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Significance of Displacement Current01:27

Significance of Displacement Current

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A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.
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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
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Displacement Current01:19

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Ampère's law, in its usual form, does not work in places where the current changes with time and is not steady. Thus, Maxwell suggested including an additional contribution, called the displacement current, Id, to the real conduction current I.
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Related Experiment Video

Updated: Mar 19, 2026

Long-term Behavioral Tracking of Freely Swimming Weakly Electric Fish
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Adaptively balanced Poisson-constrained physics-informed neural networks for robust displacement integration in

Hao Liu, Hongzhe Wang, Yang Song

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |March 17, 2026
    PubMed
    Summary

    A new physics-informed neural network (PINN) method, AB-PoissonPINN, improves displacement integration accuracy in background-oriented Schlieren (BOS) fluid dynamics analysis. This novel approach outperforms existing techniques in both simulated and real-world experiments.

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    Area of Science:

    • Fluid Dynamics
    • Computational Physics
    • Machine Learning

    Background:

    • Displacement integration is crucial for reconstructing physical fields in background-oriented Schlieren (BOS) imaging.
    • Conventional methods like high-order fitting and discrete Poisson solvers have limitations in accuracy and robustness.

    Purpose of the Study:

    • To introduce a novel physics-informed neural network (PINN) framework, the adaptively balanced Poisson-constrained PINN (AB-PoissonPINN), for improved displacement integration in BOS.
    • To evaluate the performance of AB-PoissonPINN against established numerical integration techniques.

    Main Methods:

    • Developed the AB-PoissonPINN framework, incorporating a Poisson equation constraint and a novel relative loss balancing with random backtracking (ReLoBRaLo) strategy.
    • Benchmarked AB-PoissonPINN against weighted cubic spline least squares integration (WCSLI), discrete Poisson solvers, and standard PINNs using simulated and experimental BOS data.

    Main Results:

    • AB-PoissonPINN demonstrated superior accuracy compared to WCSLI, discrete Poisson solvers, and standard PINNs.
    • The proposed method maintained high accuracy under both noise-free conditions and various levels of experimental noise.

    Conclusions:

    • The AB-PoissonPINN framework offers a significant advancement in displacement integration for BOS applications.
    • This physics-informed machine learning approach provides a more accurate and robust solution for reconstructing physical fields from experimental data.