Acta Applicandae Mathematicae

, Volume 122, Issue 1, pp 473–483 | Cite as

Shock-Induced Phase Transitions in Systems of Hard Spheres with Attractive Interactions

  • Shigeru TaniguchiEmail author
  • Masaru Sugiyama


Shock-induced phase transitions are studied by adopting the recently-developed theoretical framework, which is applicable for shock waves in three phases (gas, liquid, and solid), based on the system of hard spheres with mutual attractive interactions. The Rankine-Hugoniot conditions derived from the system of Euler equations with caloric and thermal equations of state are studied, and the admissibility (stability) of a shock wave is analyzed. Two typical scenarios of the shock-induced phase transitions from gas phase to solid phase are found. A scenario of shock-induced phase transitions involving three phases simultaneously near the triple point is also found.


Shock wave Shock-induced phase transition Hard-sphere system with attractive interaction Rankine-Hugoniot relations Stability of shock waves 

Mathematics Subject Classification

76L05 82C26 35L67 



The authors thank Prof. Tommaso Ruggeri and Dr. Andrea Mentrelli and Prof. Nanrong Zhao for valuable discussions.


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Center for Social Contribution and CollaborationNagoya Institute of TechnologyNagoyaJapan
  2. 2.Graduate School of EngineeringNagoya Institute of TechnologyNagoyaJapan

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