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Generation of localized modes in an electrical lattice using subharmonic driving
L Q English1, F Palmero, P Candiani
1Department of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA.
Physical Review Letters
|April 3, 2012
Summary
Researchers demonstrate stable intrinsic localized modes (ILMs) using subharmonic driving in nonlinear electrical lattices. The frequency of the driver dictates whether a single ILM or a train of ILMs is produced.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Electrical engineering
Background:
- Intrinsic localized modes (ILMs) are nonlinear phenomena that can confine energy within a lattice.
- Subharmonic driving offers a potential method for controlling ILM generation.
- Previous experimental observations of subharmonically driven ILMs are scarce.
Purpose of the Study:
- To experimentally and numerically demonstrate the stable production of intrinsic localized modes (ILMs) via subharmonic driving.
- To investigate the influence of driver frequency relative to the linear dispersion curve on ILM formation.
- To report the first experimental observation of subharmonically driven ILMs.
Main Methods:
- Utilizing a nonlinear electrical lattice model.
- Applying spatially homogeneous subharmonic driving.
- Conducting both numerical simulations and experimental validation.
- Analyzing the system's nonlinear spatial response based on frequency detuning.
Main Results:
- Stable intrinsic localized modes (ILMs) were successfully produced and observed experimentally.
- The spatial characteristics of the ILMs depend on the driver frequency (ω(d)) relative to the linear dispersion curve (ω(0)).
- Driving with ω(d)/2 just below ω(0) generated a single ILM in a 32-node lattice.
- Driving with ω(d)/2 within the dispersion band resulted in a spatially extended waveform resembling a train of ILMs.
Conclusions:
- Subharmonic, spatially homogeneous driving is an effective method for generating stable intrinsic localized modes (ILMs) in nonlinear electrical lattices.
- The frequency relationship between the driver and the lattice's dispersion curve precisely controls the spatial manifestation of the ILMs.
- This work presents the first reported experimental observation of subharmonically driven ILMs, highlighting their broad relevance.
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