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Localized modes and bistable scattering in nonlinear network junctions.

Andrey E Miroshnichenko1, Mario I Molina, Yuri S Kivshar

  • 1Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 16, 2007
PubMed
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Junctions in discrete networks with more than two branches create topological defects supporting localized modes. Nonlinear junctions allow tunable maximum transmission and exhibit bistable behavior near this point.

Area of Science:

  • Physics
  • Network Theory
  • Condensed Matter Physics

Background:

  • Discrete networks are fundamental in various physical systems.
  • Understanding wave phenomena at network junctions is crucial for device design.

Purpose of the Study:

  • To investigate the properties of junctions in discrete networks with N identical branches.
  • To analyze the formation of topological defects and localized modes.
  • To study wave scattering and transmission characteristics, including nonlinear effects.

Main Methods:

  • Analysis of wave scattering at network junctions.
  • Theoretical modeling of linear and nonlinear discrete networks.
  • Investigation of spatially localized modes and transmission properties.

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Main Results:

  • Junctions with N>2 branches act as topological defects.
  • Two types of spatially localized modes are supported by these defects.
  • Nonzero wave reflection occurs for all parameters in linear networks.
  • Nonlinear junctions enable tunable maximum transmission across all frequencies.
  • Bistable behavior is observed near maximum transmission in nonlinear systems.

Conclusions:

  • Network junctions with N>2 branches introduce topological defects with unique wave-confining properties.
  • Nonlinear network junctions offer novel control over wave transmission, with potential for bistable devices.