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Related Concept Videos

Bessel Function of Order Zero01:20

Bessel Function of Order Zero

A common physical example of wave propagation with radial symmetry is the ripple formed when a stone is dropped into a still pond. The disturbance originates at a central point and travels outward as a circular wave. As the radius of the wavefront increases, the same initial energy is distributed along a progressively larger circumference. Consequently, the amplitude, or height, of the wave decreases with distance from the center. This decay behavior cannot be captured by simple sine or cosine...
The de Broglie Wavelength02:32

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Deflection of a Beam01:19

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Singularity Functions for Shear01:26

Singularity Functions for Shear

In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the shear...
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

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Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...

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Related Experiment Video

Updated: Jun 16, 2026

Controlled Synthesis and Fluorescence Tracking of Highly Uniform Poly(N-isopropylacrylamide) Microgels
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Computation of bessel functions in light scattering studies.

W D Ross

    Applied Optics
    |February 2, 2010
    PubMed
    Summary

    Accurate Bessel function computations are essential for light scattering. This study presents robust recurrence methods to minimize rounding errors for both real and complex arguments, improving calculation reliability.

    Area of Science:

    • Computational physics
    • Numerical analysis
    • Electromagnetic theory

    Background:

    • Light scattering computations necessitate Bessel functions of various orders.
    • Recurrence relations are the easiest method for computing Bessel functions, but prone to accumulating rounding errors.
    • Existing methods may not provide sufficient accuracy for all applications.

    Purpose of the Study:

    • To describe satisfactory procedures for computing Bessel functions for cylinder and sphere scattering.
    • To present methods that minimize rounding errors in Bessel function calculations.
    • To address computations for both real and complex arguments.

    Main Methods:

    • For real arguments: Recurrence to high orders for Y(n)(z), estimation of J(n)(z) from two high orders of Y(n)(z), backward recurrence to maximum J(n)(z), and correction by forward recurrence.

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  • For complex arguments: Estimation of high orders of J(n)(z) without Y(n)(z), followed by backward recurrence.
  • Implementation of stable recurrence procedures for Bessel functions.

    • Main Results:

    • Demonstrated procedures for accurate Bessel function computation for cylinder and sphere functions.
    • Successfully minimized cumulative rounding errors in recurrence calculations.
    • Developed distinct, effective methods for real and complex arguments.

    Conclusions:

    • The described recurrence procedures provide accurate Bessel function values for light scattering computations.
    • These methods enhance the reliability of numerical simulations involving Bessel functions.
    • Applicable to a wide range of scientific and engineering problems requiring Bessel functions.