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The '''Cole–Cole equation''' is a [[relaxation]] model that is often used to describe [[dielectric relaxation]] in [[polymer]]s.
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It is given by the equation
:<math>
\varepsilon^*(\omega) - \varepsilon_\infty = \frac{\varepsilon_s - \varepsilon_\infty}{1+(i\omega\tau)^{1 - \alpha}}
</math>
where <math>\varepsilon^*</math> is the [[Dielectric constant#Complex permittivity|complex dielectric constant]], <math>\varepsilon_s</math> and <math>\varepsilon_\infty</math> are the "static" and "infinite frequency" dielectric constants, <math>\omega</math> is the [[angular frequency]] and <math>\tau</math> is a time constant.


The exponent parameter <math>\alpha</math>, which takes a value between 0 and 1, allows to describe different spectral shapes. When <math>\alpha=0</math>, the Cole-Cole model reduces to the [[Dielectric#Debye relaxation|Debye]] model. When <math>\alpha>0</math>, the relaxation is ''stretched'', i.e. it extends over a wider range on a logarithmic <math>\omega</math> scale than Debye relaxation.
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Cole-Cole relaxation constitutes a special case of [[Havriliak-Negami relaxation]] when the symmetry parameter (β) is equal to 1 - that is, when the relaxation peaks are symmetric. Another special case of Havriliak-Negami relaxation (β<1, α=0) is known as [[Cole-Davidson relaxation]], for an abridged and updated review of anomalous dielectric relaxation in dissored systems see Kalmykov.
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== References ==
  <li>[http://annuncianimali.altervista.org/index.php?page=item&id=133834 http://annuncianimali.altervista.org/index.php?page=item&id=133834]</li>
 
    
{{cite journal
  <li>[http://cerisier.info/spip.php?article25/ http://cerisier.info/spip.php?article25/]</li>
  | last1 = Cole
    
  | first1 = K.S.
  <li>[http://verdamilio.info/org/spip.php?article573/ http://verdamilio.info/org/spip.php?article573/]</li>
  | last2 = Cole
 
  | first2 = R.H.
</ul>
  | title = Dispersion and Absorption in Dielectrics - I Alternating Current Characteristics
  | journal = J. Chem. Phys.
  | year = 1941
  | volume = 9
  | pages = 341–352
  |bibcode = 1941JChPh...9..341C |doi = 10.1063/1.1750906 }}
 
{{cite journal
  | last1 = Cole
  | first1 = K.S.
  | last2 = Cole
  | first2 = R.H.
  | title = Dispersion and Absorption in Dielectrics - II Direct Current Characteristics
  | journal = Journal of Chemical Physics
  | year = 1942
  | volume = 10
  | pages = 98–105
  |bibcode = 1942JChPh..10...98C |doi = 10.1063/1.1723677 }}
 
{{cite journal
  | last1 = Kalmykov
  | first1 = Y.P.
   | last2 = Coffey
  | first2 = W.T.
   | last3 = Crothers
  | first3 = D.S.F.
  | last4 = Titov
  | first4 = S.V.
  | title = Microscopic Models for Dielectric Relaxation in Disordered Systems
  | journal = Physical Review E
   | year = 2004
  | volume = 70
   | pages = 041103
  |bibcode = |doi = 10.1063/1.1723677 }}
 
 
 
 
 
{{DEFAULTSORT:Cole-Cole equation}}
[[Category:Electric and magnetic fields in matter]]

Latest revision as of 04:16, 4 October 2014

Mbt Paris I think it was past 9pm

At the end of March, the coroner's court handed over copies of all the evidence gathered for the inquiry including copies of the three notes she left before her apparent suicide, a police report, toxicology results, a statement from the duty nurse who was the last person to see her alive as well as a letter from her GP which is expected to detail whether she Mbt Paris was on medication at the .

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