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

Jiayan Yang; Dongpei Zhang

doi:10.3934/dcdsb.2019045

Article Contents

2019, Volume 24, Issue 9: 5107-5120. Doi: 10.3934/dcdsb.2019045

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

Jiayan Yang^1, and
Dongpei Zhang^2, ,

1.
School of Medical Informatics and Engineering, Southwest Medical University, Luzhou, Sichuan 646000, China
2.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

^* Corresponding author: Dongpei Zhang
^* Corresponding author: Dongpei Zhang

Received: August 31, 2018

Early access: February 2019

Published: July 2019

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Abstract

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.

Keywords:

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

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

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

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

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

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

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