Skip to main content

Scattering on Janus Spheres

  • Chapter
  • First Online:
Sound Scattering on Spherical Objects
  • 437 Accesses

Abstract

Janus spheres are spherical objects whose surfaces consist of two different regions on which different boundary conditions apply. They are of interest in many fields of technology and hold an enormous potential of new applications in material sciences. Their scattering properties are not only of importance for diagnostic purposes during the production process of these objects but also for discovering new applications. However, there is very little information about it in the literature. It is therefore demonstrated in this chapter that the T-matrix approach can be successfully applied to this spherical scattering object. In so doing, a generalized Robin boundary condition is introduced whose limiting behavior allows us to combine the sharp splitting of the spherical boundary into two different regions with the T-matrix approach. Scattering results for three different types of Janus spheres are presented, and the convergence behavior of the method and the reliability of the obtained results are discussed in detail. This chapter ends with a description of the corresponding Python programs. Appendix C provides a complete listing of these programs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Sommerfeld, A.: Partial Differential Equations in Physics. Academic Press, New York (1949)

    MATH  Google Scholar 

  2. Wauer, J.: A least square T-matrix method for non-spherical dielectric particle compared with Waterman’s T-matrix method in the near and far field. JQSRT 180, 47–54 (2016)

    Article  ADS  Google Scholar 

  3. Rother, T., Kahnert, M.: Electromagnetic Wave Scattering on Nonspherical Particles: Basic Methodology and Applications. Springer, Heidelberg (2014)

    Book  Google Scholar 

  4. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Harri Deutsch, Frankfurt/Main (1984)

    MATH  Google Scholar 

  5. Zhang, J., Grzybowski, B.A., Granick, S.: Janus particle synthesis, assembly, and application. Langmuir 33, 6964–6977 (2017)

    Google Scholar 

  6. Kalhor, H.A.: Electromagnetic scattering by a dielectric slab loaded with a periodic array of strips over a ground plane. IEEE Trans. Antennas Propag. 36(1), 147–151 (1988)

    Article  ADS  Google Scholar 

  7. Pregla, R., Pascher, W.: The method of lines. In: Itoh, T. (ed.) Numerical Techniques for Microwave and Millimeter-Wave Passive Structures. Wiley, New York (1989)

    Google Scholar 

  8. Kristensson, G., Waterman, P.C.: The T-matrix for acoustic and electromagnetic scattering by circular disks. J. Acoust. Soc. Am. 72, 1612–1625 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  9. Baars, W.M.: Diffraction of sound waves. Acustica 14, 289–296 (1964)

    MATH  Google Scholar 

  10. Gillman, A.: An integral equation technique for scattering problems with mixed boundary conditions. Adv. Comput. Math. 43, 351–364 (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tom Rother .

3.1 Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (zip 29 KB)

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Rother, T. (2020). Scattering on Janus Spheres. In: Sound Scattering on Spherical Objects. Springer, Cham. https://doi.org/10.1007/978-3-030-36448-9_3

Download citation

Publish with us

Policies and ethics