Laplace's equation

(redirected from Harmonic equation)

Laplace's equation

[lə′pläs·əz i‚kwā·zhən]
(acoustics)
An equation for the speed c of sound in a gas; it may be written c = √(γ p /ρ), where p is the pressure, ρ is the density, and γ is the ratio of specific heats.
(mathematics)
The partial differential equation which states that the sum of all the nonmixed second partial derivatives equals 0; the potential functions of many physical systems satisfy this equation.
References in periodicals archive ?
From the series solutions [9] for the Helmholtz equation (1) and the harmonic equation (2), the magnetic vector potential with any current ring in the spherical coordinates can be derived through the continuity of the magnetic vector potential and the tangential components of the magnetic field on the particle surface 10].
The Robin problem forinhomogeneous harmonic equation is treated in [16,18,36].
is Laplace's operator; thus the above partial differential equation is called Laplace's equation or harmonic equation.
Accordingly, the task of the restoration is solving the above harmonic equation. We return to the previous example as shown in Figure 4, and the distorted image in Figure 4(b) can be approximated by harmonic transformation.
Another approach in [14] has used Colonial Competitive Algorithm to solve harmonic equations and to minimize low order harmonics.
Nonlinear harmonic equations required to obtain optimal switching angles can be stated by Fourier expansion of load voltage.
We should point out that the Dirac-harmonic equation is a kind of general equation which includes many existing harmonic equations as special cases, such as the A-harmonic equation; see [18, 20, 21] for more information.