Skip to main content
SpringerLink
Log in

Disentangling scaling arguments to empower complex systems analysis

  • Comment
  • Published:

From Nature Physics

View current issue Submit your manuscript

Matters Arising to this article was published on 02 November 2020

Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of these concepts empowers us to unlock their full potential.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1: Two distinct types of scaling analysis.

References

  1. Ising, E. Z. Phys. 31, 253–258 (1925).

    Article  ADS  Google Scholar 

  2. McCoy, B. M. & Wu, T. T. The Two-Dimensional Ising Model (Courier Corporation, 2014).

  3. Goldenfeld, N. Lectures on Phase Transitions and the Renormalization Group (CRC, 2018).

  4. Grimmett, G. R. Percolation (Springer, 1999).

  5. West, G. B. Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies (Penguin, 2017).

  6. D’Souza, R. M. & Nagler, J. Nat. Phys. 11, 531–538 (2015).

    Article  Google Scholar 

  7. Newman, M. E. J. Contemp. Phys. 46, 323–351 (2005).

    Article  ADS  Google Scholar 

  8. Clauset, A., Shalizi, C. R. & Newman, M. E. SIAM Rev. 51, 661–703 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  9. Taylor, B. Methodus Incrementorum Directa & Inversa [Direct and Reverse Methods of Incrementation] Prop. VII, Thm 3, Cor. 2 (London, 1715). [Translated into English: Struik, D. J. A Source Book in Mathematics 1200–1800 329–332 (Harvard Univ. Press, 1969).]

  10. Altland, A. & von Delft, J. Mathematics for Physicists: Introductory Concepts and Methods (Cambridge Univ. Press, 2019).

  11. Bender, C. M. & Orszag, S. A. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory (Springer, 2013).

  12. Miller, P. D. Applied Asymptotic Analysis (AMS, 2006).

  13. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Nat. Phys. 15, 403–412 (2019).

    Article  Google Scholar 

  14. Timme, M. & Nagler, J. Nat. Phys. 15, 308–309 (2019).

    Article  Google Scholar 

  15. Peng, J., Lin, W. & Kurths, J. Nat. Phys. https://doi.org/10.1038/s41567-020-1025-3 (2020).

  16. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Nat. Phys. https://doi.org/10.1038/s41567-020-1027-1 (2020).

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, Center for Advancing Electronics Dresden (cfaed), and Center of Excellence Physics of Life, Technical University of Dresden, Dresden, Germany

    Marc Timme & Malte Schröder

Authors
  1. Marc Timme
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Malte Schröder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marc Timme.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Timme, M., Schröder, M. Disentangling scaling arguments to empower complex systems analysis. Nat. Phys. 16, 1086–1088 (2020). https://doi.org/10.1038/s41567-020-01063-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-020-01063-5

  • Springer Nature Limited

This article is cited by

Search

Navigation