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Related Experiment Videos

Shocks preempt continuous curvature divergence in interface motion.

V Tsemekhman1, J S Wettlaufer

  • 1Applied Physics Laboratory, University of Washington, Seattle, Washington 98105-5640, USA.

Physical Review Letters
|November 3, 2001
PubMed
Summary
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Two models for interface motion in crystal growth yield different predictions. One model predicts continuous curvature divergence, while the other predicts discrete orientation loss, with shock formation preempting divergence.

Area of Science:

  • Physics
  • Materials Science
  • Applied Mathematics

Background:

  • Interface motion is crucial in crystal growth and material processing.
  • Two distinct theoretical frameworks exist for describing interface evolution.

Purpose of the Study:

  • To analyze the dichotomy between two approaches to interface motion.
  • To compare singularity formation predictions in two-dimensional crystal growth.

Main Methods:

  • Analysis of singularity formation based on interface curvature.
  • Mathematical modeling using an equation for the interface's two-vector.
  • Proof of shock formation preempting curvature divergence.

Main Results:

  • Interface curvature analysis predicts continuous divergence.

Related Experiment Videos

  • Two-vector evolution equation predicts discrete orientation loss.
  • Shock formation in the latter model prevents continuous curvature divergence.

    • Conclusions:

    • The discrete orientation loss model, involving shock formation, is shown to be the preemptive mechanism.
    • Results are applicable to kinematic interface motion problems.
    • Findings connect to experimental observations in crystal growth.