WIAS Preprint No. 1481, (2010)

Hysteresis and phase transition in many-particle storage systems


  • Dreyer, Wolfgang
  • Guhlke, Clemens
  • Herrmann, Michael

2010 Mathematics Subject Classification

  • 35Q84 80A22 74N30

2008 Physics and Astronomy Classification Scheme

  • 05.10.Gg, 05.70.Fh, 05.70.Ce, 82.47.Aa


  • thermodynamics, phase transitions, hysteresis, many particle system, Focker-Planck equation, lithium-ion batteries, rubber balloons


We study the behavior of systems consisting of ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime the evolution of the probability to find a particle of the ensemble in a certain state, may be described by a nonlocal conservation law of Fokker-Planck type. Two constant parameter control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path or if the ensemble shows the same non-monotone behavior as its constituents.

Appeared in

  • Contin. Mech. Thermodyn., 23 (2011) pp. 211--231.

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