About us

Nonlinear acoustics is a branch of physics dealing with study of properties and utilization of high-amplitude acoustic fields. Amplitudes of these fields attain such values that the methods and procedures well-known from the linear acoustic cannot be used anymore for their description. Many nonlinear effects are connected with these fields. These effects offer great application potential (radiation pressure, acoustic streaming, cavitation, generation of heat, etc.) and on the other hand, they prevent effective increase of amplitude of these fields.

Utilization of these fields enables design of technically new appliances, such as acoustics compressors and pumps, thermoacoustic engines and coolers, etc. All these appliances are distinguished by intrinsic simplicity, reliability and they are also considerate of environment. Nonlinear interactions of the high-amplitude acoustic fields can be also utilized for diagnostic purposes (imaging methods in medicine, nonlinear ultrasonic defectoscopy).

Nonlinear mechanisms accompanying the high-amplitude acoustic fields must be well understood in order that they can be generated and utilized. For these reasons, it is necessary to look for suitable model equations (here, the well-known linear wave equation cannot be used) and their solutions. By virtue of the fact that these models are represented by nonlinear partial differential equations and general exact analytical solutions are not known for them yet, it is necessary to use approximate analytical methods or numerical methods for their study.

The nonlinear-acoustics group of Department of Physics of CTU-FEE is at present concerned with these areas of research:

  • Model equations of nonlinear acoustics
  • Approximate analytical solutions of nonlinear-acoustics model equations
  • Qualitative analysis of nonlinear wave processes in various materials
  • Numerical methods for model equations of nonlinear acoustics
  • Numerical simulations of multidimensional acoustic fields by using of the high-performance computing methods
  • Methods for suppression of nonlinear effects in acoustic resonators
  • Parametric acoustic transmitters

Research of the group was and at present is supported by grant projects (IG ČVUT, GA ČR).

Selected publications

[1] Bednarik, M., Cervenka, M.: The exact solution of the Schrodinger equation with a polynomially spatially varying mass, Journal of Mathematical Physics 58, 072103, 2017. (LINK)
[2] Cervenka, M., Bednarik, M.: Effect of inhomogeneous temperature fields on acoustic streaming structures in resonators, The Journal of the Acoustical Society of America 141(6), 4418-4426, 2017. (LINK, PDF)
[3] Bednarik, M., Cervenka, M.: Description of waves in inhomogeneous domains using Heun’s equation, Waves in Random and Complex Media 2017. (LINK)
[4] Cervenka, M., Bednarik, M.: Variety of acoustic streaming in 2D resonant channels, Wave Motion 66, 21-30, 2016. (LINK)
[5] Bednarik, M., Cervenka, M., Lotton, P., Penelet, G.: Behavior of plane waves propagating through a temperature-inhomogeneous region, Journal of Sound and Vibration 362, 292-304, 2016. (LINK)
[6] Cervenka, M., Bednarik, M.: Calculation of an axial temperature distribution using the reflection coefficient of an acoustic wave, The Journal of the Acoustical Society of America 138(4), EL359-EL364, 2015. (LINK, PDF)
[7] Cervenka, M., Bednarik, M.: Acoustic particle displacement resonator, Applied Acoustics 99, 155-160, 2015. (LINK)
[8] Bednarik, M., Cervenka, M.: Finite amplitude standing waves in resonators terminated by a general impedance, The Journal of the Acoustical Society of America 137(3), 1257-1264, 2015. (LINK, PDF)
[9] Cervenka, M., Bednarik, M.: On the structure of multi-Gaussian beam expansion coefficients, Acta Acustica United with Acustica 101(1), 15-23, 2015. (LINK)
[10] Cervenka, M., Soltes, M., Bednarik, M.: Optimal shaping of acoustic resonators for the generation of high-amplitude standing waves, The Journal of the Acoustical Society of America 136(3), 1003-1012, 2014. (LINK, PDF)
[11] Balek, R., Cervenka, M., Pekarek, S.: Acoustic field effects on a negative corona discharge, Plasma Sources Science and Technology 23(3), 1-9, 2014. (LINK)
[12] Bednarik, M., Cervenka, M.: Equations for description of nonlinear standing waves in constant-cross-sectioned resonators, The Journal of the Acoustical Society of America 135(3), EL134-EL139, 2014. (LINK, PDF)
[13] Cervenka, M., Bednarik, M.: Non-paraxial model for a parametric acoustic array, The Journal of the Acoustical Society of America 134(2), 933-938, 2013. (LINK, PDF)
[14] Cervenka, M., Bednarik, M.: On the Optimization of an Acoustic Resonator Shape with Respect to Acoustic Pressure Amplitude, Acta Acustica United with Acustica 99(2), 183-192, 2013. (LINK)
[15] Kindl, J., Kalinova, B., Cervenka, M., Jilek, M., Valterova, I.: Male moth songs tempt females to accept mating: The role of acoustic and pheromonal communication in the reproductive behaviour of Aphomia sociella, Plos One 6(10), 2011. (LINK, PDF)
[16] Wohl, P., Bednarik, M., Wohl, P., Cervenka, M., Spicak, J.: Comparison of various strategies for colorectal cancer screening tests, European Journal of Gastroenterology and Hepatology 23(12), 1157-1164, 2011. (LINK)
[17] Bednarik, M., Cervenka, M.: Propagation of nonlinear acoustic plane waves in an elastic gas-filled tube, The Journal of the Acoustical Society of America 126(4), 1681-1689, 2009. (LINK, PDF)
[18] Balek, R., Pekarek, S., Cervenka, M.: Ultrasonic Field Effects on Corona Discharge in Air, IEEE Transactions on Plasma Science 36(4), 920-921, 2008. (LINK)
[19] Bednarik, M., Cervenka, M.: Nonlinear interactions in elastic resonators, Ultrasonics 44(Suppl. 1), 783-785, 2006. (LINK)
[20] Cervenka, M., Bednarik, M.: Nonlinear standing waves in 2-D acoustic resonators, Ultrasonics 44(Suppl. 1), 773-776, 2006. (LINK)
[21] Cervenka, M., Bednarik, M.: Description of Finite-amplitude Standing Acoustic Waves Using Convection-Diffusion Equations, Czechoslovak Journal of Physics 55(6), 673-680, 2005. (LINK)
[22] Bednarik, M., Konicek, P.: Asymptotic solution of the ihomogeneous Burgers equation, The Journal of the Acoustical Society of America 115(1), 91-98, 2004. (LINK, PDF)
[23] Bednarik, M., Konicek, P.: Description of quasi-plane nonlinear standing waves in cylindrical resonators, Czechoslovak Journal of Physics 54(3), 349-356, 2004. (LINK)
[24] Konicek, P., Bednarik, M.: Approximate analytical solution of inhomogeneous Burgers equation, Czechoslovak Journal of Physics 54(4), 413-422, 2004. (LINK)
[25] Bednarik, M., Konicek, P.: Propagation of quasiplane nonlinear waves in tubes and the approximate solutions of the generalized Burgers equation, The Journal of the Acoustical Society of America 112(1), 91-98, 2002. (LINK, PDF)