Finsler metric and elastic constants for weak anisotropic media

DOI10.1016/j.nonrwa.2011.05.018zbMath1231.53023OpenAlexW2052886289MaRDI QIDQ660724

Kazuhito Yamasaki, Takahiro Yajima, Hiroyuki Nagahama

Publication date: 5 February 2012

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.05.018

zbMATH Keywords

Finsler geometryelastic constants\(m\)th root metricBerwald Gauss curvatureseismic ray theoryweak anisotropic media

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Shocks and related discontinuities in solid mechanics (74J40) Seismology (including tsunami modeling), earthquakes (86A15) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (4)

Optimal normed Sobolev type inequalities on manifolds. I: The Nash prototype ⋮ Finsler geometry for nonlinear path of fluids flow through inhomogeneous media ⋮ Stable reconstruction of simple Riemannian manifolds from unknown interior sources ⋮ Hodge duality between stress space and strain space in anisotropic media

Cites Work

• Kawaguchi space, Zermelo's condition and seismic ray path
• Hamilton geometry
• The theory of sprays and Finsler spaces with applications in physics and biology
• Seismic rays as Finsler geodesics.
• Raypaths as parametric curves in anisotropic, nonuniform media: differential-geometry approach
• Fundamentals of Finslerian diffusion with applications
• Generalized orthogonality between rays and wavefronts in anisotropic inhomogeneous media
• Finsler geometry of seismic ray path in anisotropic media
• Long-wave elastic anisotropy produced by horizontal layering
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