Nonlinear Phenomena and PDEs: from optical to atomic physics and beyond Intro to Research Meeting, U

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Nonlinear Phenomena and PDEs from optical to
atomic physics and beyondIntro to Research
Meeting, UMass Physics, February 13, 2009P.G.
KevrekidisUniversity of Massachusetts

• with the gratefully acknowledged partial support
  of
• National Science Foundation
• (DMS and
  CAREER) Alexander von Humboldt
  Foundation

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An Atomic Physics Example Dark Soliton Formation

• Form a BEC in a Double Well Potential
• Eliminate the Optical Lattice and Ramp Down the
  Magnetic Trap
• Observe the Formation and Characterize the
  Interaction Between the Dark Solitons.
• We obtain very good agreement between
  Experimental Results, Numerical (3d and 1d)
  Results and Analytical Results from a Simple
  Particle Picture

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An Optical Physics Example Hexagonal/Honeycomb
Vortices
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Experimental Results on Hexagonal Vortices
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Some of the many NONLINEAR things we do

• Bose-Einstein Condensates in Atomic Physics
• Optical Fibers and Waveguides in Nonlinear Optics
• Traveling Waves and Patterns in Granular Crystals
• Breather Modes in Mechanical Systems
• Solitons in Electrical Transmission Lines
• Modeling of Angiogenesis and Tumor Dynamics in
  Biophysics
• Nonlinear Dynamics of Simple Cosmological Models
• and more...
• If you want to have some nonlinear fun, feel free
  to stop by LGRT 1524 or drop a line at
  kevrekid_at_math.umass.edu.

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Encore A Granular Crystals Example Traveling
Waves

• Theoretical Setup
• Equation of Motion for Phononic Crystal Dimer
• where
• Time Rescaling and Factoring Out Gravity
• k 3/2 Special Case of Hertzian Contacts.

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Comparison of Theory and Numerics with Experiment