2018. p. 275-286. (Advanced structured materials ; 89).
https://doi.org/10.1007/978-3-319-72440-9_13 - Engelbrecht, J., Peets, T., Tamm, K. Solitons modelled by Boussinesq-type equations // Mechanics research communications (2018) vol. 93, p. 62-65.
https://doi.org/10.1016/j.mechrescom.2017.05.008 - Salupere, A., Ratas, M. On the application of 2D discrete spectral analysis in case of the KP equation // Mechanics research communications (2018) vol. 93, p. 141-147 : ill.
https://doi.org/10.1016/j.mechrescom.2017.08.010 - Peets, T., Tamm, K., Simson, P., Engelbrecht, J. On solutions of a Boussinesq-type equation with displacement-dependent nonlinearity: A soliton doublet to the memory of Alexander Samsonov // Wave motion (2019) Vol. 85, p. 10-17.
https://doi.org/10.1016/j.wavemoti.2018.11.001 - Berezovski, A., Kolman, R., Berezovski, M. et al. Full field computing for elastic pulse dispersion in inhomogeneous bars // Composite structures (2018) vol. 204, p. 388-394 : ill.
https://doi.org/10.1016/j.compstruct.2018.07.055 - Engelbrecht, J., Tamm, K., Peets, T. Criteria for modelling wave phenomena in complex systems : the case of signals in nerves // Proceedings of the Estonian Academy of Sciences (2019) vol. 68, 3, p. 276–283 : ill.
https://doi.org/10.3176/proc.2019.3.05 http://www.kirj.ee/public/proceedings_pdf/2019/issue_3/proc-2019-3-276-283.pdf - Berezovski, A. Internal variables representation of generalized heat equations // Continuum mechanics and thermodynamics (2019) vol. 31, 6, p. 1733–1741.
https://doi.org/10.1007/s00161-018-0729-4 - Tamm, K., Engelbrecht, J., Peets, T. Temperature changes accompanying signal propagation in axons // Journal of non-equilibrium thermodynamics (2019) vol. 44, 3, p. 277–284 : ill.
https://doi.org/10.1515/jnet-2019-0012 - Engelbrecht, J., Tamm, K., Peets, T. Modeling of complex signals in nerve fibers // Medical hypotheses (2018) vol. 120, p. 90-95 : ill.
https://doi.org/10.1016/j.mehy.2018.08.021 - Engelbrecht, J., Peets, T., Tamm, K. Electromechanical coupling of waves in nerve fibres // Biomechanics and modeling in mechanobiology (2018) vol. 17, 6, p. 1771–1783 : ill.
https://doi.org/10.1007/s10237-018-1055-2 - Engelbrecht, J., Peets, T., Tamm, K., Laasmaa, M., Vendelin, M. On the complexity of signal propagation in nerve fibres // Proceedings of the Estonian Academy of Sciences (2018) vol. 67, 1, p. 28-38 : ill.
https://doi.org/10.3176/proc.2017.4.28 http://www.ester.ee/record=b2355998*est https://artiklid.elnet.ee/record=b2835629*est - Ratas, M. Application of Haar wavelet method for solving nonlinear evolution equations // International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2018 : 13-18 September 2018, Rhodes, Greece. Melville, New York : AIP, 2019. art. 330004, p. 1–4. (AIP conference proceedings ; 2116, 1).
https://doi.org/10.1063/1.5114342 - Jena, S.K., Chakraverty, S., Ratas, M., Kirs, M. Application of HoHWM in the stability analysis of nonlocal Euler-Bernoulli beam // International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2019 : 23–28 September 2019 Rhodes, Greece. Melville, New York : AIP, 2020. art. 230003. (AIP conference proceedings ; 2293).
https://doi.org/10.1063/5.0026439 - Peets, T., Tamm, K., Engelbrecht, J. Comment on "Solitons in the Heimburg-Jackson model of sound propagation in lipid bilayers are enabled by dispersion of a stiff membrane" by M. Drab et al. // The European physical journal E (2023) vol. 46, 5, art. 34.
https://doi.org/10.1140/epje/s10189-023-00299-2 - Engelbrecht, Jüri; Tamm, Kert; Peets, Tanel Axons’ signals // Horizons in neuroscience research ; 49. New York : Nova Science Publishers, 2023. p. 33-73. (Nova Medicine and Health).
https://novapublishers.com/shop/horizons-in-neuroscience-research-volume-49/ - Peets, T., Tamm, K., Engelbrecht, J. On mathematical modeling of the propagation of a wave ensemble within an individual axon // Frontiers in cellular neuroscience (2023) vol. 17, art. 1222785.
https://doi.org/10.3389/fncel.2023.1222785