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Experimental generation of intrinsic localized modes in electrical lattices

LENCOS 2009, Seville, Spain. Experimental generation of intrinsic localized modes in electrical lattices. Lars Q. English Department of Physics & Astronomy Dickinson College, Carlisle, PA. (movie: 268 kHz d river frequency ). Macroscopic lattices

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Experimental generation of intrinsic localized modes in electrical lattices

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  1. LENCOS 2009, Seville, Spain Experimental generation of intrinsic localized modes in electrical lattices Lars Q. English Department of Physics & Astronomy Dickinson College, Carlisle, PA (movie: 268 kHz driver frequency)

  2. Macroscopic lattices Experiments on electrical transmission line 1 unit cell Fast 24-channel digitizer (now 32 channels) Lattice

  3. Energy Localization in a Nonlinear Electrical Lattice The experimental system Charge density p n x

  4. Energy Localization in a Nonlinear Electrical Lattice Duffing Oscillators Uniform mode coupled to uniform Mode (k=0) NN - coupling Inter-site nonlinearity Spatially uniform driving term Soft-nonlinearity: Quadratic term dominates cubic term 540 kHz Linear dispersion curve; no driver/ damping 320 kHz ILM

  5. Energy Localization in a Nonlinear Electrical Lattice Observation of Discrete breathers /ILMs fd=300 kHz A=1.5V fd=268 kHz

  6. Energy Localization in a Nonlinear Electrical Lattice Parametric excitation / stabilization of ILMs fd=590 kHz A=4.5V Red: Node 13 Blue: Node 17 Black: Node 19

  7. Energy Localization in a Nonlinear Electrical Lattice Slight change in experimental system One Unit Cell

  8. Energy Localization in a Nonlinear Electrical Lattice Observation of Traveling ILMs Response to uniform driving below the dispersion curve

  9. Energy Localization in a Nonlinear Electrical Lattice

  10. Energy Localization in a Nonlinear Electrical Lattice Patterns of Traveling ILMs Modulational Instability Coherent structure locked to driver Incoherent Localized Structures

  11. Energy Localization in a Nonlinear Electrical Lattice Patterns of Traveling ILMs 3 ILMs 4 ILMs 464 kHz 484 kHz 3 ILMs 6 ILMs 464 kHz 502 kHz

  12. Energy Localization in a Nonlinear Electrical Lattice Patterns of Traveling ILMs Driver frequency in between regions of integer-number of ILM (here between 3 and 4 ILMs) (472 kHz) (475 kHz)

  13. Energy Localization in a Nonlinear Electrical Lattice Switching in a blocking capacitor cap turned on 386 kHz

  14. Energy Localization in a Nonlinear Electrical Lattice Experiments on 2D macroscopic lattice Preliminary results: We believe we have observed 2D localization

  15. Energy Localization in a Nonlinear Electrical Lattice Preliminary 2d-lattice data Node Node ILM

  16. Energy Localization in a Nonlinear Electrical Lattice Conclusions • Demonstrated the existence of ILMs/discrete breathers in an electrical lattice • Fast, multichannel electronic data acquisition makes possible a detailed study • of ILM profile and behavior (not possible in other systems) • Both stationary and slow-moving ILM can be excited in these lattices • (depending on the detailed electronic make-up of the unit-cell ) • These ILMs can be generated via modulational instability, parametric instability, • or by briefly switching in an impurity. • Multiple localized features, multi-pulses, can be locked to the driver • at higher driver frequencies.

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