Skip to main content

Noise-Induced Abnormal Growth

  • Chapter

Part of the book series: Institute for Nonlinear Science ((INLS))

Abstract

Noise is shown to play an active role in inducing abnormal growth patterns. Specifically, through the use of the active walker model, two types of abnormal growth—transformational and irreproducible—are shown to arise spontaneously due to noise under appropriate conditions and hence could be intrinsic in nature. Our results are discussed in relation to electrodeposit experiments. The possibility that some cancer growth may be intrinsic is speculated.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Risken, The Fokker-Planck Equation (Springer-Verlag, New York, 1989).

    Book  MATH  Google Scholar 

  2. R.D. Freimuth and L. Lam, in Modeling Complex Phenomena, edited by L. Lam and V. Naroditsky (Springer-Verlag, New York, 1992).

    Google Scholar 

  3. L. Lam and R.D. Pochy, Comput. Phys. 7, 534 (1993).

    Google Scholar 

  4. L. Lam, R.D. Freimuth, M.K. Pon, D.R. Kayser, J.T. Fredrick, and R.D. Pochy, in Pattern Formation in Complex Dissipative Systems, edited by S. Kai (World Scientific, River Edge, NJ, 1992).

    Google Scholar 

  5. D.R. Kayser, L.K. Aberle, R.D. Pochy, and L. Lam, Physica A 191, 17 (1992).

    Article  ADS  Google Scholar 

  6. R.D. Pochy, D.R. Kayser, L.K. Aberle, and L. Lam, Physica D 66, 166 (1993).

    Article  ADS  Google Scholar 

  7. L. Lam, M.C. Veinott, and R.D. Pochy, in Spatiotemporal Patterns in Nonequilibrium Complex Systems, edited by P.E. Cladis and P. Palffy-Muhoray (Addison-Wesley, Redwood City, CA, 1995).

    Google Scholar 

  8. L. Lam, R.D. Pochy, and V.M. Castillo, in Nonlinear Structures in Physical Systems, edited by L. Lam and H.C. Morris (Springer-Verlag, New York, 1990)

    Chapter  Google Scholar 

  9. L. Lam, in Defect Structure, Morphology and Properties of Deposits, edited by H.D. Merchant (Minerals, Metals, and Materials Society, Warren-dale, PA, 1995).

    Google Scholar 

  10. R.P. Pan, C.R. Sheu, and L. Lam, Chaos Solitons Fractals 6, 495 (1995).

    Google Scholar 

  11. J.D. Watson, N.H. Hopkins, J.W. Roberts, J.A. Steitz, and A.M. Weiner, Molecular Biology of the Gene (Benjamin/Cummings, Menlo Park, CA, 1987).

    Google Scholar 

  12. P.E. Cladis, Mol. Cryst. Liq. Cryst. 165, 85 (1988).

    Google Scholar 

  13. L. Lam, Liq. Cryst. 14, 1873 (1993).

    Article  Google Scholar 

  14. C. Tang, Phys. Rev. A 31, 1977 (1985).

    Article  ADS  Google Scholar 

  15. J. Nittmann and H.E. Stanley, Nature 321, 663 (1986).

    Article  ADS  Google Scholar 

  16. D. Grier, E. Ben-Jacob, R. Clarke, and L.M. Sander, Phys. Rev. Lett. 56, 1264 (1986).

    Article  ADS  Google Scholar 

  17. Y. Sawada, A. Dougherty, and J.P. Gollub, Phys. Rev. Lett. 56, 1260 (1986).

    Article  ADS  Google Scholar 

  18. L. Lam, R.P. Pan, M.C. Veinott, and Y.H. Chan, Bull. Am. Phys. Soc. 39, 140 (1994).

    Google Scholar 

  19. L. Lam, Chaps Solitons Fractals 6, 267 (1995).

    Google Scholar 

  20. L. Lam, in Introduction to Nonlinear Physics, edited by L. Lam (Springer-Verlag, New York, 1996).

    Google Scholar 

  21. H. Freund and P. Grassberger, Physica A 190, 218 (1992).

    Article  ADS  Google Scholar 

  22. M.M. Millonas, J. Theor. Biol. 159, 529 (1992).

    Article  Google Scholar 

  23. E.M. Rauch, M.M. Millonas, and D.R. Chialvo, Phys. Lett. A 207,185 (1995).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. F. Schweitzer and L. Schimansky-Geier, Physica A 206, 359 (1994).

    Article  ADS  Google Scholar 

  25. F. Schweitzer, K. Lau, and F. Family, Active Brownian walkers simulate trunk trail formation by ants, Preprint.

    Google Scholar 

  26. L. Lam, Chaos Solitons Fractals 6, 267 (1995)

    Article  ADS  MATH  Google Scholar 

  27. See also L. Lam, in Introduction to Nonlinear Physics, edited by L. Lam (Springer-Verlag, New York, 1996).

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Lam, L., Veinott, M.C., Ratoff, D.A., Pochy, R.D. (1996). Noise-Induced Abnormal Growth. In: Millonas, M. (eds) Fluctuations and Order. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3992-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3992-5_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8463-5

  • Online ISBN: 978-1-4612-3992-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics