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Related Concept Videos

Forced Oscillations01:06

Forced Oscillations

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When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.
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Damped Oscillations01:07

Damped Oscillations

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In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
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Oscillations about an Equilibrium Position01:04

Oscillations about an Equilibrium Position

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Stability is an important concept in oscillation. If an equilibrium point is stable, a slight disturbance of an object that is initially at the stable equilibrium point will cause the object to oscillate around that point. For an unstable equilibrium point, if the object is disturbed slightly, it will not return to the equilibrium point. There are three conditions for equilibrium points—stable, unstable, and half-stable. A half-stable equilibrium point is also unstable, but is named so...
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Oscillations In An LC Circuit01:30

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
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Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

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An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
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Types of Damping01:20

Types of Damping

8.1K
If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
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Most long-lived contrails form within cirrus clouds with uncertain climate impact.

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Ice clouds as nonlinear oscillators.

Hannah Bergner1, Peter Spichtinger1

  • 1Institute for Atmospheric Physics, Johannes Gutenberg University, Mainz, Germany.

Chaos (Woodbury, N.Y.)
|April 9, 2026
PubMed
Summary

Researchers developed a simple ice cloud model to understand its impact on Earth's energy budget. The model reveals nonlinear dynamics and bifurcations, offering insights into pure ice cloud behavior.

Area of Science:

  • Atmospheric Science
  • Climate Physics
  • Nonlinear Dynamics

Background:

  • Clouds significantly influence Earth's energy budget by interacting with solar and thermal radiation.
  • The net radiative effect of pure ice clouds remains uncertain, highlighting a gap in climate modeling.
  • Understanding ice cloud dynamics is crucial for accurate climate change projections.

Purpose of the Study:

  • To develop a physically consistent model for pure ice clouds.
  • To analyze the nonlinear dynamics and bifurcations within the ice cloud model.
  • To assess the model's agreement with real-world atmospheric measurements.

Main Methods:

  • Development of a simplified, physically consistent ice cloud model.
  • Application of dynamical systems theory to analyze model behavior.

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  • Investigation of nonlinear oscillations, Hopf bifurcations, and limit cycles.
  • Analysis of scaling behaviors to reduce model parameter space.

    • Main Results:

    • The ice cloud model exhibits nonlinear oscillatory behavior with two Hopf bifurcations.
    • Characterization of equilibrium states and limit cycles within the model.
    • Identification of scaling laws for bifurcations and limit cycles, simplifying parameter dependencies.
    • Demonstrated strong agreement between model predictions and observational data.

    Conclusions:

    • The developed model captures essential physics governing pure ice clouds.
    • Nonlinear dynamics and bifurcations play a key role in ice cloud radiative effects.
    • Simplified models are valuable tools for advancing the understanding of atmospheric ice clouds.