nwhm/summer-2013

Plans for May-August 2013

Areas of focus:

  • Shock formation in random media
  • c-dispersive solitary waves

Plan of work

  • All code and writing will go in the repository (or here on the wiki, for very short notes)
  • We’ll prepare a single technical report with uniform notation, then prepare journal publications from that
  • We’ll meet at 10 AM each day in David’s office to discuss things, starting with background material and moving on to current research
  • Tentative paper organization

Meeting schedule

  • May 18: no meeting
  • May 19: Review of L&Y section 2 on linear waves in periodic layered media, led by Amal
  • May 20: Review of L&Y section 3 on nonlinear waves in periodic layered media, led by Benson
  • May 21: Review of L&Y section 5 on homogenization, led by Manuel

Amal

Benson

  • Compare Spectral methods with finite volume schemes, understand effect of choice of time discretization on shock formation and post shock solutions produced by spectral schemes
  • Perform simulations in 2D and 3D. In 2D compare with finite volume numerical solutions, in 3D compare with radial 1D codes where possible
  • For systems perform simulations of wave propagation in Elasticity and Maxwell’s equations (or help someone else do them)
  • Convergence analysis for the numerical schemes?
  • See if possible to develop numerical homogenization schemes, applications wave propagation for geophysics applications; wave propagation for electronics and photonics applications; wave propagation for civil engineering applications

David

  • Look for symmetries between Z-dispersion and c-dispersion
  • Asymptotic analysis of solitary waves
  • More rigorous derivation of the generalized Lax condition for shocks in periodic/random media

Manuel

  • Clean up homogenized equations and do some sanity checks.
  • Help on symmetry between Z-dispersion and c-dispersion.
  • Study stability of homogenized equations: Compare the velocity group vs the max sound speed, check wavelength of unstable mode vs period of the heterogeneity.
  • Do simulations on: scaling of c-SW (c-Solitary Waves), interaction of c-SW, relation between width of initial pulse relative to width of material layers and dispersion generated, others…?
  • Study, numerically the entropy evolution of c-SW, elasticity in the interaction of c-SW.