Phase Change and Collisions

  • Michel FrémondEmail author
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 13)


Let us consider warm rain falling on a frozen ground. On the surface of the ground, there is a discontinuity of temperature between the temperature T 2 of the rain which is larger than the water freezing temperature T 0 and the temperature T 1 of the frozen ground which is lower than T 0. It is to be known if the rain freezes or if the frozen ground thaws. In this problem, the temperatures are discontinuous both with respect to space and with respect to time. Let us also note that the velocities are also discontinuous. In order to investigate this problem, we recall the theory of collisions without thermal effects and the theory of collision with thermal effects. For the sake of simplicity, we consider first collisions of balls schematized by points then in next chapter, collisions of continuous media either solid or liquid. This theory is developed in [114].


Phase Change Steel Ball Virtual Work Freeze Ground Internal Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria CivileUniversità di Roma “Tor Vergata”RomaItaly

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