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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
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Macroscopic lattices Experiments on electrical transmission line 1 unit cell Fast 24-channel digitizer (now 32 channels) Lattice
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The experimental system np Charge density x
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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
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Observation of Discrete breathers /ILMs f d =300 kHz A=1.5V f d =268 kHz
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Parametric excitation / stabilization of ILMs Red: Node 13 Blue: Node 17 Black: Node 19 f d =590 kHz A=4.5V
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Slight change in experimental system One Unit Cell
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Observation of Traveling ILMs Response to uniform driving below the dispersion curve
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Modulational Instability Incoherent Localized Structures Coherent structure locked to driver Patterns of Traveling ILMs
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3 ILMs4 ILMs 3 ILMs6 ILMs 464 kHz 484 kHz 464 kHz 502 kHz Patterns of Traveling ILMs
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Driver frequency in between regions of integer-number of ILM (here between 3 and 4 ILMs) Patterns of Traveling ILMs (472 kHz)(475 kHz)
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386 kHz Switching in a blocking capacitor cap turned on
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Experiments on 2D macroscopic lattice Preliminary results: We believe we have observed 2D localization
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ILM Preliminary 2d-lattice data Node
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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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