Experimental generation of intrinsic localized modes in electrical lattices Lars Q. English Department of Physics & Astronomy Dickinson College, Carlisle,

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Presentation transcript:

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) LENCOS 2009, Seville, Spain

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

The experimental system np Charge density x

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

Observation of Discrete breathers /ILMs f d =300 kHz A=1.5V f d =268 kHz

Parametric excitation / stabilization of ILMs Red: Node 13 Blue: Node 17 Black: Node 19 f d =590 kHz A=4.5V

Slight change in experimental system One Unit Cell

Observation of Traveling ILMs Response to uniform driving below the dispersion curve

Modulational Instability Incoherent Localized Structures Coherent structure locked to driver Patterns of Traveling ILMs

3 ILMs4 ILMs 3 ILMs6 ILMs 464 kHz 484 kHz 464 kHz 502 kHz Patterns of Traveling ILMs

Driver frequency in between regions of integer-number of ILM (here between 3 and 4 ILMs) Patterns of Traveling ILMs (472 kHz)(475 kHz)

386 kHz Switching in a blocking capacitor cap turned on

Experiments on 2D macroscopic lattice Preliminary results: We believe we have observed 2D localization

ILM Preliminary 2d-lattice data Node

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.