Zeitschrift für Physik B Condensed Matter

, Volume 72, Issue 4, pp 515–521 | Cite as

Generalised equal areas rules for spatially extended systems

  • E. Schöll
  • P. T. Landsberg


It is shown that equal areas rules which exist in such different fields as thermodynamics (Maxwell construction), chemical reaction theory (nonequilibrium phase transitions), and semiconductor physics (Gunn-Hilsum effect; current filamentation; grain boundaries) arise as special cases of a general relation between control parameters and boundary values of a second order ordinary differential equation,. They allow one to extract relevant information about spatial profiles of some physical variable in extended systems directly from the constitutive differential equation without explicitly solving it.


Differential Equation Neural Network Phase Transition General Relation Complex System 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • E. Schöll
    • 1
  • P. T. Landsberg
    • 2
  1. 1.Institut für Theoretische PhysikRWTH AachenAachenFederal Republic of Germany
  2. 2.Department of MathematicsUniversity of SouthamptonSouthamptonUK

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