Experimental generation of intrinsic localized modes in electrical lattices Lars Q. English...

Experimental generation of intrinsic localized modes in electrical lattices

Lars Q. EnglishDepartment 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

3

031

2

021

0

0

0

0

1

1ln1

)exp(1

)exp()(

Q

Q

Q

Q

Q

Q

Q

QV

VC

Q

VCVC

Energy Localization in a Nonlinear Electrical Lattice The experimental system

Reverse-biased diode

0

100

200

300

400

500

600

0 2 4 6 8 10

Voltage [V]

Cap

acit

an

ce [

pF

]

np

Charge density

x

21

00 )(

1

V

dd

.1

11

23

22

2

32

2

000

31

31

320

21

21

21

2

0

21

1121

320

202

0

202

02

2

dt

dV

Rdt

dQ

Q

Q

Q

Q

RC

QQQQ

QQQQ

QQQ

QQ

QQ

Qdt

Qd

dnnn

nnn

nnn

nnn

nnnn

CL20 1 1 11 CL 00 CQ

Duffing Oscillators

Spatially uniformdriving term

Inter-site nonlinearity

NN - coupling

Energy Localization in a Nonlinear Electrical Lattice

Soft-nonlinearity:Quadratic term dominates

cubic term

Uniform mode coupled to uniformMode (k=0)

Linear dispersioncurve; no driver/damping ILM

540 kHz

320 kHz

Energy Localization in a Nonlinear Electrical Lattice Observation of Discrete breathers /ILMs

fd=300 kHzA=1.5V

fd=268 kHz

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

Red: Node 13Blue: Node 17Black: Node 19

fd=590 kHzA=4.5V

Energy Localization in a Nonlinear Electrical Lattice 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 ILMs 4 ILMs

3 ILMs 6 ILMs

464 kHz 484 kHz

464 kHz 502 kHz



Driver frequency in between regions of integer-number of ILM(here between 3 and 4 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

N

ode


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.

Experimental generation of intrinsic localized modes in electrical lattices Lars Q. English...

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