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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
Second-Order Circuits01:17

Second-Order Circuits

Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

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Related Experiment Video

Updated: Jun 19, 2026

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
07:42

Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

Published on: December 15, 2021

Two-dimensional solitons with second-order nonlinearities.

L Torner, C R Menyuk, W E Torruellas

    Optics Letters
    |October 27, 2009
    PubMed
    Summary
    This summary is machine-generated.

    We predict the excitation of (2+1) solitons in quadratic nonlinear materials. This occurs with phase mismatch and linear walk-off, offering conditions for experimental observation.

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    Generation and Coherent Control of Pulsed Quantum Frequency Combs
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    Generation and Coherent Control of Pulsed Quantum Frequency Combs

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    Last Updated: Jun 19, 2026

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator
    07:42

    Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

    Published on: December 15, 2021

    Generation and Coherent Control of Pulsed Quantum Frequency Combs
    06:42

    Generation and Coherent Control of Pulsed Quantum Frequency Combs

    Published on: June 8, 2018

    Area of Science:

    • Nonlinear optics
    • Wave propagation in materials

    Background:

    • Materials exhibiting quadratic nonlinearity are crucial for optical applications.
    • Understanding intense Gaussian beam propagation is key to developing new optical phenomena.

    Purpose of the Study:

    • To investigate the propagation of intense Gaussian beams in quadratic nonlinear media.
    • To numerically predict the conditions for (2+1) soliton excitation.

    Main Methods:

    • Numerical simulations of wave propagation.
    • Analysis of conserved quantities for wave evolution.

    Main Results:

    • Numerical prediction of (2+1) soliton excitation.
    • Identification of conditions involving finite phase mismatch and linear walk-off.

    Conclusions:

    • The study provides a theoretical basis for observing (2+1) solitons.
    • Discusses experimental parameters for soliton observation in quadratic nonlinear materials.