Slide 1

Experimental generation of intrinsic localized modes in electrical latticesLars Q. EnglishDepartment of Physics & AstronomyDickinson College, Carlisle, PA

(movie: 268 kHz driver frequency)LENCOS 2009, Seville, SpainMacroscopic lattices Experiments on electrical transmission line

1 unit cellFast 24-channel digitizer(now 32 channels)Lattice

Energy Localization in a Nonlinear Electrical Lattice The experimental system

npCharge densityx

Duffing OscillatorsSpatially uniformdriving termInter-site nonlinearityNN - couplingEnergy Localization in a Nonlinear Electrical Lattice

Soft-nonlinearity:Quadratic term dominates cubic termUniform mode coupled to uniformMode (k=0)Linear dispersioncurve; no driver/damping

ILM540 kHz320 kHzEnergy Localization in a Nonlinear Electrical Lattice Observation of Discrete breathers /ILMs

fd=300 kHzA=1.5Vfd=268 kHz

Energy Localization in a Nonlinear Electrical Lattice Parametric excitation / stabilization of ILMs

Red: Node 13Blue: Node 17Black: Node 19fd=590 kHzA=4.5VEnergy Localization in a Nonlinear Electrical Lattice Slight change in experimental system

One Unit Cell Observation of Traveling ILMs

Energy Localization in a Nonlinear Electrical Lattice

Response to uniform driving below the dispersion curve

Energy Localization in a Nonlinear Electrical Lattice

Energy Localization in a Nonlinear Electrical LatticeModulational InstabilityIncoherent Localized StructuresCoherent structure locked to driver

Patterns of Traveling ILMs

Energy Localization in a Nonlinear Electrical Lattice

3 ILMs4 ILMs3 ILMs6 ILMs464 kHz 484 kHz464 kHz 502 kHzPatterns of Traveling ILMs

Energy Localization in a Nonlinear Electrical LatticeDriver frequency in between regions of integer-number of ILM(here between 3 and 4 ILMs)Patterns of Traveling ILMs

(472 kHz)(475 kHz)Energy Localization in a Nonlinear Electrical Lattice

386 kHz

Switching in a blocking capacitor

cap turned onExperiments on 2D macroscopic lattice

Preliminary results: We believe we have observed 2D localizationEnergy Localization in a Nonlinear Electrical Lattice

Energy Localization in a Nonlinear Electrical Lattice

ILMPreliminary 2d-lattice data

Node NodeEnergy Localization in a Nonlinear Electrical LatticeConclusions 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.Chart15504503753152602151651351108570605045403530252020

CVoltage [V]Capacitance [pF]Reverse-biased diode

Sheet1VC0.555014501.537523152.526032153.516541354.51105855.5706606.5507457.5408358.5309259.5201020

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CVoltage [V]Capacitance [pF]Reverse-biased diode

Sheet2

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