Nonlinear Dynamics

, Volume 80, Issue 4, pp 1861–1867 | Cite as

Nonlinear normal and anomalous response of non-interacting electric and magnetic dipoles subjected to strong AC and DC bias fields

  • W. T. Coffey
  • Y. P. Kalmykov
  • N. Wei
Original Paper


The perturbation theory approach via the Smoluchowski equation to the nonlinear dielectric relaxation of noninteracting permanent electric dipoles (Coffey and Paranjape, Proc R Ir Acad A 78:17, 1978) and the analogous Brownian magnetic relaxation of ferrofluids where Néel relaxation is ignored is revisited for the particular case of a strong dc bias field superimposed on a strong ac field. Unlike weak ac and strong bias dc fields, a frequency-dependent dc term now appears in the response as well as additional nonlinear terms at the fundamental and second harmonic frequencies. These may be experimentally observable particularly in the ferrofluid application. The corresponding results for the dc term for anomalous relaxation based on the fractional Smoluchowski equation are also given.


Nonlinear relaxation Debye theory Ferrofluids Brownian motion Anomalous relaxation 



W. T. Coffey thanks Ambassade de France en Irlande for a research visit to Perpignan. N. Wei acknowledges the Government of Ireland Scholarship Award. We thank Dr. S. V. Titov for helpful conversations.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Electronic and Electrical EngineeringTrinity CollegeDublin 2Ireland
  2. 2.Laboratoire de Mathématiques et de Physique (EA 4217)Université de Perpignan Via DomitiaPerpignanFrance

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