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Rotational sound in disordered granular materials.

Kuniyasu Saitoh1,2, Rohit K Shrivastava3, Stefan Luding3

  • 1Research Alliance Center for Mathematical Sciences, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan.

Physical Review. E
|February 21, 2019
PubMed
Summary
This summary is machine-generated.

We numerically study elastic standing waves in disordered disk systems. The rotational sound mode transitions from optical-like to acoustic-like behavior depending on disk stiffness, impacting wave dispersion.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Elastic standing waves are crucial in understanding material properties.
  • Disordered systems exhibit complex wave behaviors not seen in ordered lattices.
  • Rotational sound modes are a key feature in granular and disk-based systems.

Purpose of the Study:

  • To numerically investigate the dispersion relations of rotational sound in disordered disk systems.
  • To analyze the transition of rotational modes from optical-like to acoustic-like behavior.
  • To determine the influence of inter-disk stiffness on wave dispersion.

Main Methods:

  • Numerical simulations of elastic standing waves.
  • Analysis of dispersion relations for rotational sound.
  • Examination of vibrational density of states and velocity autocorrelations.
  • Eigenvector analysis to study mode participation.

Main Results:

  • Rotational modes show optical-like dispersion at high frequencies, similar to lattices.
  • A transition to acoustic-like behavior occurs when tangential stiffness is comparable to normal stiffness.
  • The lattice model accurately predicts dispersion for rotational modes only at high tangential stiffness.
  • Mode transition is evidenced by changes in eigenvector participation of degrees of freedom.

Conclusions:

  • The behavior of rotational sound in disordered disk systems is highly dependent on the relative stiffness of inter-disk interactions.
  • A crossover from optical-like to acoustic-like dispersion for rotational modes is observed.
  • This transition highlights the limitations of lattice models in disordered systems under certain stiffness conditions.