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Related Concept Videos

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...
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.
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Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx.
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
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Related Experiment Video

Updated: Jun 14, 2026

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Generalized Lorentzian approximations for the Voigt line shape.

P Martin, J Puerta

    Applied Optics
    |March 24, 2010
    PubMed
    Summary

    Researchers developed a simple Padé approximation for the Voigt function. This generalized Lorentzian approximation offers an easier calculation for experiments not needing high precision.

    Area of Science:

    • Computational physics
    • Spectroscopy
    • Applied mathematics

    Background:

    • The Voigt function is crucial in spectroscopy for modeling spectral line shapes.
    • Accurate calculation of the Voigt function can be computationally intensive.
    • Approximations are needed for practical applications where high precision is not critical.

    Purpose of the Study:

    • To develop a computationally simple and accurate approximation for the Voigt function.
    • To utilize the Padé method for approximating the complex Voigt function.
    • To provide a viable alternative to the exact Voigt function in specific experimental contexts.

    Main Methods:

    • Calculation of the multipole approximation to the complex Voigt function.
    • Expressing the approximation in terms of the error function and plasma dispersion function.

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  • Employing the Padé approximant technique.

    • Main Results:

    • A simplified, easy-to-calculate approximation to the Voigt function was derived.
    • The approximation is a generalized Lorentzian function.
    • The derived approximation demonstrates utility in experimental settings.

    Conclusions:

    • The Padé approximation provides a practical alternative to the exact Voigt function.
    • This method simplifies calculations in experiments where high accuracy is not paramount.
    • The generalized Lorentzian approximation is suitable for various spectroscopic applications.