Acoustic carpets

Main Article Content

Maciej Janowicz
Joanna Kaleta
Piotr Wrzeciono
Andrzej Zembrzuski

Keywords : acoustics, Euler equations, split-operator method, visualization of physical fields
Initial-boundary value problem for linear acoustics has been solved in two spatial dimensions. It has been assumed that the initial acoustic field consists of two Gaussian distributions. Dirichlet boundary conditions with zero acoustic pressure at the boundaries have been imposed. The solution has been obtained with the help of a split-operator technique which resulted in a cellular automaton with uncountably many internal states. To visualize the results, the Python library matplotlib has been employed. It has been shown that attractive graphical output results in both the transient and stationary regimes. The visualization effects are similar to, but different from, the well-known quantum-mechanical carpets.

Article Details

How to Cite
Janowicz, M., Kaleta, J., Wrzeciono, P., & Zembrzuski, A. (2016). Acoustic carpets. Machine Graphics and Vision, 25(1/4), 3–12.

Morse P. Vibrations and Sound. McGraw-Hill, New York, 1948.

Marzoli I., Saif F., Bia lynicki-Birula I., Friesch, O.M., Kaplan, A.E., and Schleich W.P. Quantum carpets made simple. Acta Phys.Slov. 48:323-333, 1998

Hall M.J.W., Reineker M.S. and Schleich W.P. Unravelling quantum carpets: a travelling wave approach. J. Phys. A 32:8275-8291, 1999. (Crossref)

Kaplan A.E., Marzoli I., Lamb Jr., W.E., and Schleich W.P. Multimode interference: Highly regular pattern formation in quantum wave-packet evolution. Phys. Rev. A 61:032101, 2000. (Crossref)

Belloni M., Doncheski M.A., and Robinett R.W. Wigner quasi-probability distribution for the infinite square well: Energy eigenstates and time-dependent wave packets. Am. J. Phys. 72:1183-1192, 2004. (Crossref)

Trotter H.F. On the product of semi-groups of operators. Proc. Am. Math. Soc. 10:545-551, 1959. (Crossref)

Feit M.D., Fleck Jr. J.A., and Steiger A. Solution of the Schrodinger equation by a spectral method. J. Comp. Phys. 47:412-433, 1982. (Crossref)

Suzuki M. Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics. J. Math. Phys. 26:601-612, 1985. (Crossref)

Białynicki-Birula I. Weyl, Dirac, and Maxwell equations on a lattice as unitary cellular automata. Phys. Rev. D 49:6920, 1994. (Crossref)

Succi S. The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Clarendon Press, Oxford, 2001.

Janowicz, M.W., Ashbourn J.M.A., Orłowski A. and Mostowski J. Cellular automaton approach to electromagnetic wave propagation in dispersive media. Proc. Roy. Soc. London Ser. A 462:2927-2948, 2006. (Crossref)

Miyasaka C., Telschow K.L., Tittmann B.R., Sadler J.T., and Park I.K. Direct visualisation of acoustic waves propagation within a single anisotropic crystalline plate with hybrid acoustic imaging system. Research in Nondesctructive Evaluation 23:197-206, 2012. (Crossref)

Szczodrak M., Kurowski A., Kotus J., Czyżzewski A., and Kostek B. A system for acoustic field measurement employing Cartesian robot. Metrol. Meas. Syst. 23:333-343, 2016. (Crossref)

Rambach R.W., Taiber J., Scheck C.M.L., Meyer C., Reboud J., Cooper J.M., and Franke T. Visualization of Surface Acoustic Waves in Thin Liquid Films. Sci. Rep. 6:21980, 2016. (Crossref)



Download data is not yet available.
Recommend Articles
Most read articles by the same author(s)