Examples of 'spherical harmonics' in a sentence
Meaning of "spherical harmonics"
spherical harmonics: A mathematical concept used in various fields including physics and signal processing to represent functions on the surface of a sphere as a linear combination of basis functions
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- The solutions to Laplace's equation using spherical coordinates
How to use "spherical harmonics" in a sentence
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spherical harmonics
These can be approximated by a sum of spherical harmonics.
See spherical harmonics for example.
Solutions are searched in terms of spherical harmonics.
These spherical harmonics have the feature of being orthogonal.
Potential of the gravitational field in terms of spherical harmonics.
Ylm are the spherical harmonics and.
Spherical harmonics are functions that oscillate over the surface of a sphere.
First vector spherical harmonics.
The spherical harmonics can be written as.
The above equations suppose that the spherical harmonics are defined by.
Such spherical harmonics are a special case of zonal spherical functions.
The symbol represents a set of functions known as the spherical harmonics.
Are vector spherical harmonics normalized so that.
This distribution can be characterized by expanding the flux in a basis of spherical harmonics.
Spherical harmonics are often used to approximate the shape of the geoid.
See also
The latter two correspond to the quantum numbers of the spherical harmonics.
Spherical harmonics representation.
This does not affect the angular portion of the spherical harmonics.
Spherical harmonics method.
The process steps are identical to those described hereafter relating to spherical harmonics.
The spherical harmonics are essentially trigonometric functions upon the sphere.
The end of the century also saw a very detailed discussion of spherical harmonics.
Vector spherical harmonics are an extension of the concept for use with vector fields.
Then we proposed a compact representation using spherical harmonics to learn and recognize the poses.
The angular portions of the solutions to such equations take the form of spherical harmonics.
The ellipsoidal harmonics are a generalization of the spherical harmonics and keep equivalent mathematical properties.
A mathematical result of considerable interest and use is called the addition theorem for spherical harmonics.
Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport.
Associated Legendre polynomials play a vital role in the definition of spherical harmonics.
Relation to spherical harmonics and Legendre polynomials.
Love waves and Rayleigh waves can also be expressed as spherical harmonics.
Scientists verified that 20 spherical harmonics are sufficient to achieve convergent results.
Where, due to the orthogonality of spherical harmonics.
The spherical harmonics turn out to be critical to practical solutions of Laplace 's equation.
In the mathematical description of atmospheric waves, spherical harmonics are used.
Spherical harmonics can be generalized to higher-dimensional Euclidean space Rn as follows.
This operator gives rise to spin-weighted spherical harmonics.
Spherical Harmonics Expansion ( SHE ) models are interesting intermediate models between these two classes of models.
Together, they make a set of functions called spherical harmonics.
This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree l = 10.
A prime example - in mathematics and physics - would be the theory of spherical harmonics.
PBGI tree nodes uses spherical harmonics ( SH ) to represent outgoing radiance.
For spherical tensors, k and q are analogous labels to ℓ and m respectively, for spherical harmonics.
Radiance can be expanded on a basis set of spherical harmonics Y { \ displaystyle Y } n, m.
SPHARM-PDM is a tool that computes point-based models using a parametric boundary description based on spherical harmonics.
His last publication, which appeared in 1878, was on spherical harmonics " Beiträge zur Theorie der Kugelfunctionen.
Preferably but without limitation, the describing polynomial expansion is selected in spherical harmonics.
For each of these sub-spaces, a sub-base of spherical harmonics is constructed.
Because of this, we can describe the pulsations with math functions called spherical harmonics.
The extension to 3D problems is straightforward thanks to the use of spherical harmonics.
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Examples of using Harmonics
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I understand you use harmonics of atomic frequencies
Harmonics can be added to the fundamental wave
Set the shield harmonics to rotate continuously
Examples of using Spherical
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Use spherical or cylindrical form to apply load
I just need one spherical test subject
Spherical reflector with a high luminous efficiency
