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Superfluidity phase transitions for liquid $ ^{4} $He system

  • * Corresponding author: Dongpei Zhang

    * Corresponding author: Dongpei Zhang
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  • The main objective of this paper is to investigate the superfluidity phase transition theory-modeling and analysis-for liquid $ ^{4} $He system. Based on the new Gibbs free energy and the potential-descending principle proposed recently in [18,25], the dynamic equations describing the $ \lambda $-transition and solid-liquid transition of liquid $ ^{4} $He system are derived. Further, by the dynamical transition theory, the two obtained models are proven to exhibit Ehrenfest second-order transition and first-order transition, respectively, which are well consistent with the physical experimental results.

    Mathematics Subject Classification: Primary: 34C23, 35Q99, 37G35; Secondary: 37L10.


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  • Figure 1.  $ T $-$ p $ phase diagram of $ ^{4} $He

    Figure 2.  The diagram for critical control parameters $ (T_c, p_c) $

    Figure 3.  The theoretical $ T $-$ p $ phase diagram for $ ^{4} $He

    Figure 4.  The topology of steady state solutions for (24)

    Figure 5.  The $ p $-$ \rho_n $ dynamical phase diagram

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