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Oscillations In An LC Circuit

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An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

Damped Oscillations

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Related Experiment Video

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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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Published on: May 30, 2014

Hole structures in nonlocally coupled noisy phase oscillators.

Yoji Kawamura¹

¹Department of Physics, Graduate School of Sciences, Kyoto University, Kyoto 606-8502, Japan. kawamura@ton.scphys.kyoto-u.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2007

Summary

Nonlocally coupled noisy phase oscillators can form a collective hole structure. This phenomenon, observed in spatial phase distributions, is linked to the complex Ginzburg-Landau equation.

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Area of Science:

Nonlinear dynamics
Complex systems
Statistical physics

Background:

Noisy phase oscillators are fundamental in modeling coupled systems.
Collective phenomena emerge from local and nonlocal interactions.
Understanding emergent structures is key in nonlinear science.

Purpose of the Study:

To investigate the emergence of collective structures in noisy oscillator systems.
To analyze the spatial phase distribution of nonlocally coupled oscillators.
To connect observed phenomena to known mathematical models.

Main Methods:

Modeling the system using a nonlinear Fokker-Planck equation.
Reducing the model to the complex Ginzburg-Landau equation near bifurcations.
Employing numerical simulations to observe system behavior.

Main Results:

Demonstration of a collective hole structure in spatial phase distributions.
Identification of the hole structure in the space-dependent order parameter.
Confirmation of the Nozaki-Bekki hole solution within the complex Ginzburg-Landau framework.

Conclusions:

Nonlocal coupling in noisy phase oscillators can lead to complex emergent structures.
The complex Ginzburg-Landau equation effectively describes these collective behaviors.
The study provides insights into pattern formation in nonlinear dynamical systems.